Atomic Data for Yb-Like Ions from Ta IV to Pt IX Relevant to Tungsten Transmutation in Fusion Plasmas

1. Introduction

The realization of fusion energy as a sustainable and large-scale energy source relies on the successful operation of magnetic-confinement devices such as ITER and, ultimately, DEMO-class reactors. In these systems, the interaction between the high-temperature plasma and plasma-facing materials plays a crucial role in determining both plasma performance and component lifetime. Spectroscopic diagnostics are among the most important tools available for monitoring plasma conditions, impurity transport, and radiative power losses, creating a continuous need for accurate atomic data for heavy ions.

Tungsten has been selected as the reference material for the ITER divertor because of its exceptional thermo-mechanical properties, including its high melting point, low sputtering yield, good thermal conductivity, and low tritium retention [1,2,3]. The adoption of a full tungsten divertor represents a major milestone in the design of ITER. However, tungsten atoms released from plasma-facing components through sputtering or erosion processes become ionized in the plasma and can generate substantial radiative losses due to their complex electronic structure and the very large number of transitions arising from their open-shell configurations. Consequently, reliable atomic data for tungsten ions are essential for plasma diagnostics, impurity transport studies, and radiation modeling in present and future fusion devices.

An additional challenge originates from neutron-induced transmutation processes occurring in tungsten under the intense 14-MeV neutron flux generated by fusion reactions. Detailed inventory calculations performed by Gilbert and Sublet [4] have shown that neutron-capture and subsequent decay processes progressively convert tungsten into neighboring heavy elements, primarily rhenium and osmium, while smaller but significant amounts of tantalum, iridium, and platinum are also produced. Depending on the irradiation conditions and operating lifetime, the concentration of these transmutation products may reach several atomic percent, leading to measurable modifications of the physical and mechanical properties of tungsten-based plasma-facing materials. Since these elements can subsequently enter the plasma through erosion mechanisms, their ionic spectra may contribute to the observed emission from fusion plasmas. Accurate atomic data are therefore required not only for tungsten ions themselves but also for the ions of the neighboring transmutation products.

The production of such data has motivated a series of recent investigations by our group. Extensive calculations of energy levels and radiative parameters were reported for Re III–V ions [5], while new datasets for osmium ions were published for Os V [6] and Os VI [7]. These studies highlighted the importance of relativistic and electron-correlation effects in heavy open-shell systems and provided data of direct relevance for spectroscopic diagnostics and plasma modeling. The present work constitutes a natural extension of these efforts toward the ytterbium-like sequence.

Among the transmutation products of tungsten, the Yb-like ions Ta IV, W V, Re VI, Os VII, Ir VIII, and Pt IX form a particularly interesting isoelectronic sequence. Their electronic structure is governed by the interplay between strong relativistic effects, extensive configuration interaction, and significant core-valence correlations. Previous experimental and theoretical studies have revealed substantial level mixing and complex coupling schemes in these ions, making accurate calculations particularly challenging. At the same time, the available spectroscopic information remains incomplete and heterogeneous along the sequence, especially for highly excited configurations and radiative transition probabilities.

In the present work, we perform a systematic investigation of the Yb-like ions Ta IV, W V, Re VI, Os VII, Ir VIII, and Pt IX using complementary pseudo-relativistic Hartree–Fock and fully relativistic multiconfiguration Dirac–Hartree–Fock approaches. Particular attention is devoted to the treatment of correlation effects and to the evolution of the atomic structure along the isoelectronic sequence. The resulting energy levels and radiative parameters provide new benchmark data for heavy-ion spectroscopy and are expected to contribute to future fusion-plasma diagnostics and modeling efforts.

2. Available Atomic Data

2.1. Tantalum (Z=73)

In 1978, Meijer and Metsch [8] found all the 14 levels of the 5d² + 5d6s + 6s² low-lying even configurations and all the 16 levels of the 5d6p and 6s6p odd configurations. In their work, they classified 114 lines in the 763.140-3076.058 Å region by using a Hilger and Watts E1 quartz prism spectrograph, the 6.65 m normal incidence vacuum spectrograph and the 6.6 m grazing incidence spectrograph of the Zeeman Laboratory. They also carried out pseudo-empirical calculations by fitting the Slater parameters and by introducing the observed energy levels in the Hartree-Fock method where the observed configurations (5d² + 5d6s + 6s² + 5d6p + 6s6p) were considered in the configuration interaction (CI) model. The fit reached a mean deviation (between the computed and observed energy levels) of 71 cm⁻¹ and 160 cm⁻¹ for the even and odd parities, respectively.

Eighteen years later, Kildiyarova $et$ $al.$ [9] observed 16 of the 20 levels in the 5d5f odd configuration which gives strong transitions to the 5d² levels. They classified 49 lines in the 555.124-648.656 Å spectral range using a triggered spark and a sliding spark source to excite the Ta IV spectrum and a 3-m normal incidence spectrograph with a reciprocal dispersion of 1.3858 cm⁻¹ to photograph it. They performed a least-squares fitting calculation by including many more configurations in the odd CI model than the previous study, namely 5dnp (n=6,7) + 5dnf (n=5,6) + 6s6p + 6s5f + 5p⁵5d³ reaching a mean deviation of 145 cm⁻¹. By plotting the average energy of the configurations introduced in the model from Ta IV to Pt IX, they conclude on strong configuration interaction (CI) between the 5d5f and 5d7p odd configurations in Ta IV, between the 5d5f and 6s6p in Re VI and Os VII and the 5p⁵5d³ open-core configuration crossed the 5d7p and 6s6p odd configurations along the Yb-like isoelectronic sequence resulting in important CI. In the same year, Churilov $et$ $al.$ [10] measured all the 12 levels of the 5d7p configuration, three of the four missing levels of the 5d5f configuration and classified 66 lines in the 551.422-932.187 Å region using a 3 m normal incidence spectrograph with a plate factor of 1.38 Å${\mathrm{mm}}^{-1}$ in the first order, a sliding spark and a triggered spark light source for exciting the spectrum. They considered one more configuration, 5d7f, in the least-squares fit procedure for the odd parity giving rise to a mean deviation of 126 cm⁻¹.

2.2. Tungsten (Z=74)

Yoca $et$ $al.$ [11] have already carried out semi-empirical and ab initio atomic structure calculations in W V with the HFR approach, the Flexible Atomic Code (FAC) and the MCDHF method. Their work was based on the compilation of the spectroscopic data for Yb-like tungsten in NIST [12] which has collected energy levels and transitions obtained by Meijer [13] who observed the W V spectrum in the 63–219 nm wavelength range by using a sliding-spark light source and also by Kildiyarova $et$ $al.$ [9] and by Churilov $et$ $al.$ [10] who extended the identifications to the region 39–57 nm using similar light sources. There were 193 lines from 391.566 to 2187.270 Å and 59 experimental energy levels belonging to the 5d², 5d6s, 5d6p, 6s6p, 5d5f and 5d7p configurations. Two levels of the 5d5f configuration are still missing with J=0 and J=6. The physical model considered in their HFR+CPOL calculations contained 45 configurations which describe a large part of the configuration interactions (CI). They compared to another HFR model (without the CPOL corrections), referenced to as HFR(CV), which contains 28 configurations among which some configurations had an open core subshell in order to take into account the core-valence interactions explicitly. In both models, they carried out a fitting procedure giving rise to a standard deviation of 20 cm⁻¹, 132 cm⁻¹ for the even and odd parities, respectively, for the HFR+CPOL model and 20 cm⁻¹, 135 cm⁻¹ for the even and odd parities, respectively, for the HFR(CV) model. They found a good agreement between the oscillator strengths computed by both these models meaning that the correlation effects with the core taken explicitly into account with the HFR(CV) model were well described by the HFR+CPOL model. They compared all methods used in their work and also with the RMBPT calculations made by Safronova $et$ $al.$ [14] and they found an overall better agreement between the HFR+CPOL method and the FAC method where the uncertainty of the results was estimated at 15-20%.

2.3. Rhenium (Z=75)

Sugar $et$ $al.$ [15] measured the spectra of Re VI using sliding-spark and triggered-spark discharges. These spectra were recorded photographically with the 10.7-m grazing-incidence and normal-incidence spectrographs and the 3-m normal incidence spectrograph. They observed 13 levels of the 5d², 5d6s even configurations and 29 levels belonging to the 5d6p, 6s6p and 5d5f odd configurations where one of the four levels of the 6s6p configuration and 16 of the 20 levels of the 5d5f configuration were identified. By first performing HFR calculations with the least-squares adjustment of the energy parameters, this enabled them to identify 112 lines between 332.044 and 1513.957 Å. They introduced in their model a limited number of configurations, namely 5d² + 5d6s + 6s² and 5d6p + 6s6p + 5d5f for the even and odd parities, respectively. The fit provided a mean deviation of 64 cm⁻¹ and 490 cm⁻¹ for the even and odd parities, respectively. They tried to improve the fit by considering more CI with the introduction of the 5d7p and 4f¹³5d³ odd configurations but they did not give the mean deviation value for the improved fit. It highlights nevertheless the importance of considering this core-excited configuration explicitly in the model to describe the significant core-valence correlations. The large sigma-value of the odd parity came from the difficulty of fitting the 5d5f odd configuration due to the collapse of the 5f orbital.

2.4. Osmium (Z=76) and Iridium (Z=77)

Van het Hof $et$ $al.$ [16] identified 77 (5d²+5d6s)-5d6p lines in Os VII and 71 lines in Ir VIII between 13 even levels and 12 odd levels for both ions. The wavelengths of the transitions obtained by excitations in a triggered spark discharge and photographed on the 3 m normal incidence spectrograph at St. Francis Xavier University, range from 391.771 to 1319.811 Å for Os VII and from 337.535 to 1172.084 Å for Ir VIII. The 5d²-5d6p arrays were measured stronger than the 5d6s-5d6p arrays in both ions. After completing the fit procedure, the standard deviations between the calculated and the observed energy levels were found to be 114 cm⁻¹ and 354 cm⁻¹ for the even and odd parities, respectively, in Os VII, and 124 cm⁻¹ and 336 cm⁻¹ for the even and odd parities, respectively, in Ir VIII.

The 72 and 58 weaker (5d²+5d6s)-5d5f lines in Os VII and in Ir VIII were identified by Kildiyarova $et$ $al.$ [17] in the 288.274-537.010 Å region and in the 237.098-292.817 Å region, respectively, as well as 18 of the 20 levels of the 5d5f configuration. They introduced 7 configurations in their HFR odd model, namely 5dnp (n=6,7) + 6s6p + 5dnf (n=5,6,7) + 5p⁵5d³ and the fit reached a mean deviation of 204 cm⁻¹ and 226 cm⁻¹ for Os VII and Ir VIII, respectively. From their semi-empirical HFR calculations, the odd level composition presented an important mixture between the 5d5f and 6s6p odd configurations as well as between the 5d5f and the 5p⁵5d³ odd configurations where for a few energy levels, the dominant spectroscopic term in the level composition belongs to the 5p⁵5d³ core-excited configuration. For example, the principal component of the level measured at 388 229 cm⁻¹ (J=2) in Ir VIII appeared as 5p⁵5d³⁵S with 19%. This underlines the importance of including this configuration explicitly in the model in order to take into account all major CI.

2.5. Platinum (Z=78)

Kildiyarova $et$ $al.$ [18] photographed the spectrum of Pt IX using a 2-m and a 10-m grazing incidence spectrographs where the source used in laboratories was a triggered spark. This enabled them to measure 9 levels of the 5d² even configurations, 12 levels of the 5d6p and 18 of the 20 levels of the 5d5f odd configurations. They were able to predict the 106 observed lines belonging to the 5d²-5d(6p + 5f) transition arrays between 216.575 and 345.804 Å thanks to the HFR calculations and a least squares fit. The 5d6s-5d6p transitions were not studied because there were not intense hot spectra at $\lambda$ > 350 Å. The configuration interaction model introduced in the calculations was 5d² + 5d6s + 6s² and 5dnp (n=6,7) + 5dnf (n=5,6,7) + 6s6p + 5f6s + 5p⁵5d³ for the even and odd parities, respectively. After the fit, the agreement between the experimental and the calculated level values for both even and odd parity systems was qualified to be quite good in a view of the standard deviation of 62 cm⁻¹ and 324 cm⁻¹ for the even and odd parities, respectively. From the computed level compositions, they concluded that there was even more mixing between the 5d5f and 5p⁵5d³ odd configurations than in Os VII and Ir VIII and the jj coupling representation seemed to be more adequate than the LS designation especially for the 5d5f levels even though both designations showed important mixing.

Azarov and Churilov [19] extended the observed spectrum from 327.777 to 1055.171 Å corresponding to the (5d² + 5d6s)-5d6p transitions thanks to high-resolution VUV spectrographs. The spectrum was excited in a plasma by a three-electrode low-inductance vacuum spark, the operating discharge voltage being 4.0–4.5 kV. They identified 4 more levels belonging to the 5d6s even configuration and classified 26 transitions where one of which, observed at 327.777 Å in [19] had already measured by Kildiyarova $et$ $al.$ [18] at 327.574 Å. They also computed the transition probabilities, $gA$, by performing HFR calculations and a fit procedure with a method based on the orthogonal operators. The fit enabled to achieve a mean deviation of 30 cm⁻¹ and 33 cm⁻¹ for the even and odd parities, respectively, optimizing only the levels observed in their work belonging to the 5d², 5d6s and 5d6p configurations.

2.6. Other Studies on Ytterbium-like Ions of Interest

Azarov [20] performed semi-empirical calculations using the orthogonal operators on the 5d², 5d6s and 5d6p configurations for all Yb-like ions from Ta IV to Hg XI. He obtained an agreement between the observed levels and the eigenvalues 5 times and 10 times better than the previous least-squares calculations with the Slater parameters for the even and odd systems, respectively. This made it possible to predict the energy of unknown levels, to supply a set of fitted parameters and to evaluate the evolution of these parameters and their effects along the isoelectronic sequence. This evolution was extrapolated to obtain the parameters for the Hg XI ions in order to verify the position of the observed energy levels. These results will also be useful for the ions of the neighboring sequences that have the 5d³ and 5d⁴ ground-state configurations.

Another previous study on the $ab$ $initio$ computations of excitation energies and transition rates in Yb-like ions (Z = 72 - 100) using the Relativistic Many-Body Perturbation Theory (RMBPT) was carried out by Safronova $et$ $al.$ [21]. They considered a model composed of the 5d², 5d6s, 6s² and the 5d6p, 5d5f and 6s6p even and odd configurations, respectively. The observed levels and the levels computed with their RMBPT method were listed for Re VI to Hg XI and only the E1 line strengths in length and velocity gauges for Re VI were tabulated. They well reproduced the low-lying observed energy levels but there was a disagreement with the highly excited levels (2 000 - 10 000 cm⁻¹) belonging to the 5d5f configurations especially due to important mixing between the 5d5f configuration and the 5p⁵5d³ core-excited configuration. They also mentioned that neither $jj$ nor $LS$ coupling describes physical states properly.

3. Numerical Methods

3.1. The Pseudo-Relativistic-Hartree-Fock (HFR) Calculations with the Core Polarization Corrections (CPOL)

The first computational approach used in this work was the pseudo-relativistic Hartree–Fock (HFR) method, originally developed by Cowan [22] in order to iteratively solve the Hartree-Fock equations which are obtained by a variational principle minimizing the average energy of each non-relativistic electronic configuration introduced in our model. The resulting Atomic State Functions of parity P, total angular momentum J with projection $M_J$ were expanded in terms of Configuration State Functions in $LS$ coupling: $\Psi (\alpha ,P,J,M_J)={\sum }_{r=1}^{n_c}{y}_r{\Phi }_r({\alpha }_r,P,L_r,S_r,J,M_J)$ where ${\alpha }_r$ define each CSF_r uniquely and $y_r$ are the mixing coefficients obtained by the so-called Self-Consistent-Field method. It is meaningful to consider the Coulomb correlation effects between electrons in the calculations of the wave function. Migdalek and Baylis [23] have suggested to describe the intravalence correlations by introducing explicitly in the calculations a large (but finite due to limited resources) number of valence configurations while the correlations with the core were described by a core polarization model potential. The method was thus modified by the Atomic physics and Astrophysics unit by introducing the polarization effects of the ionic core in the HFR method as described in [24,25] in order to take all correlation effects into account. This method is referred to as HFR+CPOL. In order to reproduce as well as possible the energy level structure, the physical HFR+CPOL model was based on the previous work in W V [11] since it had been confirmed by the very good agreement obtained between the HFR+CPOL method and two other atomic structure calculation methods, namely the Flexible Atomic Code (FAC) and the Multiconfiguration Dirac–Hartree-Fock (MCDHF) method.

Therefore, for all ions in the ytterbium isoelectronic sequence studied in this work, we have decided to introduce explicitly in the computations the same set of configurations namely 22 even configurations, 5d² + 6sns (n=6-7) + 5dns (n=6-7) +5dnd (n=6-7) + 6snd (n=6-7) + 6pnp (n=6-7) + 6pnf (n=5-7)+ 6dnd (n=6-7) + 6d7s + 7s² + 7p² + 7s7d + 7pnf (n=5-7), and 21 odd configurations, 5dnp (n=6-7) + 6snp (n=6-7) + 5dnf (n=5-7) + 6snf (n=5-7) + 6pnd (n=6-7)+ 6p7s + 6dnf (n=5-7) + 7snf (n=5-7) + 7s7p + 7p7d. The pseudo-potential which describes the core polarization effects depends on two parameters, the ionic-core radius (r_c) and the static dipole polarizability (${\alpha }_D$) of the ionic core. These parameters were evaluated for all the six Yb-like ions studied in this work by considering the same Yb III-type ionic core with 68 electrons surrounded by two valence electrons as already considered in the previous study on W V [11]. The r_c-value was estimated by the mean value of the outermost orbital of the ionic core computed in the HFR method, namely $5pr5p$, and the ${\alpha }_D$-value was obtained by an extrapolation of the known ${\alpha }_D$-values taken in [26] along the erbium isoelectronic sequence as given in the Figure 1. This figure represents first the evolution of the r_c-values along the isoelectronic sequence in green and also the extrapolation of the ${\alpha }_D$-values where the values that were already known in [26] were represented with a full black circle and the extrapolated values were shown with an empty blue circle. Note that the ${\alpha }_D$-value for W(74) had already been extrapolated and was taken from [11].

Because we cannot introduce an infinite number of configurations in the calculations and describe all configuration interactions, we have introduced a scaled factor of 0.85 which reduced all the Slater integrals of the Hamiltonian and thus modified the mixing coefficients in order to include the effects of far away interacting configurations [22]. Then, for all elements studied in this work, we performed a least-squares adjustment of the $ab$ $initio$ computed energy levels by introducing the observed energy levels in our calculations. It allowed to reproduce more accurately the level structure and to compute the radiative parameters with more precision by optimizing the radial parameters of the Hamiltonian such as the average energies ($E_{av}$), the Slater integrals ($F^k$, $G^k$ and $R^k$), the spin-orbit parameters (${\zeta }_{nl}$), as well as the effective interaction radial parameters $\alpha$ and $\beta$ that represent weak CI effects on configurations with equivalent electrons in p and/or d orbitals.

The number of fitted levels, i.e., observed levels, and the standard deviation of the fit are given in the Table 1. The additional energy levels observed in each parity of Ta IV but not observed in W V were the 6s²¹S₀ even level and the 5d5f ³P₀^o odd level. For all ions studied in this work, the radial parameters of the 5d², 5d6s, 5d6p, and 5d5f configurations were adjusted semi-empirically. The average energy of the 6s² even configuration had been fitted only for Ta IV. All radial parameters of the 5d7p, 6s6p configurations have been fitted only for Ta IV and W V and only the average energy of the 6s6p configuration had been fitted for Re VI up to Ir VIII.

For Ta IV, we obtained a better agreement between the observed and the computed energy levels with the HFR+CPOL method for the even and odd parities than Meijer and Metsch [8] had previously achieved. The standard deviation in our work was found to be 22 cm⁻¹ and 106 cm⁻¹ for the even and odd parities, respectively, while Meijer and Metsch [8] obtained a deviation slightly higher, 70 cm⁻¹ and 160 cm⁻¹ for the even and odd parities, respectively. Then, Kildiyarova $et$ $al.$ [9] and Churilov $et$ $al.$ [10] improved the deviation for the odd parities by introducing more odd configurations and they obtained 145 cm⁻¹ and 126 cm⁻¹, respectively, which is still higher than the deviation obtained in this work. The reason for our better fit could be the CPOL effects that we considered through the pseudo-potential model and also the introduction of more significant CI in the HFR method which allowed us to reproduce more accurately the observed energy level structure.

As already mentioned, the configuration model used in the HFR+CPOL method was based on Yoca $et$ $al.$ [11] who also performed a semi-empirical calculation giving rise to a standard deviation of 20 cm⁻¹ and 132 cm⁻¹ for the even and odd parities in W V, respectively. In this work, we tried to reproduce the same fitting procedure and we obtained nearly the same value of the deviation namely 26 cm⁻¹ and 123 cm⁻¹ for the even and odd parities, respectively. Moreover, we compared the transition probabilities computed in the previous work with our study and we observed a very good agreement between both calculations namely the mean ratio $g{A}_{Yoca}/g{A}_{HFR+CPOL}$=1.02 ± 0.14 where "0.14" stands for the standard deviation of the ratio.

For all ions after W V along the sequence, namely for Re VI, Os VII, Ir VIII and Pt IX, the fit became increasingly difficult, especially for the odd parity, as reflected by the increasing of the standard deviation of the fit for the odd parity in Table 1. For example, the standard deviation of the odd parity in Re VI was equal to 347 cm⁻¹ which is more 2.5 times higher than the one of the odd parity of W V.

The first reason for the higher standard deviation is that there is only one level of the 4 levels of the 6s6p configurations that have been identified in Re VI and none in the following ions which restricted the number of fitted parameters related to the 6s6p configurations. Moreover, no levels belonging to the 5d7p configurations were identified until now for all ions after W V in the Yb isoelectronic sequence, namely Re VI, Os VII, Ir VIII and Pt IX, which limited the global adjustment of the semi-empirical computed energy level structure for these four ions studied in this work. Indeed, some previous works on these ions have already presented a high deviation in the least-squares adjustment meaning that the energy level structure is complex in these ions. In Re VI, Sugar $et$ $al.$ [15] found a mean deviation of 64 cm⁻¹ and 490 cm⁻¹ for the even and odd parities, respectively, which are slightly higher than the ones obtained with our HFR+CPOL method certainly because of the CPOL effects introduced in the HFR method as well as the fit of the R^k parameters in our calculations that were kept fixed in Sugar $et$ $al.$ [15]. This allowed us to obtain a better mean deviation. Van het Hof $et$ $al.$ [16] obtained a deviation of 114 cm⁻¹ and 354 cm⁻¹ for the even and odd parities, respectively, in Os VII and 124 cm⁻¹ and 336 cm⁻¹ for the even and odd parities, respectively, in Ir VIII. Kildiyarova $et$ $al.$ [17] improved the agreement between the observed and the computed odd energy levels by introducing more configuration interactions in their model reaching a deviation of 204 cm⁻¹ and 226 cm⁻¹ for the odd parity of Os VII and Ir VIII, respectively. In Pt IX, Kildiyarova $et$ $al.$ [18] performed a fit reaching 62 cm⁻¹ and 324 cm⁻¹ for the even and odd parities, respectively. Azarov and Churilov [19] obtained a much smaller deviation, 30 cm⁻¹ and 33 cm⁻¹, for the even and odd parities, respectively, because the fit was carried out only on the 5d², 5d6s and 5d6p configurations while in Kildiyarova $et$ $al.$ [18] the 5d5f configuration was also fitted. It showed that the fit of the 5d5f configuration gave some problems as already noticed in Sugar $et$ $al.$ [15] for Re VI because of the contraction of the 5f orbital along the Yb isoelectronic sequence. For Os VII, Ir VIII and Pt IX, the authors of the previous studies obtained a better fit than with our HFR+CPOL method because of the increasing interactions between the observed configurations and especially the 5p⁵5d³ open-core configuration that were introduced explicitly in the model of Kildiyarova $et$ $al.$ [17] and Kildiyarova $et$ $al.$ [18] but not in our HFR+CPOL model where the core correlation effects were considered by a corrective pseudo-potential. Sugar $et$ $al.$ [15] also suggested to introduce the 4f¹³5d³ core-excited configuration in the model to improve the fit.

Another important reason which could explain why we obtained a high value of the standard deviation for Re VI up to Pt IX with the HFR+CPOL model is that the CPOL corrections could no longer be valid for these ions. Indeed, we considered valence-valence interactions through the configuration interactions by including explicitly in the calculations a large number of valence configurations and the correlations with the core were taken into account through a pseudo-potential which was introducing as a correction to the Hamiltonian. This correction and thus the HFR+CPOL approach is only valid if the core-excited configurations do not overlap the configurations of interest namely if the interaction effects between them remain small. We can estimate the validity of the HFR+CPOL approach by plotting the average energies of the core-excited configurations with one electron excitation from the 5p and 4f core orbitals and the valence configurations of interest for all ions computed with the HFR method along the Yb isoelectronic sequence as represented in Figure 2. The black and blue colors represent the even and odd configurations of interest, respectively. The red and green colors stand for the core-excited configurations with one hole in the 4f and 5p core orbitals, respectively.

For Ta IV and W V, the lowest 5p⁵5d²6p, 5p⁵5d³ and 5p⁵5d²6s open-core configurations are well above the configurations of interest. However, the 4f¹³5d³ core-excited configuration is closer to the 5d7p and 5d5f odd configurations but the overlap and so the configuration interactions between the 4f¹³5d³ core-excited configuration and the 5d7p and 5d5f configurations were not significant as we can see in the Figure 3. In this figure, the two red lines represent the overlap in energy of the 4f¹³5d³ core-excited configuration with the two other configurations. The energy overlap was over an interval of nearly 10 800 cm⁻¹ (≈ 6%) and 8 500 cm⁻¹ (≈ 3%) for Ta IV and W V, respectively. Therefore, the correlation effects with the core can be described by the CPOL corrections at least for the ions Ta IV and W V.

For Re VI up to Pt IX, these correlation effects with the core can no longer be described by the CPOL corrections because the core-excited configurations become too close to the configurations of interest and the interactions with the core become thus too significant to be treated as a correction to the Hamiltonian. In general, we observe this situation when the ionization stage increases [7]. Therefore, we need to introduce these core-excited configurations explicitly in our HFR model and the correlation effects with the core as well as the valence-valence correlations are thus described by the configuration interactions. We should introduce an infinite number of core-excited configurations to have a complete calculation but we cannot treat all electronic correlations owing to the limited resources. We thus introduced only the most important and the most interacting core-excited and valence configurations explicitly in our calculations. In the HFR+CPOL method, the core correlation effects are described in a different way by considering the CPOL corrections where these effects are treated as a whole with a pseudo-potential and are introduced in the Hamiltonian as a perturbation.

In addition to the conventional $LS$ representation, the Cowan code provides an alternative level classification in the so-called $jj$-coupling scheme. In this representation, each open subshell ($l_i^{w_i}$) is characterized by an angular momentum ($J_i$) obtained from the coupling ($L_i$+$S_i$→$J_i$), and the resulting subshell angular momenta are coupled successively according to

$$[({\alpha }_1{L}_1{S}_1{J}_1,{\alpha }_2{L}_2{S}_2{J}_2)J_{12},\dots ,{\alpha }_q{L}_q{S}_q{J}_q]J.$$

(1)

Following Cowan [22], this ($J_1$ $J_2$…$J_q$) representation may be regarded as a generalization of the usual $jj$-coupling scheme. It does not correspond to the fully relativistic $jj$ coupling used in MCDHF calculations, but provides a convenient alternative classification of the intermediate-coupling eigenvectors. In the present work, both $LS$ and Cowan $jj$ compositions were analyzed in order to assess the coupling properties of the calculated levels.

3.2. The Pseudo-Relativistic-Hartree-Fock (HFR) Calculations with the HFR(CV) Model

Along the ionization stages of the Yb isoelectronic sequence from Re VI to Pt IX, the 5d⁵5d³ configuration crossed over the configurations of interest strongly interacting especially with the 5d7p and 5d5f configurations as we observed in the Figure 2. This means that the configuration interactions between these configurations were important and the mixing between these configurations was increasingly significant in the semi-empirical energy level composition, as already noticed in previous studies [9,17,18]. For these ions, we instead performed HFR computations with a model that considered explicitly the core correlation effects through the configuration interactions. The second HFR model (referred to as HFR(CV)) was composed of the most interacting valence configurations to describe the intravalence correlations and the core-excited configurations with a single excitation from the 5s, 5p or 4f core orbitals that interact the most with the 5d², 5d6s, 6s², 5d6p, 6s6p, 5d5f and 5d7p configurations in order to describe explicitly the core-valence correlations. In other words, the Atomic State Function expansion was composed of 22 even configurations, 5d² + 5d6s + 6s² + 5d7s +5d6d + 5d7d + 6s7s + 6s6d + 6s7d + 6p² + 6p7p + 6p5f + 5p⁵5d²6p + 5p⁵6s²6p + 5p⁵5d6s6p + 5p⁵5d²5f + 5p⁵5d²7p + 5s5p⁶5d³ + 5s5p⁶5d²6s + 5s5p⁶5d6s² + 4f¹³5p⁶5d²6p + 4f¹³5p⁶5d6s6p, and 20 odd configurations, 5d6p + 6s6p + 5d7p + 5d5f + 5d6f + 5d7f + 6s7p + 6s5f + 6s6f + 6p6d + 6p7s + 5p⁵5d³ + 5p⁵5d²6s + 5p⁵5d6s² + 5p⁵5d6p² + 5p⁵6s6p² + 5s5p⁶5d²6p + 5s5p⁶5d6s6p + 4f¹³5p⁶5d³ + 4f¹³5p⁶5d²6s.

We have used this HFR(CV) model not only for Re VI to Pt IX but also for Ta IV and W V in order to compare the transition probabilities obtained with the HFR(CV) model and those obtained with the HFR+CPOL method in the case of Ta IV and W V. A fitting procedure was also carried out with the HFR(CV) model where the standard deviations for all ions studied in this work are represented in Table 1. As we observed in this table, the fit of the even parity was not really improved because the inclusion core-excited configurations in the CI expansions increases the level mixing. In addition, when the atomic number increases, the level composition in the even parity becomes slightly more mixed as we can see in Table 2 where the mean purity of the observed levels obtained with the HFR(CV) model is shown in the $LS$ and $jj$ representation for Ta IV up to Pt IX. One can notice that the mean purities for Ta IV and W V were very close to the ones obtained with the HFR+CPOL method. The mean purity is given by the average value of the squares of the mixing coefficients of the dominant spectroscopic terms in the level compositions for all observed levels. This mixing could explain the slight increase of the mean deviation in the even parity along the sequence. However, the fit of the odd parity was significantly improved with the HFR(CV) model compared to the HFR+CPOL model especially for Re VI up to Pt IX. The fit became nevertheless more difficult for Ir VIII and Pt IX owing to the increasing mixing especially between the 5p⁵5d³ and 5d5f configurations represented by a higher value of the standard deviation for both ions. Indeed, as shown in the Table 2 for Re VI up to Pt IX, the mixture of the $LS$ or $j{j}_{Cowan}$ terms in the level composition increases along the sequence especially for the odd parity. This important mixture did not allow us to identify clearly one level in Ir VIII measured at 406 542 ⁻¹ ($J=1$) and two levels in Pt IX measured at 438 038 cm⁻¹ ($J=1$) and 470 214 cm⁻¹ ($J=5$) because of the large deviations from the HFR(CV) level energies (2 979 cm⁻¹, 6 235 cm⁻¹ and 7 838 cm⁻¹, respectively). These levels have been thus removed from the fit and are listed with one star in Table 8 for Ir VIII and Table 9 for Pt IX. In general, we expect that when the ionic charge increases, the level structure becomes increasingly spread out represented by an increase in the energy gap between each configuration in each parity along the sequence which means that the level composition should present decreasing mixing. This is what we observed in Table 2 for the odd parity in Ta IV and in W V but in our study, it was nevertheless difficult to conclude that there were less and less mixing along the sequence because of the increasing interactions between each odd configuration and also between the core-excited configurations and the configurations of interest as showed in Figure 2.

Table 1. Number of fitted levels and deviation obtained after the fit along the Yb isoelectronic sequence from Ta IV to Pt IX with the HFR+CPOL and HFR(CV) models.

	Even parity			Odd parity
	nbr of fitted levels	${\sigma }_{HFR+CPOL}$ (cm−1)	${\sigma }_{HFR\left(CV\right)}$ (cm−1)	nbr of fitted levels	${\sigma }_{HFR+CPOL}$ (cm−1)	${\sigma }_{HFR\left(CV\right)}$ (cm−1)
Ta IV	14	22	24	47	106	118
W V	13	26	31	46	123	141
Re VI	13	30	37	29	347	253
Os VII	13	31	40	30	779	139
Ir VIII	13	35	47	29	1216	571
Pt IX	13	38	53	28	3363	422

Table 1. Number of fitted levels and deviation obtained after the fit along the Yb isoelectronic sequence from Ta IV to Pt IX with the HFR+CPOL and HFR(CV) models.

	Even parity			Odd parity
	nbr of fitted levels	${\sigma }_{HFR+CPOL}$ (cm−1)	${\sigma }_{HFR\left(CV\right)}$ (cm−1)	nbr of fitted levels	${\sigma }_{HFR+CPOL}$ (cm−1)	${\sigma }_{HFR\left(CV\right)}$ (cm−1)
Ta IV	14	22	24	47	106	118
W V	13	26	31	46	123	141
Re VI	13	30	37	29	347	253
Os VII	13	31	40	30	779	139
Ir VIII	13	35	47	29	1216	571
Pt IX	13	38	53	28	3363	422

One can also see in Table 2 that the $LS$ coupling is quite good for the even parity and the $j{j}_{Cowan}$ coupling seems to be more adequate to identify clearly the observed odd levels due to less mixing especially for the 5d5f levels but for the level designation in Pt IX neither the $LS$ representation nor the $j{j}_{Cowan}$ representation is adequate because of the small value of the mean purity of the observed levels in both representations. Thus, some levels cannot be identified unambiguously, as discussed in [18,21]. In order to follow the same consistency as the previous studies in the Yb isoelectronic sequence and make better comparisons with future studies in this same sequence, we decided to identify all levels in $LS$ coupling. The first two components in the $LS$ composition of all levels fitted with the HFR+CPOL model as well as the HFR+CPOL energy values for Ta IV and W V are available in Table 4 and Table 5, respectively. The two first components in the composition in $LS$coupling of all levels fitted with the HFR(CV) model as well as the HFR(CV) energy values for Re VI, Os VII, Ir VIII and Pt IX are shown in Table 6, Table 7, Table 8 and Table 9. In these six energy tables, the first term in the $jj$ compositions computed with the Cowan code [22] as well as with the MCDHF method [27] are also shown for better and easier future level comparisons using other methods that will be based on the $jj$ coupling.

From these tables, we can clearly conclude that the $LS$ coupling is quite good at least for the even parity as well as for the 5d6p and 6s6p odd configurations. The $j{j}_{Cowan}$ representation shows less mixing for the 5d7p and 5d5f odd configurations than the $LS$ coupling except for Pt IX where both $LS$ and $j{j}_{Cowan}$ representations give important mixing. In Table 4 and Table 5, the Ta IV and W V level compositions in the $LS$ coupling show important mixing between the 5d5f and 5d7p odd configurations, as already discussed in [9]. In Ta IV, the first dominant term in the composition of the 5d7p and 5d5f levels can sometimes reach less than 30% for example the level measured at 180 137 cm⁻¹ ($J=2$) presents an important mixture in $LS$ coupling of 25% 5d7p (²D) ³D ^o + 23% 5d5f (²D) ¹D ^o. In W V, the 5d5f and 5d7p configurations are still mixed but the mixing is slightly less important than in Ta IV as presented in Figure 2 where the average energy of these two configurations diverges. Kildiyarova $et$ $al.$ [9,17] have already observed in their semi-empirical level compositions that the 5d5f and 6s6p odd configurations are mixed for Re VI, Os VII and Ir VIII. Indeed, Figure 2 confirms their computations because the average energy of the 5d5f and 6s6p odd configurations is getting closer to each other up to Re VI and then diverges along the Yb isoelectronic sequence giving rise to a swap of the positions of these two configurations after Re VI. For example, in Re VI, a level computed at 295 260 cm⁻¹ ($J=1$) is composed of 44% 6s6p (²S) ¹P ^o + 33% 5d5f (²D) ³D ^o. In Os VII, the two most important LS spectroscopic terms in the composition of the level measured at 356 849 cm⁻¹ ($J=1$) are 61% 5d5f (²D) ³P ^o and 24% 6s6p (²S) ³P ^o. Kildiyarova $et$ $al.$ [17,18] have also observed important mixing between the 5p⁵5d³ and 5d5f odd configurations in Os VII, Ir VIII and Pt IX that is also confirmed by the Figure 2 where the average energy of the 5p⁵5d³ core-excited configuration crossed the 5d5f as well as the 5d7p odd configurations along the sequence. Indeed, a level computed at 422 778 cm⁻¹ ($J=1$) in Os VII is composed of 41% 5d7p (²D) ³D ^o + 15% 5p⁵5d³ (²D) ³P ^o. In Ir VIII and Pt IX, the mixing between the 5p⁵5d³ and 5d5f configurations is getting worse. Indeed, 5 and 8 levels present more than 15% of 5p⁵5d³ in their composition for Ir VIII and Pt IX, respectively. It is even more interesting to note that one level in Ir VIII measured at 397 557 cm⁻¹ ($J=2$) and one level in Pt IX observed at 424 403 cm⁻¹ ($J=2$) have a dominant $LS$ component of 36% 5p⁵5d³ (⁴P) ⁵S ^o and of 21% 5p⁵5d³ (⁴P) ⁵S ^o, respectively. However, the $j{j}_{Cowan}$ representation of these levels is 30% 5d5f (²D_5/2) ^o and 27% 5d5f (²D_3/2) ^o, respectively.

Table 2. The mean purity of the observed levels obtained after the fit for all Yb-like ions studied in this work namely Ta IV - Pt IX with the HFR(CV) model in $LS$ and $jj$ coupling defined by Cowan [22]. The mean purity in $jj$ coupling given by the MCDHF method is also shown.

	Ta IV			W V			Re VI
	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$
Even	0.91	0.89	0.81	0.89	0.89	0.84	0.86	0.87	0.84
Odd	0.61	0.76	0.74	0.67	0.87	0.81	0.62	0.80	0.78
	Os VII			Ir VIII			Pt IX
	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$
Even	0.84	0.86	0.86	0.83	0.85	0.88	0.81	0.84	0.89
Odd	0.59	0.77	0.74	0.55	0.73	0.74	0.47	0.64	0.70

Table 2. The mean purity of the observed levels obtained after the fit for all Yb-like ions studied in this work namely Ta IV - Pt IX with the HFR(CV) model in $LS$ and $jj$ coupling defined by Cowan [22]. The mean purity in $jj$ coupling given by the MCDHF method is also shown.

	Ta IV			W V			Re VI
	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$
Even	0.91	0.89	0.81	0.89	0.89	0.84	0.86	0.87	0.84
Odd	0.61	0.76	0.74	0.67	0.87	0.81	0.62	0.80	0.78
	Os VII			Ir VIII			Pt IX
	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$	$LS$	$j{j}_{Cowan}$	$j{j}_{MCDHF}$
Even	0.84	0.86	0.86	0.83	0.85	0.88	0.81	0.84	0.89
Odd	0.59	0.77	0.74	0.55	0.73	0.74	0.47	0.64	0.70

3.3. The Core Correlation Effects on the Transition Probabilities Computed with the HFR+CPOL and the HFR(CV) Models

After performing the fitting procedure for both HFR+CPOL and HFR(CV) models, we introduced the optimized values of the radial parameters in the calculations of the electric dipole (E1) transitions. The calculation accuracy of the transition probabilities ($gA$) and the oscillator strengths ($gf$) is thus improved with the least-squares fit of the level structure. For a comparison between a reference data set and a less reliable one, Kramida [28] suggested to plot the logarithm of the ratio of the transition probabilities computed by a less reliable method and a reference one as a function of the logarithm of the line strength. In order to estimate the effects of the core-valence (CV) correlation on the transition probabilities, we have carried out a series of HFR calculations along the sequence with the same CI expansions as in our HFR+CPOL model. The comparisons of the $gA$-values computed with the less reliable HFR and the reference HFR+CPOL methods, as represented in Figure 4 for Ta IV and Figure 5 for W V where only the transitions with log($gf$) > -4 were plotted, lead us to conclude that the HFR+CPOL method reduced the $gA$-values by nearly 20% on average, as expected [29]. The HFR method is the less accurate method because only intravalence interactions were taken into account. In both figures, the logarithm of the ratio of the weighted transition probabilities associated with the selected observed lines (221 among the 229 observed in Ta IV and 193 in W V) and computed by the HFR and HFR+CPOL methods, i.e., $log(g{A}_{HFR}/g{A}_{HFR+CPOL})$, was thus plotted as a function of the logarithm of the HFR+CPOL line strength, namely $log\left(S_{HFR+CPOL}(a.u.)\right)$. The matrix element $\langle 5d\left|\right|r\left|\right|5f\rangle$ was more affected by the polarization effects which reduced it by about 35% and 40% in Ta IV and W V, respectively, due to the penetration of the 5f orbital into the ionic core.

Figure 4 and Figure 5 also show a very good agreement between the HFR+CPOL and HFR(CV) models for Ta IV and W V which means that the CPOL potential model describes in an equivalent way the core-valence correlations introduced explicitly in the HFR(CV) model. For the 221 and 193 lines measured in experiments for Ta IV [8,9] and W V [12], respectively, the mean ratio $g{A}_{HFR\left(CV\right)}$/$g{A}_{HFR+CPOL}$ = 1.08 ± 0.24 and 1.02 ± 0.36 for Ta IV and W V, respectively.

For Re VI up to Pt IX, we performed computations with the HFR(CV) model, instead of the HFR+CPOL model as already explained, for which we were able to estimate the effects of the CV correlations on the computed $gA$-values. From Figure 6 where all observed lines have a log($gf$)-value bigger than -4 for Re VI up to Ir VIII but where two transitions in Pt IX have a log($gf$)-value lower than -4, it is shown that the HFR(CV) $gA$-values are lower than the HFR $gA$-values by approximately 30%, 25%, 35% and 34% on average for Re VI, Os VII, Ir VIII and Pt IX, respectively. The CV effects are thus more important for Ir VIII and Pt IX as we can also see in Figure 6 where the clouds of points are more spread out. Indeed, as already shown previously in Figure 2, the configuration interactions between the core-excited configurations and the ones of interest become more significant for Ir VIII and Pt IX. This demonstrates the importance of including the CV correlations explicitly in our model.

3.4. The fully Relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) Calculations

The second method called the fully Relativistic Multiconfiguration Dirac–Hartree–Fock (MCDHF) method [27], as implemented in the General Relativistic Atomic Structure Package (GRASP2018) [30], is used to estimate the accuracy of the results by comparing the transition probabilities obtained from the HFR+CPOL method for Ta IV and W V or from the HFR method with the HFR(CV) model for Re VI up to Pt IX and the MCDHF method which are two completely different approaches.

As described in [31], the Atomic State Functions (ASF) of parity P and total angular momentum J of projection M are expanded in terms of Configuration State Functions (CSF) in $jj$ coupling: $\Psi (P,J,M)={\sum }_{r=1}^{n_c}{c}_r{\Phi }_r({\gamma }_r,P,J,M)$, where ${\gamma }_r$ contains all information to define the CSF uniquely (i.e. the coupling scheme, the occupation number of orbitals, etc.) and $c_r$ are the mixing coefficients verifying the normalization condition: ${\sum }_{r=1}^{n_c}{\left|c_r\right|}^2=1$ in which $n_c$ is the CSF number introduced in the model. Each CSF in the list is built from antisymmetrised products of one-electron relativistic spin orbitals. The list of CSFs was composed of multireference (MR) and correlation CSFs. The CSFs that strongly interact with the targeted CSFs were grouped together in the MR. The correlation CSFs that correct the reference CSFs were generated by using the active set (AS) approach which consists of allowing excitations of electrons from orbitals in the MR to the correlation orbitals in the AS.

Our calculations were the same for all ions along the Yb isoelectronic sequence studied in this work and began with an optimization of all orbitals (core and 5d valence orbitals) on the ground state (5d²³F₂) with the Optimal Level (OL) mode [27]. Then, we used the previously optimized radial parts in order to perform two different optimization schemes for each parity. For the even parity, only the 6s and 5d valence orbitals were optimized on all the 14 levels of the MR even configurations (5d², 5d6s, 6s²) and the 6s, 6p, 7p, 5d and 5f valence orbitals were optimized on all the 47 levels of the MR odd configurations (5d6p, 6s6p, 5d5f, 5d7p) with the Extended Optimal Level (EOL) mode by freezing all the other orbitals already optimized in the previous calculation [27].

In the layer-by-layer (LBL) approach adopted in this study, the maximum values of the principal quantum number for each azimuthal quantum number l, $n_{max}$l, are increased by steps until a convergence is reached by adding new correlation orbitals by layer in the list. In order to achieve this convergence, three steps of valence-valence correlations, referred to as VV1, VV2 and VV3, were considered where all the single and double (SD) excitations from the spectroscopic orbitals (5d, 6s for the even MR and 5d, 6s, 5f, 6p, 7p for the odd MR) to the orbitals in the active set were allowed. We carried out an Extended Optimal Level (EOL) optimization only for the radial parts of the last layer of orbitals in the AS that was not yet optimized in the previous calculations [30]. The orbitals that were already optimized were kept frozen. The first AS (VV1) was {7s,6p,6d,5f} and {7s,8p,6d,6f} for the even and odd parities, respectively. In the second layer of valence-valence correlations (VV2), we increased the list of CSFs by considering the AS {8s,7p,7d,6f} and {8s,9p,7d,7f} for the even and odd parities and finally the AS {9s,8p,8d,7f} and {9s,10p,8d,8f} for the even and odd parities, respectively, were considered in a last layer of valence-valence correlations (VV3) giving rise to 446 and 688 CSFs for the even and odd parities, respectively. We obtained the convergence of the results and a good agreement with the experimental level energies after the third optimization step as we can see in Table 3 for Ta IV. This table shows the average relative difference between the $ab$ $initio$ energy levels computed with the MCDHF method and the observed energy levels [8,9,10], (E-E_obs)/E_obs, and also the average relative difference between the $ab$ $initio$ energy levels computed in the i^th and i-1^th steps, (E_i-E_i−1)/E_i−1, for all calculation steps in Ta IV. The latter especially reached 0.06% and 0.01% for the even and odd parities, respectively, in the last optimization step (VV3) which justified stopping the increase of the AS at this stage.

For the core-valence (CV) and core-core (CC) calculations, we did not increase the AS and dit not reoptimize the orbitals. We considered the same AS and the radial parts optimized in the last VV calculation step, namely (VV3), to perform only a Relativistic Configuration Interaction (RCI) calculation where the QED effects were introduced in the Dirac-Coulomb-Breit Hamiltonian. For the CV correlations, we first allowed one hole in the 4f core orbital with single and restrictive double (SrD) excitations from the MR to the orbitals in the AS, referred to as CV(4f). Then, we considered one hole in the 4f or 5p core orbitals with also SrD excitations from the MR to the orbitals in the AS, referred to as CV(4f,5p). For the CC correlations, we allowed one hole in both 4f and 5p core orbitals and we considered SrD excitations from the MR to the orbitals in the AS, referred to as CV+CC(4f,5p). Then, we treated more CV correlation effects by considering the CV correlations with SrD excitations and one hole only in the 5s core orbital in addition to the previous calculation step, referred to as CV+CC(4f,5p)+CV(5s). This last calculation generated 867 153 CSFs and 4 916 120 CSFs in the ASF expansions for the even and odd parities, respectively. Then, this list of CSFs was reduced due to limited computational resources. Therefore, after selecting only the CSFs that interacted with the CSFs of the MR by considering the Dirac-Coulomb (DC) Hamiltonian, the ASF expansions were reduced to 373 720 CSFs and 2 602 097 CSFs for the even and odd parities, respectively. We have also used another selection criterion by using a Dirac-Coulomb-Breit (DCB) Hamiltonian reducing the set of CSFs to 379 960 CSFs and 2 641 560 CSFs for the even and odd parities, respectively. We compared in Section 4.1 the transition probabilities obtained for Ta IV by using both sets of CSFs. Actually, we observed that the correlation effects of the additional CSFs introduced by taking into account a DCB interaction Hamiltonian are rather small. In addition, they did not improve the agreement between the HFR+CPOL and the MCDHF methods.

Table 3. Average relative difference for all layers of correlations obtained with the MCDHF method in Ta IV.

	Even parity		Odd parity
Calculation step	(E-Eobs)/Eobs (%)	(Ei-Ei−1)/Ei−1 (%)	(E-Eobs)/Eobs (%)	(Ei-Ei−1)/Ei−1 (%)
MR	9.99		1.52
VV1	4.12	5.44	1.51	0.35
VV2	3.75	0.39	1.55	0.05
VV3	3.69	0.06	1.56	0.01
CV (4f)	5.25	1.90	0.70	1.44
CV (4f,5p)	7.71	3.52	2.12	2.08
CV+CC (4f,5p)	6.90	0.85	5.11	2.83
CV+CC (4f,5p) + CV (5s)	5.65	1.18	5.24	0.12

Table 3. Average relative difference for all layers of correlations obtained with the MCDHF method in Ta IV.

	Even parity		Odd parity
Calculation step	(E-Eobs)/Eobs (%)	(Ei-Ei−1)/Ei−1 (%)	(E-Eobs)/Eobs (%)	(Ei-Ei−1)/Ei−1 (%)
MR	9.99		1.52
VV1	4.12	5.44	1.51	0.35
VV2	3.75	0.39	1.55	0.05
VV3	3.69	0.06	1.56	0.01
CV (4f)	5.25	1.90	0.70	1.44
CV (4f,5p)	7.71	3.52	2.12	2.08
CV+CC (4f,5p)	6.90	0.85	5.11	2.83
CV+CC (4f,5p) + CV (5s)	5.65	1.18	5.24	0.12

After the last RCI calculation step, referred to as CV+CC (4f,5p) + CV (5s), we obtained average relative (absolute) differences of 5.33 % (6070 cm⁻¹), 3.33 % (5318 cm⁻¹), 2.72 % (5231 cm⁻¹), 2.43 % (5767 cm⁻¹), 2.06 % (5673 cm⁻¹) and 1.80 % (5868 cm⁻¹) for Ta IV, W V, Re VI, Os VII, Ir VIII and Pt IX, respectively. The agreement between our calculations and the observed energies based on the average relative difference improves as the charge state and the atomic number increase. However, this was not the case for the average absolute difference after Re VI. The reasons for the discrepancy between the two computed average differences are, first, that the energy levels increase along the sequence decreasing the average relative differences and then, tha only a limited number of CV and CC correlations have been taken into account. In order to improve the agreement with the observed energy levels, more CV and CC correlations need to be considered in our calculations due to the strong interaction between the 5p⁵5d³ core-excited configuration and the 5d5f as well as the 5d7p valence configurations especially after Re VI as already explained in Section 3.2 with the HFR(CV) model. However, owing to the complexity of the level structure on the six ions studied in this work, more correlations could give some difficulties (too long calculation time, too much memory, etc) in the computations without necessarily improving the results or even being impossible due to the limited available resources. Actually, to be sure to have a better agreement with the observed energy levels, we should carry out Complete Active Set (CAS) calculations with all possible correlations but we instead performed Restricted Active Set (RAS) calculations with a limited number of correlations introduced in our computations due to the limitations of our hardware. The final energy levels computed with the last MCDHF-RCI calculation are compared with the experimental ones and the HFR+CPOL ones in Table 4 and Table 5 for Ta IV and W V, respectively, or with the HFR(CV) ones for Re VI up to Pt IX in Table 6, Table 7, Table 8 and Table 9. One can notice that two pairs of odd levels with $J=2$ in Ta IV that were observed to be very close in energies and computed at 176 471 cm⁻¹ - 177 385 cm⁻¹ and 183 468 cm⁻¹ - 184 343 cm⁻¹ with the HFR+CPOL method were swapped in the MCDHF method. We were able to match these levels by running a program that makes an unitary transformation from $jj$ to $LS$ coupling [32]. The dominant spectroscopic term in the level composition computed by the MCDHF method in the $LS$ and $jj$ coupling are also given in Table 4, Table 5, Table 6, Table 7, Table 8 and Table 9. We show that in general, the $jj2lsj$ program well reproduced the purity in $LS$ coupling computed by the Cowan code but when the level mixing becomes significant, there are more discrepancies between the $LS$ purities computed by the two methods (HFR and MCDHF) especially for the levels belonging to the 5d5f and 5d7p odd configurations. Indeed, for some of these levels, the differences between the $LS$ purities obtained from both methods can sometimes exceed 10% and even reach more than 30% in Pt IX. The mean purities of the observed levels computed in the $jj$ coupling with the MCDHF method for Ta IV up to Pt IX are also shown in Table 2. As the charge state increases along the Yb isoelectronic sequence, the most suitable coupling scheme appears to approach the fully relativistic $jj$ coupling calculated by the MCDHF method and even seems to be a better representation than the $jj$ coupling scheme calculated by the Cowan code for describing the energy-level structure in both parities of Ir VIII and Pt IX. However, the odd parity of Pt IX still shows important mixing especially for the 5d5f odd configuration where 10 levels appear with a purity lower than 50% in the $j{j}_{MCDHF}$ representation.

Safronova $et$ $al.$ [21] have previously performed $ab$ $initio$ RMBPT calculations in Yb-like ions (Z=72-100) and have tabulated their computed energy levels only for Re VI up to Hg XI. They obtained a better agreement than our MCDHF calculations namely the relative (absolute) energy difference is equal to 0.77 % (967 cm⁻¹), 0.70 % (956 cm⁻¹), 0.78 % (1556 cm⁻¹) and 1.03 % (2906 cm⁻¹) for Re VI, Os VII, Ir VIII and Pt IX, respectively. Their energy levels are also tabulated in Table 6, Table 7, Table 8 and Table 9. Although they well reproduced the observed level structure with an $ab$ $initio$ method, one can clearly notice that it is becoming increasingly difficult to accurately reproduce the observed energy levels when the atomic number increases along the sequence as already discussed with our MCDHF calculations in the previous paragraph.

Table 4. Comparison of the Ta IV energy levels (cm⁻¹) computed in this work using the HFR+CPOL and MCDHF methods with available experimental data.

EExp (a)	EHFR + CPOL (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}+\mathit{C}\mathit{P}\mathit{O}\mathit{L}}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	J	Composition in LS coupling (f)	jjCowan (g)	jjMCDHF (h)	LSMCDHF (i)
0	26	-26	0	0	2	90% 5d2 (3F) 3F + 9% 5d2 (1D) 1D	90% 5d2 (3F2)	86% 5d2 (0,2)	89% 5d2 (3F) 3F
4542.9	4558	-15	4299.0	-244	3	100% 5d2 (3F) 3F	100% 5d2 (3F3)	97% 5d2 (3/2,5/2)	97% 5d2 (3F) 3F
8576.4	8536	40	8285.3	-291	4	94% 5d2 (3F) 3F + 6% 5d2 (1G) 1G	94% 5d2 (3F4)	60% 5d2 (0,4)	93% 5d2 (3F) 3F
10555.3	10544	12	11196.8	641	2	63% 5d2 (1D) 1D + 24% 5d2 (3P) 3P	63% 5d2 (1D2)	74% 5d2 (3/2,5/2)	62% 5d2 (1D) 1D
11166.5	11127	39	12052.6	886	0	94% 5d2 (3P) 3P + 6% 5d2 (1S) 1S	94% 5d2 (3P0)	75% 5d2 (0,0)	93% 5d2 (3P) 3P
13599.1	13622	-22	14177.2	578	1	100% 5d2 (3P) 3P	100% 5d2 (3P1)	97% 5d2 (3/2,5/2)	97% 5d2 (3P) 3P
17607.8	17631	-23	18076.8	469	2	76% 5d2 (3P) 3P + 21% 5d2 (1D) 1D	76% 5d2 (3P2)	82% 5d2 (0,2)	73% 5d2 (3P) 3P
18217.5	18220	-2	19416.6	1199	4	94% 5d2 (1G) 1G + 6% 5d2 (3F) 3F	94% 5d2 (1G4)	60% 5d2 (3/2,5/2)	93% 5d2 (1G) 1G
28324.6	28298	26	29846.9	1522	1	100% 5d6s (2D) 3D	100% 5d6s (2D3/2)	96% 5d6s (3/2,1/2)	96% 5d6s (2D) 3D
29962.3	29995	-33	31458.4	1496	2	93% 5d6s (2D) 3D + 6% 5d6s (2D) 1D	81% 5d6s (2D3/2)	76% 5d6s (3/2,1/2)	91% 5d6s (2D) 3D
34390.9	34387	4	35695.7	1305	3	100% 5d6s (2D) 3D	100% 5d6s (2D5/2)	96% 5d6s (5/2,1/2)	96% 5d6s (2D) 3D
34573.8	34576	-2	38574.0	4000	0	89% 5d2 (1S) 1S + 6% 5d2 (3P) 3P	89% 5d2 (1S0)	70% 5d2 (0,0)	85% 5d2 (1S) 1S
41528.4	41526	2	43837.6	2309	2	87% 5d6s (2D) 1D + 7% 5d6s (2D) 3D	78% 5d6s (2D5/2)	73% 5d6s (5/2,1/2)	84% 5d6s (2D) 1D
68952.3	68952	0	73023.3	4071	0	93% 6s2 (1S) 1S + 4% 5d2 (1S) 1S	93% 6s2 (1S0)	87% 6s2 (0,0)	87% 6s2 (1S) 1S
78590.5	78758	-167	85818.4	7228	2	69% 5d6p (2D) 3Fo + 27% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	95% 5d6p (3/2,1/2)o	64% 5d6p (2D) 3Fo
81917.4	81682	236	89236.1	7319	1	71% 5d6p (2D) 3Do + 18% 5d6p (2D) 1Po	94% 5d6p (2D3/2)o	88% 5d6p (3/2,1/2)o	72% 5d6p (2D) 3Do
86977.8	86885	93	94134.7	7157	3	76% 5d6p (2D) 3Fo + 17% 5d6p (2D) 3Do	85% 5d6p (2D5/2)o	80% 5d6p (5/2,1/2)o	74% 5d6p (2D) 3Fo
86811.6	86951	-140	93822.8	7011	2	43% 5d6p (2D) 3Do + 26% 5d6p (2D) 3Po	94% 5d6p (2D5/2)o	88% 5d6p (5/2,1/2)o	43% 5d6p (2D) 3Do
89612.1	89651	-39	96462.0	6850	2	46% 5d6p (2D) 3Do + 28% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	92% 5d6p (3/2,3/2)o	44% 5d6p (2D) 3Do
92661.5	92624	37	99660.2	6999	3	53% 5d6p (2D) 3Do + 24% 5d6p (2D) 3Fo	71% 5d6p (2D3/2)o	64% 5d6p (3/2,3/2)o	57% 5d6p (2D) 3Do
93068.5	93165	-97	100297.1	7229	1	59% 5d6p (2D) 3Po + 24% 5d6p (2D) 3Do	94% 5d6p (2D3/2)o	89% 5d6p (3/2,3/2)o	58% 5d6p (2D) 3Po
94366.8	94329	38	101637.8	7271	0	97% 5d6p (2D) 3Po + 2% 6s6p (2S) 3Po	97% 5d6p (2D3/2)o	94% 5d6p (3/2,3/2)o	94% 5d6p (2D) 3Po
96591.2	96474	117	103452.2	6861	4	100% 5d6p (2D) 3Fo	100% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
98248.7	98244	5	105196.2	6947	2	70% 5d6p (2D) 3Po + 20% 5d6p (2D) 1Do	89% 5d6p (2D5/2)o	84% 5d6p (5/2,3/2)o	72% 5d6p (2D) 3Po
99934.6	99999	-64	107247.3	7313	3	69% 5d6p (2D) 1Fo + 29% 5d6p (2D) 3Do	79% 5d6p (2D5/2)o	70% 5d6p (5/2,3/2)o	74% 5d6p (2D) 1Fo
101452.8	101471	-19	108710.2	7257	1	59% 5d6p (2D) 1Po + 30% 5d6p (2D) 3Po	93% 5d6p (2D5/2)o	89% 5d6p (5/2,3/2)o	57% 5d6p (2D) 1Po
112180.1	112317	-137	120570.5	8390	0	97% 6s6p (2S) 3Po + 2% 5d6p (2D) 3Po	97% 6s6p (2S1/2)o	94% 6s6p (1/2,1/2)o	94% 6s6p (2S) 3Po
115249.4	115082	168	123581.4	8332	1	94% 6s6p (2S) 3Po + 3% 6s6p (2S) 1Po	80% 6s6p (2S1/2)o	75% 6s6p (1/2,1/2)o	91% 6s6p (2S) 3Po
123989.2	124013	-24	132026.5	8037	2	99% 6s6p (2S) 3Po + 1% 5d6p (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,3/2)o	96% 6s6p (2S) 3Po
141593.2	141597	-3	150038.6	8445	1	85% 6s6p (2S) 1Po + 6% 5d6p (2D) 1Po	76% 6s6p (2S1/2)o	70% 6s6p (1/2,3/2)o	81% 6s6p (2S) 1Po
172386.0	172324	62	180220.1	7834	4	49% 5d5f (2D) 1Go + 33% 5d5f (2D) 3Ho	65% 5d5f (2D3/2)o	53% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
173119.0	173049	70	180872.5	7754	2	72% 5d5f (2D) 3Fo + 20% 5d5f (2D) 1Do	92% 5d5f (2D3/2)o	89% 5d5f (3/2,5/2)o	67% 5d5f (2D) 3Fo
173475.0	173383	92	181373.9	7899	4	56% 5d5f (2D) 3Ho + 23% 5d5f (2D) 3Go	63% 5d5f (2D3/2)o	51% 5d5f (3/2,7/2)o	63% 5d5f (2D) 3Ho
173827.0	173787	40	181616.4	7789	3	64% 5d5f (2D) 3Fo + 26% 5d5f (2D) 3Go	74% 5d5f (2D3/2)o	71% 5d5f (3/2,7/2)o	61% 5d5f (2D) 3Fo
174832.0	174850	-18	182806.6	7975	5	79% 5d5f (2D) 3Ho + 10% 5d5f (2D) 3Go	86% 5d5f (2D3/2)o	83% 5d5f (3/2,7/2)o	77% 5d5f (2D) 3Ho
175230.0	175308	-78	183070.0	7840	3	49% 5d5f (2D) 3Go + 31% 5d5f (2D) 1Fo	79% 5d5f (2D3/2)o	75% 5d5f (3/2,5/2)o	47% 5d5f (2D) 3Go
176228.0	176217	11	183938.8	7711	1	33% 5d7p (2D) 3Do + 27% 5d5f (2D) 3Do	50% 5d7p (2D3/2)o	64% 5d7p (3/2,1/2)o	45% 5d7p (2D) 3Do
176438.0	176471	-33	184242.1	7804	2	40% 5d5f (2D) 3Po + 25% 5d5f (2D) 1Do	86% 5d5f (2D3/2)o	66% 5d5f (3/2,7/2)o	28% 5d5f (2D) 3Po
177309.0	177385	-76	183359.9	6051	2	64% 5d7p (2D) 3Fo + 24% 5d7p (2D) 1Do	94% 5d7p (2D3/2)o	76% 5d7p (3/2,1/2)o	49% 5d7p (2D) 3Fo
178438.0	178558	-120	186080.8	7643	4	54% 5d5f (2D) 3Fo + 38% 5d5f (2D) 1Go	91% 5d5f (2D5/2)o	87% 5d5f (5/2,7/2)o	52% 5d5f (2D) 3Fo
	179580				6	100% 5d5f (2D) 3Ho	100% 5d5f (2D5/2)o
179568.0	179656	-88	186954.5	7386	1	48% 5d7p (2D) 3Do + 26% 5d5f (2D) 3Do	42% 5d5f (2D3/2)o	54% 5d5f (3/2,5/2)o	36% 5d7p (2D) 3Do
180137.0	180121	16	187121.8	6985	2	25% 5d7p (2D) 3Do + 23% 5d5f (2D) 1Do	40% 5d7p (2D3/2)o	66% 5d7p (3/2,3/2)o	40% 5d7p (2D) 3Do
180222.0	180275	-53	187843.6	7622	4	70% 5d5f (2D) 3Go + 18% 5d5f (2D) 3Fo	88% 5d5f (2D5/2)o	84% 5d5f (5/2,5/2)o	67% 5d5f (2D) 3Go
180496.0	180452	44	187861.6	7366	3	23% 5d5f (2D) 3Fo + 20% 5d5f (2D) 3Go	76% 5d5f (2D5/2)o	55% 5d5f (5/2,5/2)o	18% 5d5f (2D) 3Fo
181028.0	181029	-1	188538.9	7511	5	85% 5d5f (2D) 3Go + 14% 5d5f (2D) 3Ho	68% 5d5f (2D5/2)o	67% 5d5f (5/2,7/2)o	83% 5d5f (2D) 3Go
181380.0	181493	-113	188684.0	7304	2	28% 5d5f (2D) 1Do + 25% 5d7p (2D) 3Do	45% 5d5f (2D5/2)o	41% 5d5f (5/2,7/2)o	33% 5d5f (2D) 1Do
181681.0	181633	48	188529.1	6848	1	42% 5d7p (2D) 3Po + 26% 5d5f (2D) 3Do	55% 5d7p (2D3/2)o	65% 5d7p (3/2,3/2)o	48% 5d7p (2D) 3Po
182297.0	182014	283	189116.5	6819	0	65% 5d7p (2D) 3Po + 35% 5d5f (2D) 3Po	65% 5d7p (2D3/2)o	82% 5d7p (3/2,3/2)o	82% 5d7p (2D) 3Po
182200.0	182261	-61	189114.1	6914	3	42% 5d7p (2D) 3Fo + 35% 5d5f (2D) 3Do	49% 5d7p (2D3/2)o	48% 5d7p (3/2,3/2)o	56% 5d7p (2D) 3Fo
182706.0	182690	16	190167.3	7461	3	38% 5d5f (2D) 1Fo + 29% 5d7p (2D) 3Fo	58% 5d5f (2D5/2)o	78% 5d5f (5/2,7/2)o	39% 5d5f (2D) 1Fo
183499.0	183468	31	191014.4	7515	2	45% 5d5f (2D) 3Do + 34% 5d5f (2D) 3Po	48% 5d5f (2D5/2)o	46% 5d5f (5/2,5/2)o	45% 5d5f (2D) 3Do
184290.0	184343	-53	190713.2	6423	2	37% 5d7p (2D) 3Do + 29% 5d7p (2D) 1Do	89% 5d7p (2D5/2)o	75% 5d7p (5/2,1/2)o	34% 5d7p (2D) 1Do
184728.0	184548	180	192125.8	7398	3	43% 5d7p (2D) 3Do + 32% 5d7p (2D) 1Fo	85% 5d7p (2D5/2)o	69% 5d7p (5/2,1/2)o	50% 5d7p (2D) 3Do
184605.0	184579	26	191320.1	6715	1	61% 5d5f (2D) 3Po + 11% 5d7p (2D) 1Po	44% 5d5f (2D5/2)o	64% 5d5f (5/2,5/2)o	69% 5d5f (2D) 3Po
185243.0	185164	79	193224.3	7981	5	87% 5d5f (2D) 1Ho + 7% 5d5f (2D) 3Ho	56% 5d5f (2D5/2)o	55% 5d5f (5/2,5/2)o	87% 5d5f (2D) 1Ho
185165.0	185354	-189	192684.2	7519	0	65% 5d5f (2D) 3Po + 35% 5d7p (2D) 3Po	65% 5d5f (2D5/2)o	81% 5d5f (5/2,5/2)o	81% 5d5f (2D) 3Po
185885.0	185808	77	193523.3	7638	1	44% 5d5f (2D) 1Po + 35% 5d7p (2D) 3Po	34% 5d5f (2D5/2)o	37% 5d7p (5/2,3/2)o	41% 5d5f (2D) 1Po
188291.0	188180	111	194626.3	6335	4	99% 5d7p (2D) 3Fo + 1% 6s5f (2S) 3Fo	99% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
188618.0	188561	57	195189.3	6571	3	43% 5d7p (2D) 1Fo + 47% 5d7p (2D) 3Do	89% 5d7p (2D5/2)o	79% 5d7p (5/2,3/2)o	47% 5d7p (2D) 1Fo
188780.0	188897	-117	195261.8	6482	2	66% 5d7p (2D) 3Po + 24% 5d7p (2D) 1Do	87% 5d7p (2D5/2)o	81% 5d7p (5/2,3/2)o	65% 5d7p (2D) 3Po
191903.0	192154	-251	199345.3	7442	1	53% 5d7p (2D) 1Po + 20% 5d5f (2D) 1Po	70% 5d7p (2D5/2)o	54% 5d7p (5/2,3/2)o	44% 5d7p (2D) 1Po

(a) Experimental energies from [8], [9] and [10]; (b) Our HFR+CPOL calculations; (c) ΔE_HFR+CPOL = E_HFR+CPOL − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) Only the first two components in LS coupling computed in our HFR+CPOL model are given; (g) Only the first component in jj coupling computed in our HFR+CPOL model is given; (h) The first component in jj coupling computed in our MCDHF model is given; (i) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 4. Comparison of the Ta IV energy levels (cm⁻¹) computed in this work using the HFR+CPOL and MCDHF methods with available experimental data.

EExp (a)	EHFR + CPOL (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}+\mathit{C}\mathit{P}\mathit{O}\mathit{L}}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	J	Composition in LS coupling (f)	jjCowan (g)	jjMCDHF (h)	LSMCDHF (i)
0	26	-26	0	0	2	90% 5d2 (3F) 3F + 9% 5d2 (1D) 1D	90% 5d2 (3F2)	86% 5d2 (0,2)	89% 5d2 (3F) 3F
4542.9	4558	-15	4299.0	-244	3	100% 5d2 (3F) 3F	100% 5d2 (3F3)	97% 5d2 (3/2,5/2)	97% 5d2 (3F) 3F
8576.4	8536	40	8285.3	-291	4	94% 5d2 (3F) 3F + 6% 5d2 (1G) 1G	94% 5d2 (3F4)	60% 5d2 (0,4)	93% 5d2 (3F) 3F
10555.3	10544	12	11196.8	641	2	63% 5d2 (1D) 1D + 24% 5d2 (3P) 3P	63% 5d2 (1D2)	74% 5d2 (3/2,5/2)	62% 5d2 (1D) 1D
11166.5	11127	39	12052.6	886	0	94% 5d2 (3P) 3P + 6% 5d2 (1S) 1S	94% 5d2 (3P0)	75% 5d2 (0,0)	93% 5d2 (3P) 3P
13599.1	13622	-22	14177.2	578	1	100% 5d2 (3P) 3P	100% 5d2 (3P1)	97% 5d2 (3/2,5/2)	97% 5d2 (3P) 3P
17607.8	17631	-23	18076.8	469	2	76% 5d2 (3P) 3P + 21% 5d2 (1D) 1D	76% 5d2 (3P2)	82% 5d2 (0,2)	73% 5d2 (3P) 3P
18217.5	18220	-2	19416.6	1199	4	94% 5d2 (1G) 1G + 6% 5d2 (3F) 3F	94% 5d2 (1G4)	60% 5d2 (3/2,5/2)	93% 5d2 (1G) 1G
28324.6	28298	26	29846.9	1522	1	100% 5d6s (2D) 3D	100% 5d6s (2D3/2)	96% 5d6s (3/2,1/2)	96% 5d6s (2D) 3D
29962.3	29995	-33	31458.4	1496	2	93% 5d6s (2D) 3D + 6% 5d6s (2D) 1D	81% 5d6s (2D3/2)	76% 5d6s (3/2,1/2)	91% 5d6s (2D) 3D
34390.9	34387	4	35695.7	1305	3	100% 5d6s (2D) 3D	100% 5d6s (2D5/2)	96% 5d6s (5/2,1/2)	96% 5d6s (2D) 3D
34573.8	34576	-2	38574.0	4000	0	89% 5d2 (1S) 1S + 6% 5d2 (3P) 3P	89% 5d2 (1S0)	70% 5d2 (0,0)	85% 5d2 (1S) 1S
41528.4	41526	2	43837.6	2309	2	87% 5d6s (2D) 1D + 7% 5d6s (2D) 3D	78% 5d6s (2D5/2)	73% 5d6s (5/2,1/2)	84% 5d6s (2D) 1D
68952.3	68952	0	73023.3	4071	0	93% 6s2 (1S) 1S + 4% 5d2 (1S) 1S	93% 6s2 (1S0)	87% 6s2 (0,0)	87% 6s2 (1S) 1S
78590.5	78758	-167	85818.4	7228	2	69% 5d6p (2D) 3Fo + 27% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	95% 5d6p (3/2,1/2)o	64% 5d6p (2D) 3Fo
81917.4	81682	236	89236.1	7319	1	71% 5d6p (2D) 3Do + 18% 5d6p (2D) 1Po	94% 5d6p (2D3/2)o	88% 5d6p (3/2,1/2)o	72% 5d6p (2D) 3Do
86977.8	86885	93	94134.7	7157	3	76% 5d6p (2D) 3Fo + 17% 5d6p (2D) 3Do	85% 5d6p (2D5/2)o	80% 5d6p (5/2,1/2)o	74% 5d6p (2D) 3Fo
86811.6	86951	-140	93822.8	7011	2	43% 5d6p (2D) 3Do + 26% 5d6p (2D) 3Po	94% 5d6p (2D5/2)o	88% 5d6p (5/2,1/2)o	43% 5d6p (2D) 3Do
89612.1	89651	-39	96462.0	6850	2	46% 5d6p (2D) 3Do + 28% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	92% 5d6p (3/2,3/2)o	44% 5d6p (2D) 3Do
92661.5	92624	37	99660.2	6999	3	53% 5d6p (2D) 3Do + 24% 5d6p (2D) 3Fo	71% 5d6p (2D3/2)o	64% 5d6p (3/2,3/2)o	57% 5d6p (2D) 3Do
93068.5	93165	-97	100297.1	7229	1	59% 5d6p (2D) 3Po + 24% 5d6p (2D) 3Do	94% 5d6p (2D3/2)o	89% 5d6p (3/2,3/2)o	58% 5d6p (2D) 3Po
94366.8	94329	38	101637.8	7271	0	97% 5d6p (2D) 3Po + 2% 6s6p (2S) 3Po	97% 5d6p (2D3/2)o	94% 5d6p (3/2,3/2)o	94% 5d6p (2D) 3Po
96591.2	96474	117	103452.2	6861	4	100% 5d6p (2D) 3Fo	100% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
98248.7	98244	5	105196.2	6947	2	70% 5d6p (2D) 3Po + 20% 5d6p (2D) 1Do	89% 5d6p (2D5/2)o	84% 5d6p (5/2,3/2)o	72% 5d6p (2D) 3Po
99934.6	99999	-64	107247.3	7313	3	69% 5d6p (2D) 1Fo + 29% 5d6p (2D) 3Do	79% 5d6p (2D5/2)o	70% 5d6p (5/2,3/2)o	74% 5d6p (2D) 1Fo
101452.8	101471	-19	108710.2	7257	1	59% 5d6p (2D) 1Po + 30% 5d6p (2D) 3Po	93% 5d6p (2D5/2)o	89% 5d6p (5/2,3/2)o	57% 5d6p (2D) 1Po
112180.1	112317	-137	120570.5	8390	0	97% 6s6p (2S) 3Po + 2% 5d6p (2D) 3Po	97% 6s6p (2S1/2)o	94% 6s6p (1/2,1/2)o	94% 6s6p (2S) 3Po
115249.4	115082	168	123581.4	8332	1	94% 6s6p (2S) 3Po + 3% 6s6p (2S) 1Po	80% 6s6p (2S1/2)o	75% 6s6p (1/2,1/2)o	91% 6s6p (2S) 3Po
123989.2	124013	-24	132026.5	8037	2	99% 6s6p (2S) 3Po + 1% 5d6p (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,3/2)o	96% 6s6p (2S) 3Po
141593.2	141597	-3	150038.6	8445	1	85% 6s6p (2S) 1Po + 6% 5d6p (2D) 1Po	76% 6s6p (2S1/2)o	70% 6s6p (1/2,3/2)o	81% 6s6p (2S) 1Po
172386.0	172324	62	180220.1	7834	4	49% 5d5f (2D) 1Go + 33% 5d5f (2D) 3Ho	65% 5d5f (2D3/2)o	53% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
173119.0	173049	70	180872.5	7754	2	72% 5d5f (2D) 3Fo + 20% 5d5f (2D) 1Do	92% 5d5f (2D3/2)o	89% 5d5f (3/2,5/2)o	67% 5d5f (2D) 3Fo
173475.0	173383	92	181373.9	7899	4	56% 5d5f (2D) 3Ho + 23% 5d5f (2D) 3Go	63% 5d5f (2D3/2)o	51% 5d5f (3/2,7/2)o	63% 5d5f (2D) 3Ho
173827.0	173787	40	181616.4	7789	3	64% 5d5f (2D) 3Fo + 26% 5d5f (2D) 3Go	74% 5d5f (2D3/2)o	71% 5d5f (3/2,7/2)o	61% 5d5f (2D) 3Fo
174832.0	174850	-18	182806.6	7975	5	79% 5d5f (2D) 3Ho + 10% 5d5f (2D) 3Go	86% 5d5f (2D3/2)o	83% 5d5f (3/2,7/2)o	77% 5d5f (2D) 3Ho
175230.0	175308	-78	183070.0	7840	3	49% 5d5f (2D) 3Go + 31% 5d5f (2D) 1Fo	79% 5d5f (2D3/2)o	75% 5d5f (3/2,5/2)o	47% 5d5f (2D) 3Go
176228.0	176217	11	183938.8	7711	1	33% 5d7p (2D) 3Do + 27% 5d5f (2D) 3Do	50% 5d7p (2D3/2)o	64% 5d7p (3/2,1/2)o	45% 5d7p (2D) 3Do
176438.0	176471	-33	184242.1	7804	2	40% 5d5f (2D) 3Po + 25% 5d5f (2D) 1Do	86% 5d5f (2D3/2)o	66% 5d5f (3/2,7/2)o	28% 5d5f (2D) 3Po
177309.0	177385	-76	183359.9	6051	2	64% 5d7p (2D) 3Fo + 24% 5d7p (2D) 1Do	94% 5d7p (2D3/2)o	76% 5d7p (3/2,1/2)o	49% 5d7p (2D) 3Fo
178438.0	178558	-120	186080.8	7643	4	54% 5d5f (2D) 3Fo + 38% 5d5f (2D) 1Go	91% 5d5f (2D5/2)o	87% 5d5f (5/2,7/2)o	52% 5d5f (2D) 3Fo
	179580				6	100% 5d5f (2D) 3Ho	100% 5d5f (2D5/2)o
179568.0	179656	-88	186954.5	7386	1	48% 5d7p (2D) 3Do + 26% 5d5f (2D) 3Do	42% 5d5f (2D3/2)o	54% 5d5f (3/2,5/2)o	36% 5d7p (2D) 3Do
180137.0	180121	16	187121.8	6985	2	25% 5d7p (2D) 3Do + 23% 5d5f (2D) 1Do	40% 5d7p (2D3/2)o	66% 5d7p (3/2,3/2)o	40% 5d7p (2D) 3Do
180222.0	180275	-53	187843.6	7622	4	70% 5d5f (2D) 3Go + 18% 5d5f (2D) 3Fo	88% 5d5f (2D5/2)o	84% 5d5f (5/2,5/2)o	67% 5d5f (2D) 3Go
180496.0	180452	44	187861.6	7366	3	23% 5d5f (2D) 3Fo + 20% 5d5f (2D) 3Go	76% 5d5f (2D5/2)o	55% 5d5f (5/2,5/2)o	18% 5d5f (2D) 3Fo
181028.0	181029	-1	188538.9	7511	5	85% 5d5f (2D) 3Go + 14% 5d5f (2D) 3Ho	68% 5d5f (2D5/2)o	67% 5d5f (5/2,7/2)o	83% 5d5f (2D) 3Go
181380.0	181493	-113	188684.0	7304	2	28% 5d5f (2D) 1Do + 25% 5d7p (2D) 3Do	45% 5d5f (2D5/2)o	41% 5d5f (5/2,7/2)o	33% 5d5f (2D) 1Do
181681.0	181633	48	188529.1	6848	1	42% 5d7p (2D) 3Po + 26% 5d5f (2D) 3Do	55% 5d7p (2D3/2)o	65% 5d7p (3/2,3/2)o	48% 5d7p (2D) 3Po
182297.0	182014	283	189116.5	6819	0	65% 5d7p (2D) 3Po + 35% 5d5f (2D) 3Po	65% 5d7p (2D3/2)o	82% 5d7p (3/2,3/2)o	82% 5d7p (2D) 3Po
182200.0	182261	-61	189114.1	6914	3	42% 5d7p (2D) 3Fo + 35% 5d5f (2D) 3Do	49% 5d7p (2D3/2)o	48% 5d7p (3/2,3/2)o	56% 5d7p (2D) 3Fo
182706.0	182690	16	190167.3	7461	3	38% 5d5f (2D) 1Fo + 29% 5d7p (2D) 3Fo	58% 5d5f (2D5/2)o	78% 5d5f (5/2,7/2)o	39% 5d5f (2D) 1Fo
183499.0	183468	31	191014.4	7515	2	45% 5d5f (2D) 3Do + 34% 5d5f (2D) 3Po	48% 5d5f (2D5/2)o	46% 5d5f (5/2,5/2)o	45% 5d5f (2D) 3Do
184290.0	184343	-53	190713.2	6423	2	37% 5d7p (2D) 3Do + 29% 5d7p (2D) 1Do	89% 5d7p (2D5/2)o	75% 5d7p (5/2,1/2)o	34% 5d7p (2D) 1Do
184728.0	184548	180	192125.8	7398	3	43% 5d7p (2D) 3Do + 32% 5d7p (2D) 1Fo	85% 5d7p (2D5/2)o	69% 5d7p (5/2,1/2)o	50% 5d7p (2D) 3Do
184605.0	184579	26	191320.1	6715	1	61% 5d5f (2D) 3Po + 11% 5d7p (2D) 1Po	44% 5d5f (2D5/2)o	64% 5d5f (5/2,5/2)o	69% 5d5f (2D) 3Po
185243.0	185164	79	193224.3	7981	5	87% 5d5f (2D) 1Ho + 7% 5d5f (2D) 3Ho	56% 5d5f (2D5/2)o	55% 5d5f (5/2,5/2)o	87% 5d5f (2D) 1Ho
185165.0	185354	-189	192684.2	7519	0	65% 5d5f (2D) 3Po + 35% 5d7p (2D) 3Po	65% 5d5f (2D5/2)o	81% 5d5f (5/2,5/2)o	81% 5d5f (2D) 3Po
185885.0	185808	77	193523.3	7638	1	44% 5d5f (2D) 1Po + 35% 5d7p (2D) 3Po	34% 5d5f (2D5/2)o	37% 5d7p (5/2,3/2)o	41% 5d5f (2D) 1Po
188291.0	188180	111	194626.3	6335	4	99% 5d7p (2D) 3Fo + 1% 6s5f (2S) 3Fo	99% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
188618.0	188561	57	195189.3	6571	3	43% 5d7p (2D) 1Fo + 47% 5d7p (2D) 3Do	89% 5d7p (2D5/2)o	79% 5d7p (5/2,3/2)o	47% 5d7p (2D) 1Fo
188780.0	188897	-117	195261.8	6482	2	66% 5d7p (2D) 3Po + 24% 5d7p (2D) 1Do	87% 5d7p (2D5/2)o	81% 5d7p (5/2,3/2)o	65% 5d7p (2D) 3Po
191903.0	192154	-251	199345.3	7442	1	53% 5d7p (2D) 1Po + 20% 5d5f (2D) 1Po	70% 5d7p (2D5/2)o	54% 5d7p (5/2,3/2)o	44% 5d7p (2D) 1Po

(a) Experimental energies from [8], [9] and [10]; (b) Our HFR+CPOL calculations; (c) ΔE_HFR+CPOL = E_HFR+CPOL − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) Only the first two components in LS coupling computed in our HFR+CPOL model are given; (g) Only the first component in jj coupling computed in our HFR+CPOL model is given; (h) The first component in jj coupling computed in our MCDHF model is given; (i) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 5. Comparison of the W V energy levels (cm⁻¹) computed in this work using the HFR+CPOL and MCDHF methods with available experimental data.

EExp (a)	EHFR (CPOL) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}+\mathit{C}\mathit{P}\mathit{O}\mathit{L}}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	J	Composition in LS coupling (f)	jjCowan (g)	jjMCDHF (h)	LSMCDHF (i)
0	24	-24	0	0	2	90% 5d2 (3F) 3F + 10% 5d2 (1D) 1D	90% 5d2 (3F2)	87% 5d2 (0,2)	89% 5d2 (3F) 3F
6244.7	6258	-13	5947.1	-298	3	100% 5d2 (3F) 3F	100% 5d2 (3F3)	97% 5d2 (3/2,5/2)	97% 5d2 (3F) 3F
11519.4	11482	38	11231.8	-288	4	91% 5d2 (3F) 3F + 9% 5d2 (1G) 1G	91% 5d2 (3F4)	55% 5d2 (0,4)	91% 5d2 (3F) 3F
12838.7	12798	40	13840.4	1002	0	93% 5d2 (3P) 3P + 7% 5d2 (1S) 1S	93% 5d2 (3P0)	78% 5d2 (0,0)	92% 5d2 (3P) 3P
13741.5	13731	11	14507.4	766	2	56% 5d2 (1D) 1D + 34% 5d2 (3P) 3P	56% 5d2 (1D2)	83% 5d2 (3/2,5/2)	54% 5d2 (1D) 1D
16330.6	16364	-34	16954.6	624	1	100% 5d2 (3P) 3P	100% 5d2 (3P1)	97% 5d2 (3/2,5/2)	97% 5d2 (3P) 3P
22345.8	22350	-4	23199.3	853	4	91% 5d2 (1G) 1G + 9% 5d2 (3F) 3F	91% 5d2 (1G4)	55% 5d2 (3/2,5/2)	91% 5d2 (1G) 1G
22615.4	22627	-11	23523.0	908	2	65% 5d2 (3P) 3P + 32% 5d2 (1D) 1D	65% 5d2 (3P2)	91% 5d2 (0,2)	62% 5d2 (3P) 3P
43110	43113	-3	47991.7	4882	0	92% 5d2 (1S) 1S + 7% 5d2 (3P) 3P	92% 5d2 (1S0)	77% 5d2 (0,0)	91% 5d2 (1S) 1S
58514.2	58475	39	60174.7	1660	1	100% 5d6s (2D) 3D	100% 5d6s (2D3/2)	97% 5d6s (3/2,1/2)	97% 5d6s (2D) 3D
60295.5	60341	-45	61976.4	1681	2	89% 5d6s (2D) 3D + 11% 5d6s (2D) 1D	88% 5d6s (2D3/2)	84% 5d6s (3/2,1/2)	87% 5d6s (2D) 3D
66657.7	66657	0	68087.7	1430	3	100% 5d6s (2D) 3D	100% 5d6s (2D5/2)	97% 5d6s (5/2,1/2)	97% 5d6s (2D) 3D
72958.7	72953	6	75201.4	2243	2	87% 5d6s (2D) 1D + 11% 5d6s (2D) 3D	87% 5d6s (2D5/2)	83% 5d6s (5/2,1/2)	85% 5d6s (2D) 1D
118662.8	118866	-203	124853.4	6191	2	69% 5d6p (2D) 3Fo + 26% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	96% 5d6p (3/2,1/2)o	64% 5d6p (2D) 3Fo
122325.8	122081	245	128621.2	6295	1	71% 5d6p (2D) 3Do + 19% 5d6p (2D) 1Po	95% 5d6p (2D3/2)o	90% 5d6p (3/2,1/2)o	72% 5d6p (2D) 3Do
128997.1	129162	-165	134964.1	5967	2	48% 5d6p (2D) 3Do + 27% 5d6p (2D) 3Po	95% 5d6p (2D5/2)o	91% 5d6p (5/2,1/2)o	48% 5d6p (2D) 3Do
129479.5	129334	146	135601.6	6122	3	69% 5d6p (2D) 3Fo + 21% 5d6p (2D) 3Do	90% 5d6p (2D5/2)o	85% 5d6p (5/2,1/2)o	68% 5d6p (2D) 3Fo
133430.0	133507	-77	139181.9	5752	2	41% 5d6p (2D) 3Do + 30% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	93% 5d6p (3/2,3/2)o	38% 5d6p (2D) 3Do
	134838		133076.9		0	97% 6s2 (1S) 1S + 2% 6p2 (1S) 1S	97% 6s2 (1S0)	94% 6s2 (0,0)	94% 6s2 (1S) 1S
136887.8	136815	72	142842.3	5954	3	43% 5d6p (2D) 3Do + 31% 5d6p (2D) 3Fo	80% 5d6p (2D3/2)o	73% 5d6p (3/2,3/2)o	48% 5d6p (2D) 3Do
137709.3	137793	-84	143862.0	6153	1	63% 5d6p (2D) 3Po + 23% 5d6p (2D) 3Do	96% 5d6p (2D3/2)o	91% 5d6p (3/2,3/2)o	62% 5d6p (2D) 3Po
139252.1	139196	57	145440.6	6189	0	99% 5d6p (2D) 3Po + 1% 6s6p (2S) 3Po	99% 5d6p (2D3/2)o	96% 5d6p (3/2,3/2)o	96% 5d6p (2D) 3Po
142907.9	142744	164	148658.1	5750	4	100% 5d6p (2D) 3Fo	100% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
144389.9	144445	-55	150227.2	5837	2	68% 5d6p (2D) 3Po + 23% 5d6p (2D) 1Do	92% 5d6p (2D5/2)o	87% 5d6p (5/2,3/2)o	69% 5d6p (2D) 3Po
145767.9	145807	-39	151946.6	6179	3	63% 5d6p (2D) 1Fo + 36% 5d6p (2D) 3Do	84% 5d6p (2D5/2)o	76% 5d6p (5/2,3/2)o	69% 5d6p (2D) 1Fo
149160.1	149221	-60	155402.9	6243	1	65% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	96% 5d6p (2D5/2)o	93% 5d6p (5/2,3/2)o	63% 5d6p (2D) 1Po
182036.7	182191	-154	189597.2	7561	0	99% 6s6p (2S) 3Po + 1% 5d6p (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,1/2)o	96% 6s6p (2S) 3Po
185757.2	185577	180	193252.7	7496	1	93% 6s6p (2S) 3Po + 6% 6s6p (2S) 1Po	86% 6s6p (2S1/2)o	81% 6s6p (1/2,1/2)o	91% 6s6p (2S) 3Po
198108.2	198122	-14	205232.3	7124	2	99% 6s6p (2S) 3Po + 1% 5d5f (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,3/2)o	96% 6s6p (2S) 3Po
215212.7	215220	-7	222542.3	7330	1	84% 6s6p (2S) 1Po + 6% 6s6p (2S) 3Po	80% 6s6p (2S1/2)o	74% 6s6p (1/2,3/2)o	79% 6s6p (2S) 1Po
227536.0	227405	131	235159.7	7624	4	44% 5d5f (2D) 1Go + 45% 5d5f (2D) 3Ho	78% 5d5f (2D3/2)o	61% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
228702.0	228743	-41	236275.3	7573	2	73% 5d5f (2D) 3Fo + 23% 5d5f (2D) 1Do	94% 5d5f (2D3/2)o	91% 5d5f (3/2,5/2)o	70% 5d5f (2D) 3Fo
229205.0	229002	203	236883.5	7679	4	45% 5d5f (2D) 3Ho + 23% 5d5f (2D) 3Go	74% 5d5f (2D3/2)o	58% 5d5f (3/2,7/2)o	58% 5d5f (2D) 3Ho
229873.0	229919	-46	237436.2	7563	3	66% 5d5f (2D) 3Fo + 26% 5d5f (2D) 3Go	72% 5d5f (2D3/2)o	67% 5d5f (3/2,7/2)o	63% 5d5f (2D) 3Fo
231099.0	230975	124	238889.5	7791	5	85% 5d5f (2D) 3Ho + 8% 5d5f (2D) 3Go	81% 5d5f (2D3/2)o	79% 5d5f (3/2,7/2)o	82% 5d5f (2D) 3Ho
232210.0	232490	-280	239886.2	7676	3	54% 5d5f (2D) 3Go + 23% 5d5f (2D) 1Fo	76% 5d5f (2D3/2)o	71% 5d5f (3/2,5/2)o	51% 5d5f (2D) 3Go
233804.0	233996	-192	241373.9	7570	2	37% 5d5f (2D) 1Do + 32% 5d5f (2D) 3Po	82% 5d5f (2D3/2)o	76% 5d5f (3/2,7/2)o	39% 5d5f (2D) 1Do
235598.0	235764	-166	242977.3	7379	4	55% 5d5f (2D) 3Fo + 37% 5d5f (2D) 1Go	89% 5d5f (2D5/2)o	86% 5d5f (5/2,7/2)o	54% 5d5f (2D) 3Fo
236062.0	236122	-60	243800.4	7738	1	68% 5d5f (2D) 3Do + 17% 5d5f (2D) 3Po	81% 5d5f (2D3/2)o	78% 5d5f (3/2,5/2)o	66% 5d5f (2D) 3Do
	236762				6	100% 5d5f (2D) 3Ho	100% 5d5f (2D5/2)o
238239.0	238288	-49	245646.5	7407	4	72% 5d5f (2D) 3Go + 19% 5d5f (2D) 3Fo	85% 5d5f (2D5/2)o	82% 5d5f (5/2,5/2)o	69% 5d5f (2D) 3Go
238727.0	238842	-115	246155.9	7429	2	35% 5d5f (2D) 1Do + 34% 5d5f (2D) 3Do	54% 5d5f (2D5/2)o	48% 5d5f (5/2,5/2)o	33% 5d5f (2D) 3Do
239614.0	239403	211	247034.3	7420	5	89% 5d5f (2D) 3Go + 10% 5d5f (2D) 3Ho	70% 5d5f (2D5/2)o	67% 5d5f (5/2,7/2)o	84% 5d5f (2D) 3Go
239456.0	239437	19	246968.9	7513	3	40% 5d5f (2D) 3Do + 25% 5d5f (2D) 3Fo	85% 5d5f (2D5/2)o	80% 5d5f (5/2,5/2)o	41% 5d5f (2D) 3Do
242636.0	242507	129	250232.4	7596	3	54% 5d5f (2D) 1Fo + 38% 5d5f (2D) 3Do	93% 5d5f (2D5/2)o	90% 5d5f (5/2,7/2)o	53% 5d5f (2D) 1Fo
242953.0	242885	68	250451.3	7498	2	56% 5d5f (2D) 3Po + 36% 5d5f (2D) 3Do	55% 5d5f (2D5/2)o	50% 5d5f (5/2,7/2)o	53% 5d5f (2D) 3Po
243609.0	243647	-38	251177.9	7569	1	74% 5d5f (2D) 3Po + 22% 5d5f (2D) 3Do	91% 5d5f (2D5/2)o	89% 5d5f (5/2,5/2)o	70% 5d5f (2D) 3Po
	244329		251800.1		0	99% 5d5f (2D) 3Po + 1% 5d7p (2D) 3Po	99% 5d5f (2D5/2)o	95% 5d5f (5/2,5/2)o	95% 5d5f (2D) 3Po
247139.0	246957	182	255546.1	8407	5	91% 5d5f (2D) 1Ho + 4% 5d5f (2D) 3Ho	54% 5d5f (2D5/2)o	53% 5d5f (5/2,5/2)o	89% 5d5f (2D) 1Ho
248815.0	248900	-85	255927.5	7112	1	57% 5d5f (2D) 1Po + 18% 5d7p (2D) 1Po	66% 5d5f (2D5/2)o	48% 5d7p (3/2,1/2)o	34% 5d5f (2D) 1Po
251112.0	251088	24	256606.7	5495	2	68% 5d7p (2D) 3Fo + 25% 5d7p (2D) 1Do	98% 5d7p (2D3/2)o	96% 5d7p (3/2,1/2)o	65% 5d7p (2D) 3Fo
252797.0	252898	-101	259195.1	6398	1	70% 5d7p (2D) 3Do + 16% 5d5f (2D) 1Po	66% 5d7p (2D3/2)o	37% 5d7p (3/2,1/2)o	57% 5d7p (2D) 3Do
256688.0	256666	22	262054.2	5366	2	57% 5d7p (2D) 3Do + 22% 5d7p (2D) 3Fo	96% 5d7p (2D3/2)o	94% 5d7p (3/2,3/2)o	56% 5d7p (2D) 3Do
257895.0	257732	163	263370.8	5476	3	67% 5d7p (2D) 3Fo + 25% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	91% 5d7p (3/2,3/2)o	73% 5d7p (2D) 3Fo
258778.0	258869	-91	264480.2	5702	1	70% 5d7p (2D) 3Po + 14% 5d7p (2D) 3Do	87% 5d7p (2D3/2)o	80% 5d7p (3/2,3/2)o	71% 5d7p (2D) 3Po
259100.0	259117	-17	264615.7	5516	0	99% 5d7p (2D) 3Po + 1% 5d5f (2D) 3Po	99% 5d7p (2D3/2)o	96% 5d7p (3/2,3/2)o	96% 5d7p (2D) 3Po
260035.0	260105	-70	265334.2	5299	2	33% 5d7p (2D) 3Do + 30% 5d7p (2D) 3Po	93% 5d7p (2D5/2)o	89% 5d7p (5/2,1/2)o	32% 5d7p (2D) 3Do
260388.0	260244	144	265845.5	5458	3	38% 5d7p (2D) 3Do + 30% 5d7p (2D) 1Fo	94% 5d7p (2D5/2)o	87% 5d7p (5/2,1/2)o	47% 5d7p (2D) 3Do
265733.0	265806	-73	271390.0	5657	3	54% 5d7p (2D) 3Do + 40% 5d7p (2D) 1Fo	95% 5d7p (2D5/2)o	90% 5d7p (5/2,3/2)o	47% 5d7p (2D) 1Fo
266010.0	265964	46	271220.9	5211	4	99% 5d7p (2D) 3Fo + 1% 6s5f (2S) 3Fo	99% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
266271.0	266296	-25	271474.5	5203	2	65% 5d7p (2D) 3Po + 28% 5d7p (2D) 1Do	94% 5d7p (2D5/2)o	90% 5d7p (5/2,3/2)o	65% 5d7p (2D) 3Po
269124.0	269145	-21	274913.0	5789	1	64% 5d7p (2D) 1Po + 23% 5d7p (2D) 3Po	92% 5d7p (2D5/2)o	87% 5d7p (5/2,3/2)o	63% 5d7p (2D) 1Po

(a) Experimental energies from [12]; (b) Our HFR+CPOL calculations; (c) ΔE_HFR+CPOL = E_HFR+CPOL − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) Only the first two components in LS coupling computed in our HFR+CPOL model are given; (g) Only the first component in jj coupling computed in our HFR+CPOL model is given; (h) The first component in jj coupling computed in our MCDHF model is given; (i) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 5. Comparison of the W V energy levels (cm⁻¹) computed in this work using the HFR+CPOL and MCDHF methods with available experimental data.

EExp (a)	EHFR (CPOL) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}+\mathit{C}\mathit{P}\mathit{O}\mathit{L}}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	J	Composition in LS coupling (f)	jjCowan (g)	jjMCDHF (h)	LSMCDHF (i)
0	24	-24	0	0	2	90% 5d2 (3F) 3F + 10% 5d2 (1D) 1D	90% 5d2 (3F2)	87% 5d2 (0,2)	89% 5d2 (3F) 3F
6244.7	6258	-13	5947.1	-298	3	100% 5d2 (3F) 3F	100% 5d2 (3F3)	97% 5d2 (3/2,5/2)	97% 5d2 (3F) 3F
11519.4	11482	38	11231.8	-288	4	91% 5d2 (3F) 3F + 9% 5d2 (1G) 1G	91% 5d2 (3F4)	55% 5d2 (0,4)	91% 5d2 (3F) 3F
12838.7	12798	40	13840.4	1002	0	93% 5d2 (3P) 3P + 7% 5d2 (1S) 1S	93% 5d2 (3P0)	78% 5d2 (0,0)	92% 5d2 (3P) 3P
13741.5	13731	11	14507.4	766	2	56% 5d2 (1D) 1D + 34% 5d2 (3P) 3P	56% 5d2 (1D2)	83% 5d2 (3/2,5/2)	54% 5d2 (1D) 1D
16330.6	16364	-34	16954.6	624	1	100% 5d2 (3P) 3P	100% 5d2 (3P1)	97% 5d2 (3/2,5/2)	97% 5d2 (3P) 3P
22345.8	22350	-4	23199.3	853	4	91% 5d2 (1G) 1G + 9% 5d2 (3F) 3F	91% 5d2 (1G4)	55% 5d2 (3/2,5/2)	91% 5d2 (1G) 1G
22615.4	22627	-11	23523.0	908	2	65% 5d2 (3P) 3P + 32% 5d2 (1D) 1D	65% 5d2 (3P2)	91% 5d2 (0,2)	62% 5d2 (3P) 3P
43110	43113	-3	47991.7	4882	0	92% 5d2 (1S) 1S + 7% 5d2 (3P) 3P	92% 5d2 (1S0)	77% 5d2 (0,0)	91% 5d2 (1S) 1S
58514.2	58475	39	60174.7	1660	1	100% 5d6s (2D) 3D	100% 5d6s (2D3/2)	97% 5d6s (3/2,1/2)	97% 5d6s (2D) 3D
60295.5	60341	-45	61976.4	1681	2	89% 5d6s (2D) 3D + 11% 5d6s (2D) 1D	88% 5d6s (2D3/2)	84% 5d6s (3/2,1/2)	87% 5d6s (2D) 3D
66657.7	66657	0	68087.7	1430	3	100% 5d6s (2D) 3D	100% 5d6s (2D5/2)	97% 5d6s (5/2,1/2)	97% 5d6s (2D) 3D
72958.7	72953	6	75201.4	2243	2	87% 5d6s (2D) 1D + 11% 5d6s (2D) 3D	87% 5d6s (2D5/2)	83% 5d6s (5/2,1/2)	85% 5d6s (2D) 1D
118662.8	118866	-203	124853.4	6191	2	69% 5d6p (2D) 3Fo + 26% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	96% 5d6p (3/2,1/2)o	64% 5d6p (2D) 3Fo
122325.8	122081	245	128621.2	6295	1	71% 5d6p (2D) 3Do + 19% 5d6p (2D) 1Po	95% 5d6p (2D3/2)o	90% 5d6p (3/2,1/2)o	72% 5d6p (2D) 3Do
128997.1	129162	-165	134964.1	5967	2	48% 5d6p (2D) 3Do + 27% 5d6p (2D) 3Po	95% 5d6p (2D5/2)o	91% 5d6p (5/2,1/2)o	48% 5d6p (2D) 3Do
129479.5	129334	146	135601.6	6122	3	69% 5d6p (2D) 3Fo + 21% 5d6p (2D) 3Do	90% 5d6p (2D5/2)o	85% 5d6p (5/2,1/2)o	68% 5d6p (2D) 3Fo
133430.0	133507	-77	139181.9	5752	2	41% 5d6p (2D) 3Do + 30% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	93% 5d6p (3/2,3/2)o	38% 5d6p (2D) 3Do
	134838		133076.9		0	97% 6s2 (1S) 1S + 2% 6p2 (1S) 1S	97% 6s2 (1S0)	94% 6s2 (0,0)	94% 6s2 (1S) 1S
136887.8	136815	72	142842.3	5954	3	43% 5d6p (2D) 3Do + 31% 5d6p (2D) 3Fo	80% 5d6p (2D3/2)o	73% 5d6p (3/2,3/2)o	48% 5d6p (2D) 3Do
137709.3	137793	-84	143862.0	6153	1	63% 5d6p (2D) 3Po + 23% 5d6p (2D) 3Do	96% 5d6p (2D3/2)o	91% 5d6p (3/2,3/2)o	62% 5d6p (2D) 3Po
139252.1	139196	57	145440.6	6189	0	99% 5d6p (2D) 3Po + 1% 6s6p (2S) 3Po	99% 5d6p (2D3/2)o	96% 5d6p (3/2,3/2)o	96% 5d6p (2D) 3Po
142907.9	142744	164	148658.1	5750	4	100% 5d6p (2D) 3Fo	100% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
144389.9	144445	-55	150227.2	5837	2	68% 5d6p (2D) 3Po + 23% 5d6p (2D) 1Do	92% 5d6p (2D5/2)o	87% 5d6p (5/2,3/2)o	69% 5d6p (2D) 3Po
145767.9	145807	-39	151946.6	6179	3	63% 5d6p (2D) 1Fo + 36% 5d6p (2D) 3Do	84% 5d6p (2D5/2)o	76% 5d6p (5/2,3/2)o	69% 5d6p (2D) 1Fo
149160.1	149221	-60	155402.9	6243	1	65% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	96% 5d6p (2D5/2)o	93% 5d6p (5/2,3/2)o	63% 5d6p (2D) 1Po
182036.7	182191	-154	189597.2	7561	0	99% 6s6p (2S) 3Po + 1% 5d6p (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,1/2)o	96% 6s6p (2S) 3Po
185757.2	185577	180	193252.7	7496	1	93% 6s6p (2S) 3Po + 6% 6s6p (2S) 1Po	86% 6s6p (2S1/2)o	81% 6s6p (1/2,1/2)o	91% 6s6p (2S) 3Po
198108.2	198122	-14	205232.3	7124	2	99% 6s6p (2S) 3Po + 1% 5d5f (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,3/2)o	96% 6s6p (2S) 3Po
215212.7	215220	-7	222542.3	7330	1	84% 6s6p (2S) 1Po + 6% 6s6p (2S) 3Po	80% 6s6p (2S1/2)o	74% 6s6p (1/2,3/2)o	79% 6s6p (2S) 1Po
227536.0	227405	131	235159.7	7624	4	44% 5d5f (2D) 1Go + 45% 5d5f (2D) 3Ho	78% 5d5f (2D3/2)o	61% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
228702.0	228743	-41	236275.3	7573	2	73% 5d5f (2D) 3Fo + 23% 5d5f (2D) 1Do	94% 5d5f (2D3/2)o	91% 5d5f (3/2,5/2)o	70% 5d5f (2D) 3Fo
229205.0	229002	203	236883.5	7679	4	45% 5d5f (2D) 3Ho + 23% 5d5f (2D) 3Go	74% 5d5f (2D3/2)o	58% 5d5f (3/2,7/2)o	58% 5d5f (2D) 3Ho
229873.0	229919	-46	237436.2	7563	3	66% 5d5f (2D) 3Fo + 26% 5d5f (2D) 3Go	72% 5d5f (2D3/2)o	67% 5d5f (3/2,7/2)o	63% 5d5f (2D) 3Fo
231099.0	230975	124	238889.5	7791	5	85% 5d5f (2D) 3Ho + 8% 5d5f (2D) 3Go	81% 5d5f (2D3/2)o	79% 5d5f (3/2,7/2)o	82% 5d5f (2D) 3Ho
232210.0	232490	-280	239886.2	7676	3	54% 5d5f (2D) 3Go + 23% 5d5f (2D) 1Fo	76% 5d5f (2D3/2)o	71% 5d5f (3/2,5/2)o	51% 5d5f (2D) 3Go
233804.0	233996	-192	241373.9	7570	2	37% 5d5f (2D) 1Do + 32% 5d5f (2D) 3Po	82% 5d5f (2D3/2)o	76% 5d5f (3/2,7/2)o	39% 5d5f (2D) 1Do
235598.0	235764	-166	242977.3	7379	4	55% 5d5f (2D) 3Fo + 37% 5d5f (2D) 1Go	89% 5d5f (2D5/2)o	86% 5d5f (5/2,7/2)o	54% 5d5f (2D) 3Fo
236062.0	236122	-60	243800.4	7738	1	68% 5d5f (2D) 3Do + 17% 5d5f (2D) 3Po	81% 5d5f (2D3/2)o	78% 5d5f (3/2,5/2)o	66% 5d5f (2D) 3Do
	236762				6	100% 5d5f (2D) 3Ho	100% 5d5f (2D5/2)o
238239.0	238288	-49	245646.5	7407	4	72% 5d5f (2D) 3Go + 19% 5d5f (2D) 3Fo	85% 5d5f (2D5/2)o	82% 5d5f (5/2,5/2)o	69% 5d5f (2D) 3Go
238727.0	238842	-115	246155.9	7429	2	35% 5d5f (2D) 1Do + 34% 5d5f (2D) 3Do	54% 5d5f (2D5/2)o	48% 5d5f (5/2,5/2)o	33% 5d5f (2D) 3Do
239614.0	239403	211	247034.3	7420	5	89% 5d5f (2D) 3Go + 10% 5d5f (2D) 3Ho	70% 5d5f (2D5/2)o	67% 5d5f (5/2,7/2)o	84% 5d5f (2D) 3Go
239456.0	239437	19	246968.9	7513	3	40% 5d5f (2D) 3Do + 25% 5d5f (2D) 3Fo	85% 5d5f (2D5/2)o	80% 5d5f (5/2,5/2)o	41% 5d5f (2D) 3Do
242636.0	242507	129	250232.4	7596	3	54% 5d5f (2D) 1Fo + 38% 5d5f (2D) 3Do	93% 5d5f (2D5/2)o	90% 5d5f (5/2,7/2)o	53% 5d5f (2D) 1Fo
242953.0	242885	68	250451.3	7498	2	56% 5d5f (2D) 3Po + 36% 5d5f (2D) 3Do	55% 5d5f (2D5/2)o	50% 5d5f (5/2,7/2)o	53% 5d5f (2D) 3Po
243609.0	243647	-38	251177.9	7569	1	74% 5d5f (2D) 3Po + 22% 5d5f (2D) 3Do	91% 5d5f (2D5/2)o	89% 5d5f (5/2,5/2)o	70% 5d5f (2D) 3Po
	244329		251800.1		0	99% 5d5f (2D) 3Po + 1% 5d7p (2D) 3Po	99% 5d5f (2D5/2)o	95% 5d5f (5/2,5/2)o	95% 5d5f (2D) 3Po
247139.0	246957	182	255546.1	8407	5	91% 5d5f (2D) 1Ho + 4% 5d5f (2D) 3Ho	54% 5d5f (2D5/2)o	53% 5d5f (5/2,5/2)o	89% 5d5f (2D) 1Ho
248815.0	248900	-85	255927.5	7112	1	57% 5d5f (2D) 1Po + 18% 5d7p (2D) 1Po	66% 5d5f (2D5/2)o	48% 5d7p (3/2,1/2)o	34% 5d5f (2D) 1Po
251112.0	251088	24	256606.7	5495	2	68% 5d7p (2D) 3Fo + 25% 5d7p (2D) 1Do	98% 5d7p (2D3/2)o	96% 5d7p (3/2,1/2)o	65% 5d7p (2D) 3Fo
252797.0	252898	-101	259195.1	6398	1	70% 5d7p (2D) 3Do + 16% 5d5f (2D) 1Po	66% 5d7p (2D3/2)o	37% 5d7p (3/2,1/2)o	57% 5d7p (2D) 3Do
256688.0	256666	22	262054.2	5366	2	57% 5d7p (2D) 3Do + 22% 5d7p (2D) 3Fo	96% 5d7p (2D3/2)o	94% 5d7p (3/2,3/2)o	56% 5d7p (2D) 3Do
257895.0	257732	163	263370.8	5476	3	67% 5d7p (2D) 3Fo + 25% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	91% 5d7p (3/2,3/2)o	73% 5d7p (2D) 3Fo
258778.0	258869	-91	264480.2	5702	1	70% 5d7p (2D) 3Po + 14% 5d7p (2D) 3Do	87% 5d7p (2D3/2)o	80% 5d7p (3/2,3/2)o	71% 5d7p (2D) 3Po
259100.0	259117	-17	264615.7	5516	0	99% 5d7p (2D) 3Po + 1% 5d5f (2D) 3Po	99% 5d7p (2D3/2)o	96% 5d7p (3/2,3/2)o	96% 5d7p (2D) 3Po
260035.0	260105	-70	265334.2	5299	2	33% 5d7p (2D) 3Do + 30% 5d7p (2D) 3Po	93% 5d7p (2D5/2)o	89% 5d7p (5/2,1/2)o	32% 5d7p (2D) 3Do
260388.0	260244	144	265845.5	5458	3	38% 5d7p (2D) 3Do + 30% 5d7p (2D) 1Fo	94% 5d7p (2D5/2)o	87% 5d7p (5/2,1/2)o	47% 5d7p (2D) 3Do
265733.0	265806	-73	271390.0	5657	3	54% 5d7p (2D) 3Do + 40% 5d7p (2D) 1Fo	95% 5d7p (2D5/2)o	90% 5d7p (5/2,3/2)o	47% 5d7p (2D) 1Fo
266010.0	265964	46	271220.9	5211	4	99% 5d7p (2D) 3Fo + 1% 6s5f (2S) 3Fo	99% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
266271.0	266296	-25	271474.5	5203	2	65% 5d7p (2D) 3Po + 28% 5d7p (2D) 1Do	94% 5d7p (2D5/2)o	90% 5d7p (5/2,3/2)o	65% 5d7p (2D) 3Po
269124.0	269145	-21	274913.0	5789	1	64% 5d7p (2D) 1Po + 23% 5d7p (2D) 3Po	92% 5d7p (2D5/2)o	87% 5d7p (5/2,3/2)o	63% 5d7p (2D) 1Po

(a) Experimental energies from [12]; (b) Our HFR+CPOL calculations; (c) ΔE_HFR+CPOL = E_HFR+CPOL − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) Only the first two components in LS coupling computed in our HFR+CPOL model are given; (g) Only the first component in jj coupling computed in our HFR+CPOL model is given; (h) The first component in jj coupling computed in our MCDHF model is given; (i) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 6. Comparison of the Re VI energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

Eexp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	42	-42	0	0	0	0	2	88% 5d2 (3F) 3F + 11% 5d2 (1D) 1D	88% 5d2 (3F2)	89% 5d2 (0,2)	88% 5d2 (3F) 3F
8166.6	8173	-7	7811.2	-355.4	8491	324	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
14379.3	14318	62	15507.5	1128.2	14495	116	0	91% 5d2 (3P) 3P + 8% 5d2 (1S) 1S	91% 5d2 (3P0)	80% 5d2 (0,0)	92% 5d2 (3P) 3P
14679.4	14630	50	14408.3	-271.1	15095	416	4	87% 5d2 (3F) 3F + 12% 5d2 (1G) 1G	87% 5d2 (3F4)	50% 5d2 (0,4)	88% 5d2 (3F) 3F
16576.7	16560	17	17395.0	818.3	16866	289	2	51% 5d2 (1D) 1D + 39% 5d2 (3P) 3P	51% 5d2 (1D2)	87% 5d2 (3/2,5/2)	50% 5d2 (1D) 1D
19141.6	19198	-56	19802.2	660.6	19556	414	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	97% 5d2 (3/2,5/2)	97% 5d2 (3P) 3P
26657.1	26664	-7	27779.9	1122.8	26807	150	4	87% 5d2 (1G) 1G + 12% 5d2 (3F) 3F	87% 5d2 (1G4)	50% 5d2 (3/2,5/2)	88% 5d2 (1G) 1G
27722.9	27734	-11	28388.4	665.5	28371	648	2	60% 5d2 (3P) 3P + 37% 5d2 (1D) 1D	60% 5d2 (3P2)	94% 5d2 (0,2)	57% 5d2 (3P) 3P
50491.7	50497	-5	55899.8	5408.1	51056	564	0	91% 5d2 (1S) 1S + 8% 5d2 (3P) 3P	91% 5d2 (1S0)	79% 5d2 (0,0)	91% 5d2 (1S) 1S
92312.3	92262	51	94061.4	1749.1	92656	344	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	97% 5d6s (3/2,1/2)	97% 5d6s (2D) 3D
94262.0	94318	-56	96068.2	1806.2	94554	292	2	84% 5d6s (2D) 3D + 15% 5d6s (2D) 1D	91% 5d6s (2D3/2)	88% 5d6s (3/2,1/2)	84% 5d6s (2D) 3D
102712.2	102716	-4	104217.7	1505.5	103444	732	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	97% 5d6s (5/2,1/2)	97% 5d6s (2D) 3D
108709.2	108700	10	110936.2	2227.0	109374	665	2	84% 5d6s (2D) 1D + 15% 5d6s (2D) 3D	90% 5d6s (2D5/2)	87% 5d6s (5/2,1/2)	83% 5d6s (2D) 1D
162134.4	162373	-238	167589.6	5455.2	163618	1484	2	68% 5d6p (2D) 3Fo + 26% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	96% 5d6p (3/2,1/2)o	65% 5d6p (2D) 3Fo
166076.9	165812	264	171668.1	5591.2	166538	461	1	69% 5d6p (2D) 3Do + 19% 5d6p (2D) 1Po	95% 5d6p (2D3/2)o	91% 5d6p (3/2,1/2)o	70% 5d6p (2D) 3Do
174761.5	174841	-79	179999.1	5237.6	176168	1407	2	49% 5d6p (2D) 3Do + 28% 5d6p (2D) 3Po	95% 5d6p (2D5/2)o	92% 5d6p (5/2,1/2)o	49% 5d6p (2D) 3Do
175501.8	175432	70	180904.1	5402.3	177212	1710	3	63% 5d6p (2D) 3Fo + 24% 5d6p (2D) 3Do	93% 5d6p (2D5/2)o	89% 5d6p (5/2,1/2)o	63% 5d6p (2D) 3Fo
181154.9	181139	15	186123.9	4969.0	182853	1698	2	39% 5d6p (2D) 3Do + 30% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	93% 5d6p (3/2,3/2)o	37% 5d6p (2D) 3Do
185021.6	184981	41	190242.0	5220.4	186672	1650	3	37% 5d6p (2D) 3Do + 36% 5d6p (2D) 3Fo	84% 5d6p (2D3/2)o	79% 5d6p (3/2,3/2)o	40% 5d6p (2D) 3Do
185962.9	186041	-78	191357.6	5394.7	187037	1074	1	62% 5d6p (2D) 3Po + 24% 5d6p (2D) 3Do	96% 5d6p (2D3/2)o	93% 5d6p (3/2,3/2)o	62% 5d6p (2D) 3Po
187780.4	187765	15	193221.3	5440.9	189199	1419	0	99% 5d6p (2D) 3Po + 1% 5p55d26s (3P) 3Po	99% 5d6p (2D3/2)o	97% 5d6p (3/2,3/2)o	97% 5d6p (2D) 3Po
193260.0	193155	105	198214.6	4954.6	195446	2186	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
194539.1	194501	38	199582.5	5043.4	196486	1947	2	66% 5d6p (2D) 3Po + 25% 5d6p (2D) 1Do	93% 5d6p (2D5/2)o	90% 5d6p (5/2,3/2)o	66% 5d6p (2D) 3Po
195691.3	195866	-174	201064.2	5372.9	197742	2051	3	60% 5d6p (2D) 1Fo + 38% 5d6p (2D) 3Do	86% 5d6p (2D5/2)o	81% 5d6p (5/2,3/2)o	63% 5d6p (2D) 1Fo
200436.6	200416	20	205970.4	5533.8	200506	69	1	66% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	94% 5d6p (5/2,3/2)o	65% 5d6p (2D) 1Po
	200991		201163.0		198652		0	97% 6s2 (1S) 1S + 1% 6p2 (1S) 1S	97% 6s2 (1S0)	95% 6s2 (0,0)	95% 6s2 (1S) 1S
	261173		265855.3		261637		0	99% 6s6p (2S) 3Po + 1% 5d5f (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,1/2)o	96% 6s6p (2S) 3Po
	264732		270004.4		265550		1	90% 6s6p (2S) 3Po + 8% 6s6p (2S) 1Po	87% 6s6p (2S1/2)o	84% 6s6p (1/2,1/2)o	88% 6s6p (2S) 3Po
279156.0	279274	-118	285664.6	6508.6	281644	2488	2	93% 6s6p (2S) 3Po + 5% 5d5f (2D) 3Po	93% 6s6p (2S1/2)o	92% 6s6p (1/2,3/2)o	92% 6s6p (2S) 3Po
280575.0	280571	4	288303.6	7728.6	282611	2036	4	51% 5d5f (2D) 1Go + 33% 5d5f (2D) 3Ho	67% 5d5f (2D3/2)o	63% 5d5f (3/2,5/2)o	52% 5d5f (2D) 1Go
281906.0	281774	132	289611.1	7705.1	282986	1080	2	70% 5d5f (2D) 3Fo + 22% 5d5f (2D) 1Do	91% 5d5f (2D3/2)o	91% 5d5f (3/2,5/2)o	68% 5d5f (2D) 3Fo
282853.0	282943	-90	290630.9	7777.9	283375	522	4	55% 5d5f (2D) 3Ho + 21% 5d5f (2D) 3Go	63% 5d5f (2D3/2)o	60% 5d5f (3/2,7/2)o	56% 5d5f (2D) 3Ho
283559.0	283419	140	291256.6	7697.6	284803	1244	3	54% 5d5f (2D) 3Fo + 37% 5d5f (2D) 3Go	55% 5d5f (2D3/2)o	60% 5d5f (3/2,7/2)o	59% 5d5f (2D) 3Fo
285346.0	285793	-447	293269.3	7923.3	286237	891	5	85% 5d5f (2D) 3Ho + 9% 5d5f (2D) 3Go	79% 5d5f (2D3/2)o	77% 5d5f (3/2,7/2)o	84% 5d5f (2D) 3Ho
286426.0	286292	134	294318.7	7892.7	287360	934	3	40% 5d5f (2D) 3Go + 22% 5d5f (2D) 3Fo	55% 5d5f (2D3/2)o	60% 5d5f (3/2,5/2)o	47% 5d5f (2D) 3Go
288853.0	289092	-239	296564.5	7711.5	289100	247	2	40% 5d5f (2D) 1Do + 24% 5d5f (2D) 3Po	72% 5d5f (2D3/2)o	66% 5d5f (3/2,7/2)o	44% 5d5f (2D) 1Do
290208.0	289767	441	297788.2	7580.2	289565	-643	1	40% 5d5f (2D) 3Do + 25% 5d5f (2D) 1Po	71% 5d5f (2D3/2)o	64% 5d5f (3/2,5/2)o	34% 5d5f (2D) 3Do
290824.0	291009	-185	298265.3	7441.3	292767	1943	4	50% 5d5f (2D) 3Fo + 36% 5d5f (2D) 1Go	83% 5d5f (2D5/2)o	84% 5d5f (5/2,7/2)o	52% 5d5f (2D) 3Fo
	293123				296143		6	99% 5d5f (2D) 3Ho + 1% 5p55d3 (2G) 3Ho	99% 5d5f (2D5/2)o
293741.0	293616	125	301310.8	7569.8	294002	261	4	65% 5d5f (2D) 3Go + 23% 5d5f (2D) 3Fo	77% 5d5f (2D5/2)o	78% 5d5f (5/2,5/2)o	67% 5d5f (2D) 3Go
294688.0	294780	-92	302382.0	7694.0	295265	577	2	39% 5d5f (2D) 3Do + 28% 5d5f (2D) 1Do	55% 5d5f (2D5/2)o	49% 5d5f (5/2,5/2)o	40% 5d5f (2D) 3Do
	295260		302586.6		295457		1	44% 6s6p (2S) 1Po + 33% 5d5f (2D) 3Do	41% 6s6p (2S1/2)o	35% 5d5f (5/2,7/2)o	38% 6s6p (2S) 1Po
295836.0	295690	146	303617.8	7781.8	295676	-160	3	47% 5d5f (2D) 3Do + 21% 5d5f (2D) 3Fo	77% 5d5f (2D5/2)o	73% 5d5f (5/2,5/2)o	50% 5d5f (2D) 3Do
295928.0	295856	72	303475.5	7547.5	295717	-211	5	83% 5d5f (2D) 3Go + 11% 5d5f (2D) 3Ho	66% 5d5f (2D5/2)o	66% 5d5f (5/2,7/2)o	83% 5d5f (2D) 3Go
301178.0	300428	750	308309.5	7131.5	301078	-100	2	57% 5d5f (2D) 3Po + 32% 5d5f (2D) 3Do	55% 5d5f (2D5/2)o	50% 5d5f (5/2,7/2)o	55% 5d5f (2D) 3Po
300794.0	300844	-50	308728.2	7934.2	300071	-723	3	59% 5d5f (2D) 1Fo + 31% 5d5f (2D) 3Do	90% 5d5f (2D5/2)o	87% 5d5f (5/2,7/2)o	61% 5d5f (2D) 1Fo
	300998		309100.9		301570		1	75% 5d5f (2D) 3Po + 20% 5d5f (2D) 3Do	88% 5d5f (2D5/2)o	87% 5d5f (5/2,5/2)o	73% 5d5f (2D) 3Po
	301670		309823.6		302331		0	96% 5d5f (2D) 3Po + 1% 5p55d3 (2D) 3Po	96% 5d5f (2D5/2)o	94% 5d5f (5/2,5/2)o	94% 5d5f (2D) 3Po
307440.0	308142	-702	316369.2	8929.2	303559	-3881	5	89% 5d5f (2D) 1Ho + 4% 5d5f (2D) 3Ho	51% 5d5f (2D5/2)o	51% 5d5f (5/2,5/2)o	89% 5d5f (2D) 1Ho
	314924		323131.1		317422		1	61% 5d5f (2D) 1Po + 24% 6s6p (2S) 1Po	56% 5d5f (2D5/2)o	52% 5d5f (5/2,7/2)o	58% 5d5f (2D) 1Po
	335215		335535.0				2	67% 5d7p (2D) 3Fo + 26% 5d7p (2D) 1Do	99% 5d7p (2D3/2)o	97% 5d7p (3/2,1/2)o	65% 5d7p (2D) 3Fo
	336239		337016.9				1	74% 5d7p (2D) 3Do + 17% 5d7p (2D) 1Po	91% 5d7p (2D3/2)o	86% 5d7p (3/2,1/2)o	73% 5d7p (2D) 3Do
	342126		342870.5				2	53% 5d7p (2D) 3Do + 21% 5d7p (2D) 3Fo	86% 5d7p (2D3/2)o	94% 5d7p (3/2,3/2)o	59% 5d7p (2D) 3Do
	343618		344504.2				3	64% 5d7p (2D) 3Fo + 27% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	92% 5d7p (3/2,3/2)o	72% 5d7p (2D) 3Fo
	344162		345293.6				1	67% 5d7p (2D) 3Po + 19% 5d7p (2D) 3Do	93% 5d7p (2D3/2)o	90% 5d7p (3/2,3/2)o	67% 5d7p (2D) 3Po
	344767		345861.4				0	99% 5d7p (2D) 3Po + 1% 5p55d3 (2D) 3Po	99% 5d7p (2D3/2)o	97% 5d7p (3/2,3/2)o	97% 5d7p (2D) 3Po
	346674		346544.1				2	32% 5d7p (2D) 3Po + 31% 5d7p (2D) 3Do	94% 5d7p (2D5/2)o	91% 5d7p (5/2,1/2)o	31% 5d7p (2D) 3Po
	346976		347089.9				3	33% 5d7p (2D) 3Do + 25% 5d7p (2D) 1Fo	80% 5d7p (2D5/2)o	90% 5d7p (5/2,1/2)o	43% 5d7p (2D) 3Do
	353998		354525.6				3	51% 5d7p (2D) 3Do + 42% 5d7p (2D) 1Fo	94% 5d7p (2D5/2)o	92% 5d7p (5/2,3/2)o	49% 5d7p (2D) 3Do
	354325		354600.2				4	98% 5d7p (2D) 3Fo + 1% 5p55d3 (4F) 3Go	98% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
	354360		354723.0				2	56% 5d7p (2D) 3Po + 26% 5d7p (2D) 1Do	83% 5d7p (2D5/2)o	92% 5d7p (5/2,3/2)o	63% 5d7p (2D) 3Po
	357399		358273.9				1	65% 5d7p (2D) 1Po + 25% 5d7p (2D) 3Po	95% 5d7p (2D5/2)o	93% 5d7p (5/2,3/2)o	65% 5d7p (2D) 1Po

(a) Experimental energies from [15]; (b) Our HFR(CV) calculations; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 6. Comparison of the Re VI energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

Eexp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	42	-42	0	0	0	0	2	88% 5d2 (3F) 3F + 11% 5d2 (1D) 1D	88% 5d2 (3F2)	89% 5d2 (0,2)	88% 5d2 (3F) 3F
8166.6	8173	-7	7811.2	-355.4	8491	324	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
14379.3	14318	62	15507.5	1128.2	14495	116	0	91% 5d2 (3P) 3P + 8% 5d2 (1S) 1S	91% 5d2 (3P0)	80% 5d2 (0,0)	92% 5d2 (3P) 3P
14679.4	14630	50	14408.3	-271.1	15095	416	4	87% 5d2 (3F) 3F + 12% 5d2 (1G) 1G	87% 5d2 (3F4)	50% 5d2 (0,4)	88% 5d2 (3F) 3F
16576.7	16560	17	17395.0	818.3	16866	289	2	51% 5d2 (1D) 1D + 39% 5d2 (3P) 3P	51% 5d2 (1D2)	87% 5d2 (3/2,5/2)	50% 5d2 (1D) 1D
19141.6	19198	-56	19802.2	660.6	19556	414	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	97% 5d2 (3/2,5/2)	97% 5d2 (3P) 3P
26657.1	26664	-7	27779.9	1122.8	26807	150	4	87% 5d2 (1G) 1G + 12% 5d2 (3F) 3F	87% 5d2 (1G4)	50% 5d2 (3/2,5/2)	88% 5d2 (1G) 1G
27722.9	27734	-11	28388.4	665.5	28371	648	2	60% 5d2 (3P) 3P + 37% 5d2 (1D) 1D	60% 5d2 (3P2)	94% 5d2 (0,2)	57% 5d2 (3P) 3P
50491.7	50497	-5	55899.8	5408.1	51056	564	0	91% 5d2 (1S) 1S + 8% 5d2 (3P) 3P	91% 5d2 (1S0)	79% 5d2 (0,0)	91% 5d2 (1S) 1S
92312.3	92262	51	94061.4	1749.1	92656	344	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	97% 5d6s (3/2,1/2)	97% 5d6s (2D) 3D
94262.0	94318	-56	96068.2	1806.2	94554	292	2	84% 5d6s (2D) 3D + 15% 5d6s (2D) 1D	91% 5d6s (2D3/2)	88% 5d6s (3/2,1/2)	84% 5d6s (2D) 3D
102712.2	102716	-4	104217.7	1505.5	103444	732	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	97% 5d6s (5/2,1/2)	97% 5d6s (2D) 3D
108709.2	108700	10	110936.2	2227.0	109374	665	2	84% 5d6s (2D) 1D + 15% 5d6s (2D) 3D	90% 5d6s (2D5/2)	87% 5d6s (5/2,1/2)	83% 5d6s (2D) 1D
162134.4	162373	-238	167589.6	5455.2	163618	1484	2	68% 5d6p (2D) 3Fo + 26% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	96% 5d6p (3/2,1/2)o	65% 5d6p (2D) 3Fo
166076.9	165812	264	171668.1	5591.2	166538	461	1	69% 5d6p (2D) 3Do + 19% 5d6p (2D) 1Po	95% 5d6p (2D3/2)o	91% 5d6p (3/2,1/2)o	70% 5d6p (2D) 3Do
174761.5	174841	-79	179999.1	5237.6	176168	1407	2	49% 5d6p (2D) 3Do + 28% 5d6p (2D) 3Po	95% 5d6p (2D5/2)o	92% 5d6p (5/2,1/2)o	49% 5d6p (2D) 3Do
175501.8	175432	70	180904.1	5402.3	177212	1710	3	63% 5d6p (2D) 3Fo + 24% 5d6p (2D) 3Do	93% 5d6p (2D5/2)o	89% 5d6p (5/2,1/2)o	63% 5d6p (2D) 3Fo
181154.9	181139	15	186123.9	4969.0	182853	1698	2	39% 5d6p (2D) 3Do + 30% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	93% 5d6p (3/2,3/2)o	37% 5d6p (2D) 3Do
185021.6	184981	41	190242.0	5220.4	186672	1650	3	37% 5d6p (2D) 3Do + 36% 5d6p (2D) 3Fo	84% 5d6p (2D3/2)o	79% 5d6p (3/2,3/2)o	40% 5d6p (2D) 3Do
185962.9	186041	-78	191357.6	5394.7	187037	1074	1	62% 5d6p (2D) 3Po + 24% 5d6p (2D) 3Do	96% 5d6p (2D3/2)o	93% 5d6p (3/2,3/2)o	62% 5d6p (2D) 3Po
187780.4	187765	15	193221.3	5440.9	189199	1419	0	99% 5d6p (2D) 3Po + 1% 5p55d26s (3P) 3Po	99% 5d6p (2D3/2)o	97% 5d6p (3/2,3/2)o	97% 5d6p (2D) 3Po
193260.0	193155	105	198214.6	4954.6	195446	2186	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
194539.1	194501	38	199582.5	5043.4	196486	1947	2	66% 5d6p (2D) 3Po + 25% 5d6p (2D) 1Do	93% 5d6p (2D5/2)o	90% 5d6p (5/2,3/2)o	66% 5d6p (2D) 3Po
195691.3	195866	-174	201064.2	5372.9	197742	2051	3	60% 5d6p (2D) 1Fo + 38% 5d6p (2D) 3Do	86% 5d6p (2D5/2)o	81% 5d6p (5/2,3/2)o	63% 5d6p (2D) 1Fo
200436.6	200416	20	205970.4	5533.8	200506	69	1	66% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	94% 5d6p (5/2,3/2)o	65% 5d6p (2D) 1Po
	200991		201163.0		198652		0	97% 6s2 (1S) 1S + 1% 6p2 (1S) 1S	97% 6s2 (1S0)	95% 6s2 (0,0)	95% 6s2 (1S) 1S
	261173		265855.3		261637		0	99% 6s6p (2S) 3Po + 1% 5d5f (2D) 3Po	99% 6s6p (2S1/2)o	96% 6s6p (1/2,1/2)o	96% 6s6p (2S) 3Po
	264732		270004.4		265550		1	90% 6s6p (2S) 3Po + 8% 6s6p (2S) 1Po	87% 6s6p (2S1/2)o	84% 6s6p (1/2,1/2)o	88% 6s6p (2S) 3Po
279156.0	279274	-118	285664.6	6508.6	281644	2488	2	93% 6s6p (2S) 3Po + 5% 5d5f (2D) 3Po	93% 6s6p (2S1/2)o	92% 6s6p (1/2,3/2)o	92% 6s6p (2S) 3Po
280575.0	280571	4	288303.6	7728.6	282611	2036	4	51% 5d5f (2D) 1Go + 33% 5d5f (2D) 3Ho	67% 5d5f (2D3/2)o	63% 5d5f (3/2,5/2)o	52% 5d5f (2D) 1Go
281906.0	281774	132	289611.1	7705.1	282986	1080	2	70% 5d5f (2D) 3Fo + 22% 5d5f (2D) 1Do	91% 5d5f (2D3/2)o	91% 5d5f (3/2,5/2)o	68% 5d5f (2D) 3Fo
282853.0	282943	-90	290630.9	7777.9	283375	522	4	55% 5d5f (2D) 3Ho + 21% 5d5f (2D) 3Go	63% 5d5f (2D3/2)o	60% 5d5f (3/2,7/2)o	56% 5d5f (2D) 3Ho
283559.0	283419	140	291256.6	7697.6	284803	1244	3	54% 5d5f (2D) 3Fo + 37% 5d5f (2D) 3Go	55% 5d5f (2D3/2)o	60% 5d5f (3/2,7/2)o	59% 5d5f (2D) 3Fo
285346.0	285793	-447	293269.3	7923.3	286237	891	5	85% 5d5f (2D) 3Ho + 9% 5d5f (2D) 3Go	79% 5d5f (2D3/2)o	77% 5d5f (3/2,7/2)o	84% 5d5f (2D) 3Ho
286426.0	286292	134	294318.7	7892.7	287360	934	3	40% 5d5f (2D) 3Go + 22% 5d5f (2D) 3Fo	55% 5d5f (2D3/2)o	60% 5d5f (3/2,5/2)o	47% 5d5f (2D) 3Go
288853.0	289092	-239	296564.5	7711.5	289100	247	2	40% 5d5f (2D) 1Do + 24% 5d5f (2D) 3Po	72% 5d5f (2D3/2)o	66% 5d5f (3/2,7/2)o	44% 5d5f (2D) 1Do
290208.0	289767	441	297788.2	7580.2	289565	-643	1	40% 5d5f (2D) 3Do + 25% 5d5f (2D) 1Po	71% 5d5f (2D3/2)o	64% 5d5f (3/2,5/2)o	34% 5d5f (2D) 3Do
290824.0	291009	-185	298265.3	7441.3	292767	1943	4	50% 5d5f (2D) 3Fo + 36% 5d5f (2D) 1Go	83% 5d5f (2D5/2)o	84% 5d5f (5/2,7/2)o	52% 5d5f (2D) 3Fo
	293123				296143		6	99% 5d5f (2D) 3Ho + 1% 5p55d3 (2G) 3Ho	99% 5d5f (2D5/2)o
293741.0	293616	125	301310.8	7569.8	294002	261	4	65% 5d5f (2D) 3Go + 23% 5d5f (2D) 3Fo	77% 5d5f (2D5/2)o	78% 5d5f (5/2,5/2)o	67% 5d5f (2D) 3Go
294688.0	294780	-92	302382.0	7694.0	295265	577	2	39% 5d5f (2D) 3Do + 28% 5d5f (2D) 1Do	55% 5d5f (2D5/2)o	49% 5d5f (5/2,5/2)o	40% 5d5f (2D) 3Do
	295260		302586.6		295457		1	44% 6s6p (2S) 1Po + 33% 5d5f (2D) 3Do	41% 6s6p (2S1/2)o	35% 5d5f (5/2,7/2)o	38% 6s6p (2S) 1Po
295836.0	295690	146	303617.8	7781.8	295676	-160	3	47% 5d5f (2D) 3Do + 21% 5d5f (2D) 3Fo	77% 5d5f (2D5/2)o	73% 5d5f (5/2,5/2)o	50% 5d5f (2D) 3Do
295928.0	295856	72	303475.5	7547.5	295717	-211	5	83% 5d5f (2D) 3Go + 11% 5d5f (2D) 3Ho	66% 5d5f (2D5/2)o	66% 5d5f (5/2,7/2)o	83% 5d5f (2D) 3Go
301178.0	300428	750	308309.5	7131.5	301078	-100	2	57% 5d5f (2D) 3Po + 32% 5d5f (2D) 3Do	55% 5d5f (2D5/2)o	50% 5d5f (5/2,7/2)o	55% 5d5f (2D) 3Po
300794.0	300844	-50	308728.2	7934.2	300071	-723	3	59% 5d5f (2D) 1Fo + 31% 5d5f (2D) 3Do	90% 5d5f (2D5/2)o	87% 5d5f (5/2,7/2)o	61% 5d5f (2D) 1Fo
	300998		309100.9		301570		1	75% 5d5f (2D) 3Po + 20% 5d5f (2D) 3Do	88% 5d5f (2D5/2)o	87% 5d5f (5/2,5/2)o	73% 5d5f (2D) 3Po
	301670		309823.6		302331		0	96% 5d5f (2D) 3Po + 1% 5p55d3 (2D) 3Po	96% 5d5f (2D5/2)o	94% 5d5f (5/2,5/2)o	94% 5d5f (2D) 3Po
307440.0	308142	-702	316369.2	8929.2	303559	-3881	5	89% 5d5f (2D) 1Ho + 4% 5d5f (2D) 3Ho	51% 5d5f (2D5/2)o	51% 5d5f (5/2,5/2)o	89% 5d5f (2D) 1Ho
	314924		323131.1		317422		1	61% 5d5f (2D) 1Po + 24% 6s6p (2S) 1Po	56% 5d5f (2D5/2)o	52% 5d5f (5/2,7/2)o	58% 5d5f (2D) 1Po
	335215		335535.0				2	67% 5d7p (2D) 3Fo + 26% 5d7p (2D) 1Do	99% 5d7p (2D3/2)o	97% 5d7p (3/2,1/2)o	65% 5d7p (2D) 3Fo
	336239		337016.9				1	74% 5d7p (2D) 3Do + 17% 5d7p (2D) 1Po	91% 5d7p (2D3/2)o	86% 5d7p (3/2,1/2)o	73% 5d7p (2D) 3Do
	342126		342870.5				2	53% 5d7p (2D) 3Do + 21% 5d7p (2D) 3Fo	86% 5d7p (2D3/2)o	94% 5d7p (3/2,3/2)o	59% 5d7p (2D) 3Do
	343618		344504.2				3	64% 5d7p (2D) 3Fo + 27% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	92% 5d7p (3/2,3/2)o	72% 5d7p (2D) 3Fo
	344162		345293.6				1	67% 5d7p (2D) 3Po + 19% 5d7p (2D) 3Do	93% 5d7p (2D3/2)o	90% 5d7p (3/2,3/2)o	67% 5d7p (2D) 3Po
	344767		345861.4				0	99% 5d7p (2D) 3Po + 1% 5p55d3 (2D) 3Po	99% 5d7p (2D3/2)o	97% 5d7p (3/2,3/2)o	97% 5d7p (2D) 3Po
	346674		346544.1				2	32% 5d7p (2D) 3Po + 31% 5d7p (2D) 3Do	94% 5d7p (2D5/2)o	91% 5d7p (5/2,1/2)o	31% 5d7p (2D) 3Po
	346976		347089.9				3	33% 5d7p (2D) 3Do + 25% 5d7p (2D) 1Fo	80% 5d7p (2D5/2)o	90% 5d7p (5/2,1/2)o	43% 5d7p (2D) 3Do
	353998		354525.6				3	51% 5d7p (2D) 3Do + 42% 5d7p (2D) 1Fo	94% 5d7p (2D5/2)o	92% 5d7p (5/2,3/2)o	49% 5d7p (2D) 3Do
	354325		354600.2				4	98% 5d7p (2D) 3Fo + 1% 5p55d3 (4F) 3Go	98% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
	354360		354723.0				2	56% 5d7p (2D) 3Po + 26% 5d7p (2D) 1Do	83% 5d7p (2D5/2)o	92% 5d7p (5/2,3/2)o	63% 5d7p (2D) 3Po
	357399		358273.9				1	65% 5d7p (2D) 1Po + 25% 5d7p (2D) 3Po	95% 5d7p (2D5/2)o	93% 5d7p (5/2,3/2)o	65% 5d7p (2D) 1Po

(a) Experimental energies from [15]; (b) Our HFR(CV) calculations; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 7. Comparison of the Os VII energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

EExp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	48	-48	0	0	0	0	2	87% 5d2 (3F) 3F + 12% 5d2 (1D) 1D	87% 5d2 (3F2)	90% 5d2 (0,2)	87% 5d2 (3F) 3F
10308	10309	-1	9891	-417	10604	296	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
15837	15768	69	17101	1264	16117	280	0	90% 5d2 (3P) 3P + 9% 5d2 (1S) 1S	90% 5d2 (3P0)	82% 5d2 (0,0)	91% 5d2 (3P) 3P
18049	17997	52	17802	-247	18409	360	4	83% 5d2 (3F) 3F + 17% 5d2 (1G) 1G	83% 5d2 (3F4)	53% 5d2 (3/2,5/2)	85% 5d2 (3F) 3F
19444	19429	14	20274	830	19852	408	2	48% 5d2 (1D) 1D + 41% 5d2 (3P) 3P	48% 5d2 (1D2)	89% 5d2 (3/2,5/2)	46% 5d2 (1D) 1D
22098	22164	-66	22777	679	22624	526	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	98% 5d2 (3/2,5/2)	98% 5d2 (3P) 3P
31274	31284	-10	32298	1024	31496	222	4	83% 5d2 (1G) 1G + 17% 5d2 (3F) 3F	83% 5d2 (1G4)	53% 5d2 (0,4)	85% 5d2 (1G) 1G
33127	33130	-3	33825	698	33932	805	2	57% 5d2 (3P) 3P + 40% 5d2 (1D) 1D	57% 5d2 (3P2)	95% 5d2 (0,2)	54% 5d2 (3P) 3P
57710	57717	-7	63494	5784	58851	1141	0	90% 5d2 (1S) 1S + 9% 5d2 (3P) 3P	90% 5d2 (1S0)	82% 5d2 (0,0)	91% 5d2 (1S) 1S
129301	129246	55	131107	1806	129438	137	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	97% 5d6s (3/2,1/2)	97% 5d6s (2D) 3D
131416	131475	-59	133302	1886	131488	72	2	82% 5d6s (2D) 3D + 18% 5d6s (2D) 1D	93% 5d6s (2D3/2)	90% 5d6s (3/2,1/2)	81% 5d6s (2D) 3D
142163	142171	-8	143702	1539	142679	516	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	97% 5d6s (5/2,1/2)	97% 5d6s (2D) 3D
148023	148010	13	150239	2216	148595	572	2	81% 5d6s (2D) 1D + 18% 5d6s (2D) 3D	93% 5d6s (2D5/2)	90% 5d6s (5/2,1/2)	81% 5d6s (2D) 1D
208659	208909	-250	214001	5342	209906	1247	2	69% 5d6p (2D) 3Fo + 26% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	97% 5d6p (3/2,1/2)o	66% 5d6p (2D) 3Fo
212862	212597	265	218378	5516	213084	222	1	68% 5d6p (2D) 3Do + 20% 5d6p (2D) 1Po	96% 5d6p (2D3/2)o	92% 5d6p (3/2,1/2)o	69% 5d6p (2D) 3Do
223790	223875	-85	228918	5128	224886	1096	2	48% 5d6p (2D) 3Do + 18% 5d6p (2D) 1Do	96% 5d6p (2D5/2)o	93% 5d6p (5/2,1/2)o	49% 5d6p (2D) 3Do
224741	224656	85	230043	5302	226212	1471	3	60% 5d6p (2D) 3Fo + 25% 5d6p (2D) 3Do	94% 5d6p (2D5/2)o	91% 5d6p (5/2,1/2)o	60% 5d6p (2D) 3Fo
232453	232432	21	237261	4808	233874	1421	2	39% 5d6p (2D) 3Do + 30% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	94% 5d6p (3/2,3/2)o	37% 5d6p (2D) 3Do
236726	236675	51	241829	5103	238186	1460	3	32% 5d6p (2D) 3Do + 39% 5d6p (2D) 3Fo	88% 5d6p (2D3/2)o	84% 5d6p (3/2,3/2)o	37% 5d6p (2D) 3Fo
237682	237780	-98	242949	5267	238656	974	1	62% 5d6p (2D) 3Po + 25% 5d6p (2D) 3Do	96% 5d6p (2D3/2)o	94% 5d6p (3/2,3/2)o	61% 5d6p (2D) 3Po
239794	239766	28	245116	5322	241043	1249	0	99% 5d6p (2D) 3Po + 1% 5p55d26p (3P) 3P	99% 5d6p (2D3/2)o	97% 5d6p (3/2,3/2)o	97% 5d6p (2D) 3Po
247354	247241	113	252132	4778	249334	1980	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
248430	248394	36	253303	4873	250142	1712	2	63% 5d6p (2D) 3Po + 27% 5d6p (2D) 1Do	94% 5d6p (2D5/2)o	91% 5d6p (5/2,3/2)o	64% 5d6p (2D) 3Po
249401	249570	-169	254588	5187	251254	1853	3	56% 5d6p (2D) 1Fo + 43% 5d6p (2D) 3Do	89% 5d6p (2D5/2)o	85% 5d6p (5/2,3/2)o	59% 5d6p (2D) 1Fo
255246	255245	1	260689	5443	255391	145	1	66% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	95% 5d6p (5/2,3/2)o	65% 5d6p (2D) 1Po
	276640		275686		272504		0	97% 6s2 (1S) 1S + 1% 6p2 (1S) 1S	97% 6s2 (1S0)	95% 6s2 (0,0)	95% 6s2 (1S) 1S
331454	331337	117	339910	8456	333410	1956	4	49% 5d5f (2D) 1Go + 36% 5d5f (2D) 3Ho	70% 5d5f (2D3/2)o	61% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
332501	332375	126	341045	8544	333322	821	2	65% 5d5f (2D) 3Fo + 27% 5d5f (2D) 1Do	92% 5d5f (2D3/2)o	91% 5d5f (3/2,5/2)o	65% 5d5f (2D) 3Fo
334240	334141	99	342907	8667	334390	150	3	55% 5d5f (2D) 3Go + 32% 5d5f (2D) 3Fo	56% 5d5f (2D3/2)o	46% 5d5f (3/2,5/2)o	46% 5d5f (2D) 3Go
334302	334239	63	342810	8508	336142	1840	4	50% 5d5f (2D) 3Ho + 23% 5d5f (2D) 3Go	66% 5d5f (2D3/2)o	58% 5d5f (3/2,7/2)o	56% 5d5f (2D) 3Ho
337436	337458	-22	346327	8891	338249	813	3	41% 5d5f (2D) 3Fo + 20% 5d5f (2D) 3Go	50% 5d5f (2D3/2)o	38% 5d5f (3/2,5/2)o	34% 5d5f (2D) 3Fo
337535	337706	-171	346205	8670	339706	2171	5	83% 5d5f (2D) 3Ho + 9% 5d5f (2D) 3Go	78% 5d5f (2D3/2)o	76% 5d5f (3/2,7/2)o	83% 5d5f (2D) 3Ho
340330	340346	-16	349066	8736	341072	742	2	32% 5d5f (2D) 1Do + 30% 5d5f (2D) 3Po	78% 5d5f (2D3/2)o	71% 5d5f (3/2,7/2)o	37% 5d5f (2D) 1Do
341844	342087	-243	350167	8323	341677	-167	1	53% 5d5f (2D) 3Do + 18% 5d5f (2D) 3Po	77% 5d5f (2D3/2)o	49% 5d5f (3/2,5/2)o	37% 6s6p (2S) 3Po
343897	344164	-267	352118	8221	345648	1751	4	32% 5d5f (2D) 3Fo + 38% 5d5f (2D) 1Go	63% 5d5f (2D5/2)o	75% 5d5f (5/2,7/2)o	43% 5d5f (2D) 3Fo
	346212		348458		343490		0	88% 6s6p (2S) 3Po + 11% 5d5f (2D) 3Po	88% 6s6p (2S1/2)o	92% 6s6p (1/2,1/2)o	92% 6s6p (2S) 3Po
346144	346286	-142	354690	8546	347287	1143	4	48% 5d5f (2D) 3Go + 41% 5d5f (2D) 3Fo	57% 5d5f (2D5/2)o	68% 5d5f (5/2,5/2)o	57% 5d5f (2D) 3Go
	346729				349940		6	99% 5d5f (2D) 3Ho + 1% 5p55d3 (2G) 3Ho	99% 5d5f (2D5/2)o
347386	347387	-1	356158	8772	348392	1006	2	33% 5d5f (2D) 3Do + 29% 5d5f (2D) 1Do	55% 5d5f (2D5/2)o	46% 5d5f (5/2,5/2)o	33% 5d5f (2D) 3Do
349155	348836	319	358073	8918	349683	528	3	49% 5d5f (2D) 3Do + 23% 5d5f (2D) 3Fo	71% 5d5f (2D5/2)o	67% 5d5f (5/2,5/2)o	52% 5d5f (2D) 3Do
349324	349306	18	357799	8475	349829	505	5	78% 5d5f (2D) 3Go + 12% 5d5f (2D) 3Ho	61% 5d5f (2D5/2)o	63% 5d5f (5/2,7/2)o	79% 5d5f (2D) 3Go
	350129		355506		349008		1	55% 6s6p (2S) 3Po + 24% 5d5f (2D) 3Do	56% 6s6p (2S1/2)o	37% 6s6p (1/2,1/2)o	49% 5d5f (2D) 3Do
354012	353869	143	362736	8724	354838	826	2	53% 5d5f (2D) 3Po + 31% 5d5f (2D) 3Do	55% 5d5f (2D5/2)o	47% 5d5f (5/2,7/2)o	46% 5d5f (2D) 3Po
356322	356314	8	365435	9113	356198	-124	3	64% 5d5f (2D) 1Fo + 22% 5d5f (2D) 3Do	82% 5d5f (2D5/2)o	82% 5d5f (5/2,7/2)o	64% 5d5f (2D) 1Fo
356849	356848	1	365560	8711	357819	970	1	61% 5d5f (2D) 3Po + 24% 6s6p (2S) 3Po	53% 5d5f (2D5/2)o	70% 5d5f (5/2,5/2)o	73% 5d5f (2D) 3Po
	361332		366127		358117		0	82% 5d5f (2D) 3Po + 11% 6s6p (2S) 3Po	82% 5d5f (2D5/2)o	88% 5d5f (5/2,5/2)o	88% 5d5f (2D) 3Po
363927	363827	100	372440	8513	362544	-1383	1	70% 5d5f (2D) 1Po + 8% 6s6p (2S) 3Po	69% 5d5f (2D5/2)o	63% 5d5f (5/2,7/2)o	66% 5d5f (2D) 1Po
364949	365080	-131	375258	10309	361850	-3099	5	84% 5d5f (2D) 1Ho + 4% 5d5f (2D) 3Ho	48% 5d5f (2D5/2)o	49% 5d5f (5/2,5/2)o	86% 5d5f (2D) 1Ho
	371386		375808		371823		2	96% 6s6p (2S) 3Po + 3% 5d5f (2D) 3Po	96% 6s6p (2S1/2)o	91% 6s6p (1/2,3/2)o	91% 6s6p (2S) 3Po
	394669		401553		396700		1	74% 6s6p (2S) 1Po + 9% 5d5f (2D) 1Po	71% 6s6p (2S1/2)o	65% 6s6p (1/2,3/2)o	69% 6s6p (2S) 1Po
	421856		420579				2	56% 5d7p (2D) 3Fo + 23% 5d7p (2D) 1Do	84% 5d7p (2D3/2)o	93% 5d7p (3/2,1/2)o	63% 5d7p (2D) 3Fo
	422778		421875				1	41% 5d7p (2D) 3Do + 15% 5p55d3 (2D) 3Po	50% 5d7p (2D3/2)o	89% 5d7p (3/2,1/2)o	69% 5d7p (2D) 3Do
	430690		430058				2	57% 5d7p (2D) 3Do + 17% 5d7p (2D) 3Fo	84% 5d7p (2D3/2)o	89% 5d7p (3/2,3/2)o	60% 5d7p (2D) 3Do
	432028		432014				3	57% 5d7p (2D) 3Fo + 24% 5d7p (2D) 1Fo	86% 5d7p (2D3/2)o	90% 5d7p (3/2,3/2)o	71% 5d7p (2D) 3Fo
	432622		432718				1	62% 5d7p (2D) 3Po + 20% 5d7p (2D) 3Do	89% 5d7p (2D3/2)o	92% 5d7p (3/2,3/2)o	64% 5d7p (2D) 3Po
	433617		433561				0	98% 5d7p (2D) 3Po + 1% 5p55d3 (2D) 3Po	98% 5d7p (2D3/2)o	97% 5d7p (3/2,3/2)o	97% 5d7p (2D) 3Po
	434936		433983				2	26% 5d7p (2D) 3Po + 25% 5d7p (2D) 1Do	72% 5d7p (2D5/2)o	88% 5d7p (5/2,1/2)o	32% 5d7p (2D) 3Po
	435510		434851				3	27% 5d7p (2D) 1Fo + 24% 5d7p (2D) 3Do	48% 5d7p (2D5/2)o	57% 5d7p (5/2,1/2)o	22% 5d7p (2D) 3Do
	445125		444717				2	46% 5d7p (2D) 3Po + 21% 5d7p (2D) 1Do	68% 5d7p (2D5/2)o	85% 5d7p (5/2,3/2)o	56% 5d7p (2D) 3Po
	445223		444271				3	45% 5d7p (2D) 3Do + 32% 5d7p (2D) 1Fo	79% 5d7p (2D5/2)o	93% 5d7p (5/2,3/2)o	52% 5d7p (2D) 3Do
	445747		444550				4	86% 5d7p (2D) 3Fo + 3% 4f135d3 (4F) 5Go	86% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	94% 5d7p (2D) 3Fo
	448677		448411				1	64% 5d7p (2D) 1Po + 26% 5d7p (2D) 3Po	95% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	64% 5d7p (2D) 1Po

(a) Experimental energies from [16] and [17]; (b) Our HFR(CV) calculations; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 7. Comparison of the Os VII energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

EExp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	48	-48	0	0	0	0	2	87% 5d2 (3F) 3F + 12% 5d2 (1D) 1D	87% 5d2 (3F2)	90% 5d2 (0,2)	87% 5d2 (3F) 3F
10308	10309	-1	9891	-417	10604	296	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
15837	15768	69	17101	1264	16117	280	0	90% 5d2 (3P) 3P + 9% 5d2 (1S) 1S	90% 5d2 (3P0)	82% 5d2 (0,0)	91% 5d2 (3P) 3P
18049	17997	52	17802	-247	18409	360	4	83% 5d2 (3F) 3F + 17% 5d2 (1G) 1G	83% 5d2 (3F4)	53% 5d2 (3/2,5/2)	85% 5d2 (3F) 3F
19444	19429	14	20274	830	19852	408	2	48% 5d2 (1D) 1D + 41% 5d2 (3P) 3P	48% 5d2 (1D2)	89% 5d2 (3/2,5/2)	46% 5d2 (1D) 1D
22098	22164	-66	22777	679	22624	526	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	98% 5d2 (3/2,5/2)	98% 5d2 (3P) 3P
31274	31284	-10	32298	1024	31496	222	4	83% 5d2 (1G) 1G + 17% 5d2 (3F) 3F	83% 5d2 (1G4)	53% 5d2 (0,4)	85% 5d2 (1G) 1G
33127	33130	-3	33825	698	33932	805	2	57% 5d2 (3P) 3P + 40% 5d2 (1D) 1D	57% 5d2 (3P2)	95% 5d2 (0,2)	54% 5d2 (3P) 3P
57710	57717	-7	63494	5784	58851	1141	0	90% 5d2 (1S) 1S + 9% 5d2 (3P) 3P	90% 5d2 (1S0)	82% 5d2 (0,0)	91% 5d2 (1S) 1S
129301	129246	55	131107	1806	129438	137	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	97% 5d6s (3/2,1/2)	97% 5d6s (2D) 3D
131416	131475	-59	133302	1886	131488	72	2	82% 5d6s (2D) 3D + 18% 5d6s (2D) 1D	93% 5d6s (2D3/2)	90% 5d6s (3/2,1/2)	81% 5d6s (2D) 3D
142163	142171	-8	143702	1539	142679	516	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	97% 5d6s (5/2,1/2)	97% 5d6s (2D) 3D
148023	148010	13	150239	2216	148595	572	2	81% 5d6s (2D) 1D + 18% 5d6s (2D) 3D	93% 5d6s (2D5/2)	90% 5d6s (5/2,1/2)	81% 5d6s (2D) 1D
208659	208909	-250	214001	5342	209906	1247	2	69% 5d6p (2D) 3Fo + 26% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	97% 5d6p (3/2,1/2)o	66% 5d6p (2D) 3Fo
212862	212597	265	218378	5516	213084	222	1	68% 5d6p (2D) 3Do + 20% 5d6p (2D) 1Po	96% 5d6p (2D3/2)o	92% 5d6p (3/2,1/2)o	69% 5d6p (2D) 3Do
223790	223875	-85	228918	5128	224886	1096	2	48% 5d6p (2D) 3Do + 18% 5d6p (2D) 1Do	96% 5d6p (2D5/2)o	93% 5d6p (5/2,1/2)o	49% 5d6p (2D) 3Do
224741	224656	85	230043	5302	226212	1471	3	60% 5d6p (2D) 3Fo + 25% 5d6p (2D) 3Do	94% 5d6p (2D5/2)o	91% 5d6p (5/2,1/2)o	60% 5d6p (2D) 3Fo
232453	232432	21	237261	4808	233874	1421	2	39% 5d6p (2D) 3Do + 30% 5d6p (2D) 1Do	96% 5d6p (2D3/2)o	94% 5d6p (3/2,3/2)o	37% 5d6p (2D) 3Do
236726	236675	51	241829	5103	238186	1460	3	32% 5d6p (2D) 3Do + 39% 5d6p (2D) 3Fo	88% 5d6p (2D3/2)o	84% 5d6p (3/2,3/2)o	37% 5d6p (2D) 3Fo
237682	237780	-98	242949	5267	238656	974	1	62% 5d6p (2D) 3Po + 25% 5d6p (2D) 3Do	96% 5d6p (2D3/2)o	94% 5d6p (3/2,3/2)o	61% 5d6p (2D) 3Po
239794	239766	28	245116	5322	241043	1249	0	99% 5d6p (2D) 3Po + 1% 5p55d26p (3P) 3P	99% 5d6p (2D3/2)o	97% 5d6p (3/2,3/2)o	97% 5d6p (2D) 3Po
247354	247241	113	252132	4778	249334	1980	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
248430	248394	36	253303	4873	250142	1712	2	63% 5d6p (2D) 3Po + 27% 5d6p (2D) 1Do	94% 5d6p (2D5/2)o	91% 5d6p (5/2,3/2)o	64% 5d6p (2D) 3Po
249401	249570	-169	254588	5187	251254	1853	3	56% 5d6p (2D) 1Fo + 43% 5d6p (2D) 3Do	89% 5d6p (2D5/2)o	85% 5d6p (5/2,3/2)o	59% 5d6p (2D) 1Fo
255246	255245	1	260689	5443	255391	145	1	66% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	95% 5d6p (5/2,3/2)o	65% 5d6p (2D) 1Po
	276640		275686		272504		0	97% 6s2 (1S) 1S + 1% 6p2 (1S) 1S	97% 6s2 (1S0)	95% 6s2 (0,0)	95% 6s2 (1S) 1S
331454	331337	117	339910	8456	333410	1956	4	49% 5d5f (2D) 1Go + 36% 5d5f (2D) 3Ho	70% 5d5f (2D3/2)o	61% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
332501	332375	126	341045	8544	333322	821	2	65% 5d5f (2D) 3Fo + 27% 5d5f (2D) 1Do	92% 5d5f (2D3/2)o	91% 5d5f (3/2,5/2)o	65% 5d5f (2D) 3Fo
334240	334141	99	342907	8667	334390	150	3	55% 5d5f (2D) 3Go + 32% 5d5f (2D) 3Fo	56% 5d5f (2D3/2)o	46% 5d5f (3/2,5/2)o	46% 5d5f (2D) 3Go
334302	334239	63	342810	8508	336142	1840	4	50% 5d5f (2D) 3Ho + 23% 5d5f (2D) 3Go	66% 5d5f (2D3/2)o	58% 5d5f (3/2,7/2)o	56% 5d5f (2D) 3Ho
337436	337458	-22	346327	8891	338249	813	3	41% 5d5f (2D) 3Fo + 20% 5d5f (2D) 3Go	50% 5d5f (2D3/2)o	38% 5d5f (3/2,5/2)o	34% 5d5f (2D) 3Fo
337535	337706	-171	346205	8670	339706	2171	5	83% 5d5f (2D) 3Ho + 9% 5d5f (2D) 3Go	78% 5d5f (2D3/2)o	76% 5d5f (3/2,7/2)o	83% 5d5f (2D) 3Ho
340330	340346	-16	349066	8736	341072	742	2	32% 5d5f (2D) 1Do + 30% 5d5f (2D) 3Po	78% 5d5f (2D3/2)o	71% 5d5f (3/2,7/2)o	37% 5d5f (2D) 1Do
341844	342087	-243	350167	8323	341677	-167	1	53% 5d5f (2D) 3Do + 18% 5d5f (2D) 3Po	77% 5d5f (2D3/2)o	49% 5d5f (3/2,5/2)o	37% 6s6p (2S) 3Po
343897	344164	-267	352118	8221	345648	1751	4	32% 5d5f (2D) 3Fo + 38% 5d5f (2D) 1Go	63% 5d5f (2D5/2)o	75% 5d5f (5/2,7/2)o	43% 5d5f (2D) 3Fo
	346212		348458		343490		0	88% 6s6p (2S) 3Po + 11% 5d5f (2D) 3Po	88% 6s6p (2S1/2)o	92% 6s6p (1/2,1/2)o	92% 6s6p (2S) 3Po
346144	346286	-142	354690	8546	347287	1143	4	48% 5d5f (2D) 3Go + 41% 5d5f (2D) 3Fo	57% 5d5f (2D5/2)o	68% 5d5f (5/2,5/2)o	57% 5d5f (2D) 3Go
	346729				349940		6	99% 5d5f (2D) 3Ho + 1% 5p55d3 (2G) 3Ho	99% 5d5f (2D5/2)o
347386	347387	-1	356158	8772	348392	1006	2	33% 5d5f (2D) 3Do + 29% 5d5f (2D) 1Do	55% 5d5f (2D5/2)o	46% 5d5f (5/2,5/2)o	33% 5d5f (2D) 3Do
349155	348836	319	358073	8918	349683	528	3	49% 5d5f (2D) 3Do + 23% 5d5f (2D) 3Fo	71% 5d5f (2D5/2)o	67% 5d5f (5/2,5/2)o	52% 5d5f (2D) 3Do
349324	349306	18	357799	8475	349829	505	5	78% 5d5f (2D) 3Go + 12% 5d5f (2D) 3Ho	61% 5d5f (2D5/2)o	63% 5d5f (5/2,7/2)o	79% 5d5f (2D) 3Go
	350129		355506		349008		1	55% 6s6p (2S) 3Po + 24% 5d5f (2D) 3Do	56% 6s6p (2S1/2)o	37% 6s6p (1/2,1/2)o	49% 5d5f (2D) 3Do
354012	353869	143	362736	8724	354838	826	2	53% 5d5f (2D) 3Po + 31% 5d5f (2D) 3Do	55% 5d5f (2D5/2)o	47% 5d5f (5/2,7/2)o	46% 5d5f (2D) 3Po
356322	356314	8	365435	9113	356198	-124	3	64% 5d5f (2D) 1Fo + 22% 5d5f (2D) 3Do	82% 5d5f (2D5/2)o	82% 5d5f (5/2,7/2)o	64% 5d5f (2D) 1Fo
356849	356848	1	365560	8711	357819	970	1	61% 5d5f (2D) 3Po + 24% 6s6p (2S) 3Po	53% 5d5f (2D5/2)o	70% 5d5f (5/2,5/2)o	73% 5d5f (2D) 3Po
	361332		366127		358117		0	82% 5d5f (2D) 3Po + 11% 6s6p (2S) 3Po	82% 5d5f (2D5/2)o	88% 5d5f (5/2,5/2)o	88% 5d5f (2D) 3Po
363927	363827	100	372440	8513	362544	-1383	1	70% 5d5f (2D) 1Po + 8% 6s6p (2S) 3Po	69% 5d5f (2D5/2)o	63% 5d5f (5/2,7/2)o	66% 5d5f (2D) 1Po
364949	365080	-131	375258	10309	361850	-3099	5	84% 5d5f (2D) 1Ho + 4% 5d5f (2D) 3Ho	48% 5d5f (2D5/2)o	49% 5d5f (5/2,5/2)o	86% 5d5f (2D) 1Ho
	371386		375808		371823		2	96% 6s6p (2S) 3Po + 3% 5d5f (2D) 3Po	96% 6s6p (2S1/2)o	91% 6s6p (1/2,3/2)o	91% 6s6p (2S) 3Po
	394669		401553		396700		1	74% 6s6p (2S) 1Po + 9% 5d5f (2D) 1Po	71% 6s6p (2S1/2)o	65% 6s6p (1/2,3/2)o	69% 6s6p (2S) 1Po
	421856		420579				2	56% 5d7p (2D) 3Fo + 23% 5d7p (2D) 1Do	84% 5d7p (2D3/2)o	93% 5d7p (3/2,1/2)o	63% 5d7p (2D) 3Fo
	422778		421875				1	41% 5d7p (2D) 3Do + 15% 5p55d3 (2D) 3Po	50% 5d7p (2D3/2)o	89% 5d7p (3/2,1/2)o	69% 5d7p (2D) 3Do
	430690		430058				2	57% 5d7p (2D) 3Do + 17% 5d7p (2D) 3Fo	84% 5d7p (2D3/2)o	89% 5d7p (3/2,3/2)o	60% 5d7p (2D) 3Do
	432028		432014				3	57% 5d7p (2D) 3Fo + 24% 5d7p (2D) 1Fo	86% 5d7p (2D3/2)o	90% 5d7p (3/2,3/2)o	71% 5d7p (2D) 3Fo
	432622		432718				1	62% 5d7p (2D) 3Po + 20% 5d7p (2D) 3Do	89% 5d7p (2D3/2)o	92% 5d7p (3/2,3/2)o	64% 5d7p (2D) 3Po
	433617		433561				0	98% 5d7p (2D) 3Po + 1% 5p55d3 (2D) 3Po	98% 5d7p (2D3/2)o	97% 5d7p (3/2,3/2)o	97% 5d7p (2D) 3Po
	434936		433983				2	26% 5d7p (2D) 3Po + 25% 5d7p (2D) 1Do	72% 5d7p (2D5/2)o	88% 5d7p (5/2,1/2)o	32% 5d7p (2D) 3Po
	435510		434851				3	27% 5d7p (2D) 1Fo + 24% 5d7p (2D) 3Do	48% 5d7p (2D5/2)o	57% 5d7p (5/2,1/2)o	22% 5d7p (2D) 3Do
	445125		444717				2	46% 5d7p (2D) 3Po + 21% 5d7p (2D) 1Do	68% 5d7p (2D5/2)o	85% 5d7p (5/2,3/2)o	56% 5d7p (2D) 3Po
	445223		444271				3	45% 5d7p (2D) 3Do + 32% 5d7p (2D) 1Fo	79% 5d7p (2D5/2)o	93% 5d7p (5/2,3/2)o	52% 5d7p (2D) 3Do
	445747		444550				4	86% 5d7p (2D) 3Fo + 3% 4f135d3 (4F) 5Go	86% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	94% 5d7p (2D) 3Fo
	448677		448411				1	64% 5d7p (2D) 1Po + 26% 5d7p (2D) 3Po	95% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	64% 5d7p (2D) 1Po

(a) Experimental energies from [16] and [17]; (b) Our HFR(CV) calculations; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 8. Comparison of the Ir VIII energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

EExp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	59	-59	0	0	0	0	2	85% 5d2 (3F) 3F + 13% 5d2 (1D) 1D	85% 5d2 (3F2)	92% 5d2 (0,2)	86% 5d2 (3F) 3F
12672	12662	10	12187	-485	12932	260	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
17254	17171	83	18639	1385	17670	416	0	89% 5d2 (3P) 3P + 11% 5d2 (1S) 1S	89% 5d2 (3P0)	83% 5d2 (0,0)	90% 5d2 (3P) 3P
21615	21561	54	21397	-218	21920	305	4	78% 5d2 (3F) 3F + 21% 5d2 (1G) 1G	78% 5d2 (3F4)	59% 5d2 (3/2,5/2)	81% 5d2 (3F) 3F
22436	22425	11	23253	817	22905	469	2	45% 5d2 (1D) 1D + 43% 5d2 (3P) 3P	45% 5d2 (1D2)	91% 5d2 (3/2,5/2)	44% 5d2 (1D) 1D
25221	25301	-80	25904	683	25841	620	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	98% 5d2 (3/2,5/2)	98% 5d2 (3P) 3P
36253	36268	-14	37144	891	36522	269	4	78% 5d2 (1G) 1G + 21% 5d2 (3F) 3F	78% 5d2 (1G4)	59% 5d2 (0,4)	81% 5d2 (1G) 1G
38878	38872	6	39578	700	39735	857	2	55% 5d2 (3P) 3P + 41% 5d2 (1D) 1D	55% 5d2 (3P2)	96% 5d2 (0,2)	53% 5d2 (3P) 3P
65022	65032	-10	71073	6051	66656	1634	0	89% 5d2 (1S) 1S + 11% 5d2 (3P) 3P	89% 5d2 (1S0)	83% 5d2 (0,0)	90% 5d2 (1S) 1S
169223	169163	60	171071	1848	169138	-85	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	98% 5d6s (3/2,1/2)	98% 5d6s (2D) 3D
171485	171549	-64	173436	1951	171413	-72	2	79% 5d6s (2D) 3D + 20% 5d6s (2D) 1D	94% 5d6s (2D3/2)	92% 5d6s (3/2,1/2)	79% 5d6s (2D) 3D
184748	184760	-12	186305	1557	185041	293	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	98% 5d6s (5/2,1/2)	98% 5d6s (2D) 3D
190553	190537	16	192754	2201	191018	465	2	79% 5d6s (2D) 1D + 20% 5d6s (2D) 3D	94% 5d6s (2D5/2)	92% 5d6s (5/2,1/2)	79% 5d6s (2D) 1D
258017	258291	-274	262476	4459	259044	1027	2	69% 5d6p (2D) 3Fo + 25% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	97% 5d6p (3/2,1/2)o	67% 5d6p (2D) 3Fo
262461	262182	279	267143	4682	262439	-22	1	67% 5d6p (2D) 3Do + 21% 5d6p (2D) 1Po	96% 5d6p (2D3/2)o	93% 5d6p (3/2,1/2)o	67% 5d6p (2D) 3Do
275872	275932	-60	280115	4243	276670	798	2	48% 5d6p (2D) 3Do + 17% 5d6p (2D) 1Do	96% 5d6p (2D5/2)o	94% 5d6p (5/2,1/2)o	48% 5d6p (2D) 3Do
276994	276924	70	281423	4429	278237	1243	3	57% 5d6p (2D) 3Fo + 26% 5d6p (2D) 3Do	96% 5d6p (2D5/2)o	93% 5d6p (5/2,1/2)o	57% 5d6p (2D) 3Fo
287122	287057	65	290984	3862	288280	1158	2	40% 5d6p (2D) 3Do + 29% 5d6p (2D) 1Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	38% 5d6p (2D) 3Do
291792	291770	22	295991	4199	293068	1276	3	42% 5d6p (2D) 3Fo + 29% 5d6p (2D) 1Fo	90% 5d6p (2D3/2)o	87% 5d6p (3/2,3/2)o	40% 5d6p (2D) 3Fo
292734	292827	-93	297076	4342	293545	811	1	61% 5d6p (2D) 3Po + 27% 5d6p (2D) 3Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	61% 5d6p (2D) 3Po
295142	295123	19	299551	4409	296204	1062	0	99% 5d6p (2D) 3Po + 1% 5p55d26s (3P) 3Po	99% 5d6p (2D3/2)o	97% 5d6p (3/2,3/2)o	97% 5d6p (2D) 3Po
305005	304898	107	308821	3816	306792	1787	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
305894	305837	57	309804	3910	307362	1468	2	61% 5d6p (2D) 3Po + 28% 5d6p (2D) 1Do	95% 5d6p (2D5/2)o	93% 5d6p (5/2,3/2)o	62% 5d6p (2D) 3Po
306697	306899	-202	310915	4218	308315	1618	3	53% 5d6p (2D) 1Fo + 45% 5d6p (2D) 3Do	91% 5d6p (2D5/2)o	87% 5d6p (5/2,3/2)o	55% 5d6p (2D) 1Fo
313520	313503	17	318064	4544	313586	66	1	65% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	98% 5d6p (2D5/2)o	96% 5d6p (5/2,3/2)o	65% 5d6p (2D) 1Po
	358146		356037		352159		0	97% 6s2 (1S) 1S + 1% 5p55d6p2 (2P) 1S	97% 6s2 (1S0)	96% 6s2 (0,0)	96% 6s2 (1S) 1S
380334	379362	972	388672	8338	382478	2144	4	54% 5d5f (2D) 1Go + 27% 5d5f (2D) 3Ho	59% 5d5f (2D3/2)o	55% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
379116	379853	-737	389228	10112	381777	2661	2	54% 5d5f (2D) 3Fo + 30% 5d5f (2D) 1Do	85% 5d5f (2D3/2)o	88% 5d5f (3/2,5/2)o	61% 5d5f (2D) 3Fo
380724	380808	-84	390300	9576	383305	2581	3	64% 5d5f (2D) 3Go + 15% 5p55d3 (2H) 3Go	65% 5d5f (2D3/2)o	63% 5d5f (3/2,5/2)o	62% 5d5f (2D) 3Go
383508	382996	512	392062	8554	385817	2309	4	55% 5d5f (2D) 3Ho + 25% 5d5f (2D) 3Go	56% 5d5f (2D3/2)o	53% 5d5f (3/2,7/2)o	57% 5d5f (2D) 3Ho
385282	385955	-673	394896	9614	388358	3076	3	53% 5d5f (2D) 3Fo + 20% 5d5f (2D) 3Do	63% 5d5f (2D3/2)o	58% 5d5f (3/2,7/2)o	53% 5d5f (2D) 3Fo
387545	387381	164	396360	8815	390378	2833	5	80% 5d5f (2D) 3Ho + 11% 5d5f (2D) 3Go	75% 5d5f (2D3/2)o	76% 5d5f (3/2,7/2)o	79% 5d5f (2D) 3Ho
388229	389059	-830	398472	10243	391578	3349	2	21% 5d5f (2D) 1Do + 18% 5d5f (2D) 3Po	57% 5d5f (2D3/2)o	70% 5d5f (3/2,7/2)o	32% 5d5f (2D) 1Do
391888	391613	275	401864	9976	394150	2262	1	53% 5d5f (2D) 3Do + 14% 5d5f (2D) 3Po	64% 5d5f (2D3/2)o	71% 5d5f (3/2,5/2)o	59% 5d5f (2D) 3Do
393669	393173	496	402799	9130	396931	3262	4	38% 5d5f (2D) 3Go + 27% 5d5f (2D) 1Go	64% 5d5f (2D5/2)o	51% 5d5f (5/2,5/2)o	27% 5d5f (2D) 3Go
396001	396124	-123	404674	8673	398865	2864	4	47% 5d5f (2D) 3Fo + 16% 5p55d3 (4F) 5Fo	50% 5d5f (2D5/2)o	58% 5d5f (5/2,7/2)o	58% 5d5f (2D) 3Fo
	397570				402394		6	93% 5d5f (2D) 3Ho + 5% 5p55d3 (2G) 3Ho	93% 5d5f (2D5/2)o
397003	398226	-1223	408506	11503	401804	4801	3	40% 5d5f (2D) 3Do + 27% 5d5f (2D) 3Fo	60% 5d5f (2D5/2)o	62% 5d5f (5/2,5/2)o	48% 5d5f (2D) 3Do
397557	398234	-677	405998	8441	399983	2426	2	36% 5p55d3 (4P) 5So + 30% 5d5f (2D) 3Do	30% 5d5f (2D5/2)o	44% 5d5f (5/2,5/2)o	23% 5d5f (2D) 1Do
399128	398757	371	408390	9262	402320	3192	5	68% 5d5f (2D) 3Go + 14% 5d5f (2D) 3Ho	55% 5d5f (2D5/2)o	58% 5d5f (5/2,7/2)o	70% 5d5f (2D) 3Go
406542	403566 ★		415628	9086	408218	1676	1	45% 5d5f (2D) 3Po + 10% 5d5f (2D) 3Do	50% 5d5f (2D5/2)o	80% 5d5f (5/2,5/2)o	64% 5d5f (2D) 3Po
	403892		416349		408884		0	71% 5d5f (2D) 3Po + 16% 6s6p (2S) 3Po	71% 5d5f (2D5/2)o	85% 5d5f (5/2,5/2)o	85% 5d5f (2D) 3Po
405867	405498	369	414731	8864	408411	2544	2	55% 5d5f (2D) 3Po + 18% 5d5f (2D) 3Do	53% 5d5f (2D5/2)o	38% 5d5f (5/2,7/2)o	35% 5d5f (2D) 3Po
408418	408641	-223	418406	9988	410808	2390	3	24% 5d5f (2D) 1Fo + 15% 5p55d3 (4F) 3Go	35% 5d5f (2D5/2)o	73% 5d5f (5/2,7/2)o	63% 5d5f (2D) 1Fo
420291	418485	1806	429632	9341	418559	-1732	5	41% 5d5f (2D) 1Ho + 16% 5p55d3 (2G) 1Ho	31% 5d5f (2D5/2)o	46% 5d5f (5/2,5/2)o	76% 5d5f (2D) 1Ho
421774	422435	-661	430607	8833	420585	-1189	1	41% 5d5f (2D) 1Po + 12% 5d5f (2D) 3Po	55% 5d5f (2D5/2)o	67% 5d5f (5/2,7/2)o	67% 5d5f (2D) 1Po
	430758		438282		434121		0	76% 6s6p (2S) 3Po + 12% 5d5f (2D) 3Po	76% 6s6p (2S1/2)o	94% 6s6p (1/2,1/2)o	94% 6s6p (2S) 3Po
	436330		445179		440737		1	77% 6s6p (2S) 3Po + 6% 5d5f (2D) 3Po	68% 6s6p (2S1/2)o	75% 6s6p (1/2,1/2)o	81% 6s6p (2S) 3Po
	457194		468858		465428		2	57% 6s6p (2S) 3Po + 8% 5p55d3 (4F) 5Go	57% 6s6p (2S1/2)o	97% 6s6p (1/2,3/2)o	97% 6s6p (2S) 3Po
	482590		493613		489065		1	75% 6s6p (2S) 1Po + 8% 6s6p (2S) 3Po	75% 6s6p (2S1/2)o	80% 6s6p (1/2,3/2)o	80% 6s6p (2S) 1Po
	512905		511411				1	37% 5d7p (2D) 3Do + 21% 5p55d3 (2D) 3Do	50% 5d7p (2D3/2)o	89% 5d7p (3/2,1/2)o	64% 5d7p (2D) 3Do
	513128		510365				2	68% 5d7p (2D) 3Fo + 24% 5d7p (2D) 1Do	98% 5d7p (2D3/2)o	93% 5d7p (3/2,1/2)o	66% 5d7p (2D) 3Fo
	524789		520286				2	62% 5d7p (2D) 3Do + 21% 5d7p (2D) 3Fo	96% 5d7p (2D3/2)o	76% 5d7p (3/2,3/2)o	43% 5d7p (2D) 3Do
	526829		524333				3	66% 5d7p (2D) 3Fo + 26% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	86% 5d7p (3/2,3/2)o	70% 5d7p (2D) 3Fo
	527256		525124				1	62% 5d7p (2D) 3Po + 24% 5d7p (2D) 3Do	95% 5d7p (2D3/2)o	92% 5d7p (3/2,3/2)o	60% 5d7p (2D) 3Po
	528258		526622				0	98% 5d7p (2D) 3Po + 1% 5p55d3 (4P) 5Do	98% 5d7p (2D3/2)o	91% 5d7p (3/2,3/2)o	91% 5d7p (2D) 3Po
	529729		526946				2	37% 5d7p (2D) 3Po + 27% 5d7p (2D) 1Do	94% 5d7p (2D5/2)o	88% 5d7p (5/2,1/2)o	32% 5d7p (2D) 3Po
	530102		527614				3	36% 5d7p (2D) 3Do + 32% 5d7p (2D) 1Fo	95% 5d7p (2D5/2)o	77% 5d7p (5/2,1/2)o	28% 5d7p (2D) 3Do
	541842		537600				3	57% 5d7p (2D) 3Do + 38% 5d7p (2D) 1Fo	95% 5d7p (2D5/2)o	55% 5d7p (5/2,3/2)o	37% 5d7p (2D) 3Do
	542365		539655				2	58% 5d7p (2D) 3Po + 33% 5d7p (2D) 1Do	96% 5d7p (2D5/2)o	93% 5d7p (5/2,3/2)o	52% 5d7p (2D) 3Po
	542454		539608				4	99% 5d7p (2D) 3Fo + 1% 6s5f (2S) 3Fo	99% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
	545919		543901				1	56% 5d7p (2D) 1Po + 26% 5d7p (2D) 3Po	88% 5d7p (2D5/2)o	76% 5d7p (5/2,3/2)o	52% 5d7p (2D) 1Po

(a) Experimental energies from [16] and [17]; (b) Our HFR(CV) calculations where the one star symbol stands for a level not included in the fit; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 8. Comparison of the Ir VIII energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

EExp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	59	-59	0	0	0	0	2	85% 5d2 (3F) 3F + 13% 5d2 (1D) 1D	85% 5d2 (3F2)	92% 5d2 (0,2)	86% 5d2 (3F) 3F
12672	12662	10	12187	-485	12932	260	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
17254	17171	83	18639	1385	17670	416	0	89% 5d2 (3P) 3P + 11% 5d2 (1S) 1S	89% 5d2 (3P0)	83% 5d2 (0,0)	90% 5d2 (3P) 3P
21615	21561	54	21397	-218	21920	305	4	78% 5d2 (3F) 3F + 21% 5d2 (1G) 1G	78% 5d2 (3F4)	59% 5d2 (3/2,5/2)	81% 5d2 (3F) 3F
22436	22425	11	23253	817	22905	469	2	45% 5d2 (1D) 1D + 43% 5d2 (3P) 3P	45% 5d2 (1D2)	91% 5d2 (3/2,5/2)	44% 5d2 (1D) 1D
25221	25301	-80	25904	683	25841	620	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	98% 5d2 (3/2,5/2)	98% 5d2 (3P) 3P
36253	36268	-14	37144	891	36522	269	4	78% 5d2 (1G) 1G + 21% 5d2 (3F) 3F	78% 5d2 (1G4)	59% 5d2 (0,4)	81% 5d2 (1G) 1G
38878	38872	6	39578	700	39735	857	2	55% 5d2 (3P) 3P + 41% 5d2 (1D) 1D	55% 5d2 (3P2)	96% 5d2 (0,2)	53% 5d2 (3P) 3P
65022	65032	-10	71073	6051	66656	1634	0	89% 5d2 (1S) 1S + 11% 5d2 (3P) 3P	89% 5d2 (1S0)	83% 5d2 (0,0)	90% 5d2 (1S) 1S
169223	169163	60	171071	1848	169138	-85	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	98% 5d6s (3/2,1/2)	98% 5d6s (2D) 3D
171485	171549	-64	173436	1951	171413	-72	2	79% 5d6s (2D) 3D + 20% 5d6s (2D) 1D	94% 5d6s (2D3/2)	92% 5d6s (3/2,1/2)	79% 5d6s (2D) 3D
184748	184760	-12	186305	1557	185041	293	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	98% 5d6s (5/2,1/2)	98% 5d6s (2D) 3D
190553	190537	16	192754	2201	191018	465	2	79% 5d6s (2D) 1D + 20% 5d6s (2D) 3D	94% 5d6s (2D5/2)	92% 5d6s (5/2,1/2)	79% 5d6s (2D) 1D
258017	258291	-274	262476	4459	259044	1027	2	69% 5d6p (2D) 3Fo + 25% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	97% 5d6p (3/2,1/2)o	67% 5d6p (2D) 3Fo
262461	262182	279	267143	4682	262439	-22	1	67% 5d6p (2D) 3Do + 21% 5d6p (2D) 1Po	96% 5d6p (2D3/2)o	93% 5d6p (3/2,1/2)o	67% 5d6p (2D) 3Do
275872	275932	-60	280115	4243	276670	798	2	48% 5d6p (2D) 3Do + 17% 5d6p (2D) 1Do	96% 5d6p (2D5/2)o	94% 5d6p (5/2,1/2)o	48% 5d6p (2D) 3Do
276994	276924	70	281423	4429	278237	1243	3	57% 5d6p (2D) 3Fo + 26% 5d6p (2D) 3Do	96% 5d6p (2D5/2)o	93% 5d6p (5/2,1/2)o	57% 5d6p (2D) 3Fo
287122	287057	65	290984	3862	288280	1158	2	40% 5d6p (2D) 3Do + 29% 5d6p (2D) 1Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	38% 5d6p (2D) 3Do
291792	291770	22	295991	4199	293068	1276	3	42% 5d6p (2D) 3Fo + 29% 5d6p (2D) 1Fo	90% 5d6p (2D3/2)o	87% 5d6p (3/2,3/2)o	40% 5d6p (2D) 3Fo
292734	292827	-93	297076	4342	293545	811	1	61% 5d6p (2D) 3Po + 27% 5d6p (2D) 3Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	61% 5d6p (2D) 3Po
295142	295123	19	299551	4409	296204	1062	0	99% 5d6p (2D) 3Po + 1% 5p55d26s (3P) 3Po	99% 5d6p (2D3/2)o	97% 5d6p (3/2,3/2)o	97% 5d6p (2D) 3Po
305005	304898	107	308821	3816	306792	1787	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	97% 5d6p (5/2,3/2)o	97% 5d6p (2D) 3Fo
305894	305837	57	309804	3910	307362	1468	2	61% 5d6p (2D) 3Po + 28% 5d6p (2D) 1Do	95% 5d6p (2D5/2)o	93% 5d6p (5/2,3/2)o	62% 5d6p (2D) 3Po
306697	306899	-202	310915	4218	308315	1618	3	53% 5d6p (2D) 1Fo + 45% 5d6p (2D) 3Do	91% 5d6p (2D5/2)o	87% 5d6p (5/2,3/2)o	55% 5d6p (2D) 1Fo
313520	313503	17	318064	4544	313586	66	1	65% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	98% 5d6p (2D5/2)o	96% 5d6p (5/2,3/2)o	65% 5d6p (2D) 1Po
	358146		356037		352159		0	97% 6s2 (1S) 1S + 1% 5p55d6p2 (2P) 1S	97% 6s2 (1S0)	96% 6s2 (0,0)	96% 6s2 (1S) 1S
380334	379362	972	388672	8338	382478	2144	4	54% 5d5f (2D) 1Go + 27% 5d5f (2D) 3Ho	59% 5d5f (2D3/2)o	55% 5d5f (3/2,5/2)o	53% 5d5f (2D) 1Go
379116	379853	-737	389228	10112	381777	2661	2	54% 5d5f (2D) 3Fo + 30% 5d5f (2D) 1Do	85% 5d5f (2D3/2)o	88% 5d5f (3/2,5/2)o	61% 5d5f (2D) 3Fo
380724	380808	-84	390300	9576	383305	2581	3	64% 5d5f (2D) 3Go + 15% 5p55d3 (2H) 3Go	65% 5d5f (2D3/2)o	63% 5d5f (3/2,5/2)o	62% 5d5f (2D) 3Go
383508	382996	512	392062	8554	385817	2309	4	55% 5d5f (2D) 3Ho + 25% 5d5f (2D) 3Go	56% 5d5f (2D3/2)o	53% 5d5f (3/2,7/2)o	57% 5d5f (2D) 3Ho
385282	385955	-673	394896	9614	388358	3076	3	53% 5d5f (2D) 3Fo + 20% 5d5f (2D) 3Do	63% 5d5f (2D3/2)o	58% 5d5f (3/2,7/2)o	53% 5d5f (2D) 3Fo
387545	387381	164	396360	8815	390378	2833	5	80% 5d5f (2D) 3Ho + 11% 5d5f (2D) 3Go	75% 5d5f (2D3/2)o	76% 5d5f (3/2,7/2)o	79% 5d5f (2D) 3Ho
388229	389059	-830	398472	10243	391578	3349	2	21% 5d5f (2D) 1Do + 18% 5d5f (2D) 3Po	57% 5d5f (2D3/2)o	70% 5d5f (3/2,7/2)o	32% 5d5f (2D) 1Do
391888	391613	275	401864	9976	394150	2262	1	53% 5d5f (2D) 3Do + 14% 5d5f (2D) 3Po	64% 5d5f (2D3/2)o	71% 5d5f (3/2,5/2)o	59% 5d5f (2D) 3Do
393669	393173	496	402799	9130	396931	3262	4	38% 5d5f (2D) 3Go + 27% 5d5f (2D) 1Go	64% 5d5f (2D5/2)o	51% 5d5f (5/2,5/2)o	27% 5d5f (2D) 3Go
396001	396124	-123	404674	8673	398865	2864	4	47% 5d5f (2D) 3Fo + 16% 5p55d3 (4F) 5Fo	50% 5d5f (2D5/2)o	58% 5d5f (5/2,7/2)o	58% 5d5f (2D) 3Fo
	397570				402394		6	93% 5d5f (2D) 3Ho + 5% 5p55d3 (2G) 3Ho	93% 5d5f (2D5/2)o
397003	398226	-1223	408506	11503	401804	4801	3	40% 5d5f (2D) 3Do + 27% 5d5f (2D) 3Fo	60% 5d5f (2D5/2)o	62% 5d5f (5/2,5/2)o	48% 5d5f (2D) 3Do
397557	398234	-677	405998	8441	399983	2426	2	36% 5p55d3 (4P) 5So + 30% 5d5f (2D) 3Do	30% 5d5f (2D5/2)o	44% 5d5f (5/2,5/2)o	23% 5d5f (2D) 1Do
399128	398757	371	408390	9262	402320	3192	5	68% 5d5f (2D) 3Go + 14% 5d5f (2D) 3Ho	55% 5d5f (2D5/2)o	58% 5d5f (5/2,7/2)o	70% 5d5f (2D) 3Go
406542	403566 ★		415628	9086	408218	1676	1	45% 5d5f (2D) 3Po + 10% 5d5f (2D) 3Do	50% 5d5f (2D5/2)o	80% 5d5f (5/2,5/2)o	64% 5d5f (2D) 3Po
	403892		416349		408884		0	71% 5d5f (2D) 3Po + 16% 6s6p (2S) 3Po	71% 5d5f (2D5/2)o	85% 5d5f (5/2,5/2)o	85% 5d5f (2D) 3Po
405867	405498	369	414731	8864	408411	2544	2	55% 5d5f (2D) 3Po + 18% 5d5f (2D) 3Do	53% 5d5f (2D5/2)o	38% 5d5f (5/2,7/2)o	35% 5d5f (2D) 3Po
408418	408641	-223	418406	9988	410808	2390	3	24% 5d5f (2D) 1Fo + 15% 5p55d3 (4F) 3Go	35% 5d5f (2D5/2)o	73% 5d5f (5/2,7/2)o	63% 5d5f (2D) 1Fo
420291	418485	1806	429632	9341	418559	-1732	5	41% 5d5f (2D) 1Ho + 16% 5p55d3 (2G) 1Ho	31% 5d5f (2D5/2)o	46% 5d5f (5/2,5/2)o	76% 5d5f (2D) 1Ho
421774	422435	-661	430607	8833	420585	-1189	1	41% 5d5f (2D) 1Po + 12% 5d5f (2D) 3Po	55% 5d5f (2D5/2)o	67% 5d5f (5/2,7/2)o	67% 5d5f (2D) 1Po
	430758		438282		434121		0	76% 6s6p (2S) 3Po + 12% 5d5f (2D) 3Po	76% 6s6p (2S1/2)o	94% 6s6p (1/2,1/2)o	94% 6s6p (2S) 3Po
	436330		445179		440737		1	77% 6s6p (2S) 3Po + 6% 5d5f (2D) 3Po	68% 6s6p (2S1/2)o	75% 6s6p (1/2,1/2)o	81% 6s6p (2S) 3Po
	457194		468858		465428		2	57% 6s6p (2S) 3Po + 8% 5p55d3 (4F) 5Go	57% 6s6p (2S1/2)o	97% 6s6p (1/2,3/2)o	97% 6s6p (2S) 3Po
	482590		493613		489065		1	75% 6s6p (2S) 1Po + 8% 6s6p (2S) 3Po	75% 6s6p (2S1/2)o	80% 6s6p (1/2,3/2)o	80% 6s6p (2S) 1Po
	512905		511411				1	37% 5d7p (2D) 3Do + 21% 5p55d3 (2D) 3Do	50% 5d7p (2D3/2)o	89% 5d7p (3/2,1/2)o	64% 5d7p (2D) 3Do
	513128		510365				2	68% 5d7p (2D) 3Fo + 24% 5d7p (2D) 1Do	98% 5d7p (2D3/2)o	93% 5d7p (3/2,1/2)o	66% 5d7p (2D) 3Fo
	524789		520286				2	62% 5d7p (2D) 3Do + 21% 5d7p (2D) 3Fo	96% 5d7p (2D3/2)o	76% 5d7p (3/2,3/2)o	43% 5d7p (2D) 3Do
	526829		524333				3	66% 5d7p (2D) 3Fo + 26% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	86% 5d7p (3/2,3/2)o	70% 5d7p (2D) 3Fo
	527256		525124				1	62% 5d7p (2D) 3Po + 24% 5d7p (2D) 3Do	95% 5d7p (2D3/2)o	92% 5d7p (3/2,3/2)o	60% 5d7p (2D) 3Po
	528258		526622				0	98% 5d7p (2D) 3Po + 1% 5p55d3 (4P) 5Do	98% 5d7p (2D3/2)o	91% 5d7p (3/2,3/2)o	91% 5d7p (2D) 3Po
	529729		526946				2	37% 5d7p (2D) 3Po + 27% 5d7p (2D) 1Do	94% 5d7p (2D5/2)o	88% 5d7p (5/2,1/2)o	32% 5d7p (2D) 3Po
	530102		527614				3	36% 5d7p (2D) 3Do + 32% 5d7p (2D) 1Fo	95% 5d7p (2D5/2)o	77% 5d7p (5/2,1/2)o	28% 5d7p (2D) 3Do
	541842		537600				3	57% 5d7p (2D) 3Do + 38% 5d7p (2D) 1Fo	95% 5d7p (2D5/2)o	55% 5d7p (5/2,3/2)o	37% 5d7p (2D) 3Do
	542365		539655				2	58% 5d7p (2D) 3Po + 33% 5d7p (2D) 1Do	96% 5d7p (2D5/2)o	93% 5d7p (5/2,3/2)o	52% 5d7p (2D) 3Po
	542454		539608				4	99% 5d7p (2D) 3Fo + 1% 6s5f (2S) 3Fo	99% 5d7p (2D5/2)o	97% 5d7p (5/2,3/2)o	97% 5d7p (2D) 3Fo
	545919		543901				1	56% 5d7p (2D) 1Po + 26% 5d7p (2D) 3Po	88% 5d7p (2D5/2)o	76% 5d7p (5/2,3/2)o	52% 5d7p (2D) 1Po

(a) Experimental energies from [16] and [17]; (b) Our HFR(CV) calculations where the one star symbol stands for a level not included in the fit; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 9. Comparison of the Pt IX energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

Eexp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	67	-68	0	0	0	0	2	84% 5d2 (3F) 3F + 14% 5d2 (1D) 1D	84% 5d2 (3F2)	92% 5d2 (0,2)	85% 5d2 (3F) 3F
15253	15232	21	14695	-558	15490	237	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
18617	18522	95	20135	1518	19174	557	0	87% 5d2 (3P) 3P + 12% 5d2 (1S) 1S	87% 5d2 (3P0)	85% 5d2 (0,0)	89% 5d2 (3P) 3P
25362	25309	53	25171	-191	25633	271	4	74% 5d2 (3F) 3F + 25% 5d2 (1G) 1G	74% 5d2 (3F4)	64% 5d2 (3/2,5/2)	77% 5d2 (3F) 3F
25575	25571	4	26377	802	26146	571	2	44% 5d2 (3P) 3P + 43% 5d2 (1D) 1D	44% 5d2 (3P2)	92% 5d2 (3/2,5/2)	46% 5d2 (3P) 3P
28517	28609	-92	29201	684	29238	721	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	98% 5d2 (3/2,5/2)	98% 5d2 (3P) 3P
41618	41637	-18	42357	739	41949	331	4	74% 5d2 (1G) 1G + 25% 5d2 (3F) 3F	74% 5d2 (1G4)	64% 5d2 (0,4)	77% 5d2 (1G) 1G
44997	44979	18	45676	679	45962	965	2	54% 5d2 (3P) 3P + 42% 5d2 (1D) 1D	54% 5d2 (3P2)	97% 5d2 (0,2)	52% 5d2 (3P) 3P
72535	72548	-13	78787	6252	74624	2089	0	88% 5d2 (1S) 1S + 12% 5d2 (3P) 3P	88% 5d2 (1S0)	85% 5d2 (0,0)	89% 5d2 (1S) 1S
211877	211812	65	213733	1856	211579	-298	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	98% 5d6s (3/2,1/2)	98% 5d6s (2D) 3D
214275	214344	-69	216254	1979	214009	-266	2	77% 5d6s (2D) 3D + 22% 5d6s (2D) 1D	96% 5d6s (2D3/2)	94% 5d6s (3/2,1/2)	77% 5d6s (2D) 3D
230283	230299	-17	231803	1520	230364	81	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	98% 5d6s (5/2,1/2)	98% 5d6s (2D) 3D
236084	236064	20	238228	2144	236412	328	2	77% 5d6s (2D) 1D + 22% 5d6s (2D) 3D	95% 5d6s (2D5/2)	93% 5d6s (5/2,1/2)	77% 5d6s (2D) 1D
310069	310357	-288	314051	3982	310888	819	2	69% 5d6p (2D) 3Fo + 25% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	97% 5d6p (3/2,1/2)o	68% 5d6p (2D) 3Fo
314764	314469	295	318997	4233	314456	-308	1	65% 5d6p (2D) 3Do + 22% 5d6p (2D) 1Po	96% 5d6p (2D3/2)o	94% 5d6p (3/2,1/2)o	65% 5d6p (2D) 3Do
330855	330896	-41	334637	3782	331369	514	2	47% 5d6p (2D) 3Do + 33% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	94% 5d6p (5/2,1/2)o	47% 5d6p (2D) 3Do
332120	332075	45	336098	3978	333148	1028	3	55% 5d6p (2D) 3Fo + 26% 5d6p (2D) 3Do	96% 5d6p (2D5/2)o	94% 5d6p (5/2,1/2)o	55% 5d6p (2D) 3Fo
345029	344936	93	348370	3341	345942	913	2	40% 5d6p (2D) 3Do + 28% 5d6p (2D) 1Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	39% 5d6p (2D) 3Do
350085	350095	-10	353800	3715	351186	1101	3	44% 5d6p (2D) 3Fo + 30% 5d6p (2D) 1Fo	92% 5d6p (2D3/2)o	89% 5d6p (3/2,3/2)o	42% 5d6p (2D) 3Fo
350993	351077	-84	354836	3843	351634	641	1	60% 5d6p (2D) 3Po + 28% 5d6p (2D) 3Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	60% 5d6p (2D) 3Po
353695	353686	9	357620	3925	354580	885	0	99% 5d6p (2D) 3Po + 1% 5p55d26s (3P) 3Po	99% 5d6p (2D3/2)o	98% 5d6p (3/2,3/2)o	98% 5d6p (2D) 3Po
366094	365981	113	369376	3282	367714	1620	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	98% 5d6p (5/2,3/2)o	98% 5d6p (2D) 3Fo
366809	366736	73	370182	3373	368050	1241	2	59% 5d6p (2D) 3Po + 30% 5d6p (2D) 1Do	96% 5d6p (2D5/2)o	94% 5d6p (5/2,3/2)o	60% 5d6p (2D) 3Po
367446	367670	-224	371128	3682	368814	1368	3	51% 5d6p (2D) 1Fo + 48% 5d6p (2D) 3Do	92% 5d6p (2D5/2)o	89% 5d6p (5/2,3/2)o	52% 5d6p (2D) 1Fo
375151	375129	22	379227	4076	375052	-99	1	65% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	96% 5d6p (5/2,3/2)o	64% 5d6p (2D) 1Po
422093	421526	567	434305	12212	430253	8160	3	56% 5d5f (2D) 3Go + 25% 5p55d3 (2H) 3Go	61% 5d5f (2D3/2)o	64% 5d5f (3/2,5/2)o	62% 5d5f (2D) 3Go
424403	424574	-171	433360	8957	428519	4116	2	21% 5p55d3 (4P) 5So + 19% 5d5f (2D) 3Fo	27% 5d5f (2D3/2)o	54% 5d5f (3/2,5/2)o	35% 5d5f (2D) 3Fo
425349	425278	71	435736	10387	430103	4754	4	48% 5d5f (2D) 1Go + 13% 5d5f (2D) 3Fo	51% 5d5f (2D3/2)o	45% 5d5f (3/2,7/2)o	51% 5d5f (2D) 1Go
425627	427253	-1626	441092	15465	436878	11251	3	21% 5d5f (2D) 3Fo + 16% 5d5f (2D) 3Do	41% 5d5f (2D3/2)o	60% 5d5f (3/2,7/2)o	48% 5d5f (2D) 3Fo
430412	429753	659	439625	9213	434072	3660	4	52% 5d5f (2D) 3Ho + 30% 5d5f (2D) 3Go	57% 5d5f (2D3/2)o	51% 5d5f (3/2,5/2)o	58% 5d5f (2D) 3Ho
438038	431803 ★		448330	10292	443224	5186	1	36% 5d5f (2D) 3Do + 18% 5p55d3 (2F) 3Do	37% 5d5f (2D3/2)o	56% 5d5f (3/2,5/2)o	49% 5d5f (2D) 3Do
435302	435436	-134	436764	1462	440422	5120	2	30% 5d5f (2D) 3Do + 9% 5d5f (2D) 3Po	39% 5d5f (2D3/2)o	34% 5d5f (3/2,7/2)o	33% 5p55d3 (4P) 5So
436230	436460	-230	444746	8516	439680	3450	5	30% 5d5f (2D) 3Ho + 20% 5p55d3 (4F) 5Go	44% 5d5f (2D3/2)o	73% 5d5f (3/2,7/2)o	68% 5d5f (2D) 3Ho
436157	436556	-399	454557	18400	452259	16102	3	23% 5d5f (2D) 3Fo + 13% 5d5f (2D) 3Do	34% 5d5f (2D3/2)o	43% 5d5f (5/2,5/2)o	29% 5d5f (2D) 3Fo
439406	439622	-216	453756	14350	446783	7377	4	24% 5d5f (2D) 1Go + 22% 5d5f (2D) 3Ho	45% 5d5f (2D5/2)o	67% 5d5f (5/2,5/2)o	33% 5d5f (2D) 3Go
442048	442023	25	454323	12275	449925	7877	2	34% 5d5f (2D) 3Fo + 24% 5d5f (2D) 1Do	49% 5d5f (2D5/2)o	42% 5d5f (5/2,5/2)o	26% 5d5f (2D) 3Do
443691	443846	-155	456426	12735	453392	9701	5	39% 5d5f (2D) 3Go + 24% 5d5f (2D) 3Ho	37% 5d5f (2D5/2)o	43% 5d5f (5/2,7/2)o	50% 5d5f (2D) 3Go
	444923		441747		437184		0	97% 6s2 (1S) 1S + 1% 5p55d6s6p (2P) 1S	97% 6s2 (1S0)	96% 6s2 (0,0)	96% 6s2 (1S) 1S
445365	445030	335	450111	4746	449051	3686	4	63% 5d5f (2D) 3Fo + 8% 5p55d3 (2D) 3Fo	60% 5d5f (2D5/2)o	82% 5d5f (5/2,7/2)o	61% 5d5f (2D) 3Fo
	450696				453792		6	74% 5d5f (2D) 3Ho + 24% 5p55d3 (4F) 5Go	74% 5d5f (2D5/2)o
456053	455928	125	465556	9503	459678	3625	1	44% 5d5f (2D) 3Po + 19% 5p55d3 (2D) 3Po	43% 5d5f (2D5/2)o	68% 5d5f (5/2,5/2)o	48% 5d5f (2D) 3Po
456798	456104	694	464849	8051	460122	3324	2	25% 5d5f (2D) 3Po + 15% 5d5f (2D) 3Do	22% 5d5f (2D5/2)o	50% 5d5f (5/2,7/2)o	49% 5d5f (2D) 3Po
456143	456388	-245	465144	9001	460493	4350	0	66% 5d5f (2D) 3Po + 22% 5p55d3 (2D) 3Po	66% 5d5f (2D5/2)o	66% 5d5f (5/2,5/2)o	66% 5d5f (2D) 3Po
461735	462302	-567	468271	6536	464085	2350	3	19% 5d5f (2D) 1Fo + 14% 5p55d3 (2P) 3Do	23% 5d5f (2D5/2)o	43% 5d5f (5/2,7/2)o	52% 5d5f (2D) 1Fo
470214	462376 ★		481815	11601	473757	3543	5	29% 5d5f (2D) 1Ho + 16% 5p55d3 (2G) 1Ho	24% 5d5f (2D5/2)o	22% 5d5f (5/2,5/2)o	21% 5p55d3 (4F) 5Fo
	470533		485216		477574		1	50% 5d5f (2D) 1Po + 9% 5p55d3 (2D) 3Po	53% 5d5f (2D5/2)o	38% 5d5f (5/2,7/2)o	35% 5d5f (2D) 1Po
	535008		531849		527597		0	93% 6s6p (2S) 3Po + 2% 5p55d3 (4P) 5Do	93% 6s6p (2S1/2)o	97% 6s6p (1/2,1/2)o	97% 6s6p (2S) 3Po
	540991		538875		534533		1	88% 6s6p (2S) 3Po + 11% 6s6p (2S) 1Po	91% 6s6p (2S1/2)o	82% 6s6p (1/2,1/2)o	82% 6s6p (2S) 3Po
	570078		568977		565480		2	99% 6s6p (2S) 3Po + 1% 5p55d6s2 (3P) 3Po	99% 6s6p (2S1/2)o	97% 6s6p (1/2,3/2)o	97% 6s6p (2S) 3Po
	592711		593970		589085		1	83% 6s6p (2S) 1Po + 11% 6s6p (2S) 3Po	88% 6s6p (2S1/2)o	80% 6s6p (1/2,3/2)o	78% 6s6p (2S) 1Po
	609950		604745				2	65% 5d7p (2D) 3Fo + 22% 5d7p (2D) 1Do	93% 5d7p (2D3/2)o	95% 5d7p (3/2,1/2)o	66% 5d7p (2D) 3Fo
	610836		607516				1	65% 5d7p (2D) 3Do + 21% 5d7p (2D) 1Po	93% 5d7p (2D3/2)o	87% 5d7p (3/2,1/2)o	63% 5d7p (2D) 3Do
	623853		620569				2	59% 5d7p (2D) 3Do + 11% 5d7p (2D) 3Fo	70% 5d7p (2D3/2)o	69% 5d7p (3/2,3/2)o	54% 5d7p (2D) 3Do
	626063		622277				3	60% 5d7p (2D) 3Fo + 29% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	54% 5d7p (3/2,3/2)o	60% 5d7p (2D) 3Fo
	627103		623149				1	30% 5d7p (2D) 3Po + 24% 5p55d26s (3F) 5Do	48% 5d7p (2D3/2)o	78% 5d7p (3/2,3/2)o	53% 5d7p (2D) 3Po
	628388		623875				0	96% 5d7p (2D) 3Po + 2% 5p55d26s (3F) 5Do	96% 5d7p (2D3/2)o	79% 5d7p (3/2,3/2)o	79% 5d7p (2D) 3Po
	628498		625376				3	29% 5d7p (2D) 3Do + 28% 5d7p (2D) 3Fo	80% 5d7p (2D5/2)o	73% 5d7p (5/2,1/2)o	27% 5d7p (2D) 1Fo
	629481		623517				2	19% 5d7p (2D) 3Po + 16% 5d7p (2D) 1Do	49% 5d7p (2D5/2)o	52% 5d7p (5/2,1/2)o	20% 5d7p (2D) 3Po
	643504		639651				3	36% 5d7p (2D) 3Do + 16% 5d7p (2D) 1Fo	54% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	55% 5d7p (2D) 3Do
	644419		640169				2	24% 5d7p (2D) 3Po + 22% 5d7p (2D) 1Do	51% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	56% 5d7p (2D) 3Po
	645295		640477				4	76% 5d7p (2D) 3Fo + 2% 5p55d3 (2G) 3Fo	76% 5d7p (2D5/2)o	77% 5d7p (5/2,3/2)o	77% 5d7p (2D) 3Fo
	648201		644644				1	62% 5d7p (2D) 1Po + 28% 5d7p (2D) 3Po	95% 5d7p (2D5/2)o	96% 5d7p (5/2,3/2)o	63% 5d7p (2D) 1Po

(a) Experimental energies from [18] and [19]; (b) Our HFR(CV) calculations where the one star symbol stands for a level not included in the fit; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

Table 9. Comparison of the Pt IX energy levels (cm⁻¹) computed in this work using the HFR(CV) and MCDHF methods with the RMBPT values and available experimental data.

Eexp (a)	EHFR (CV) (b)	$\Delta {\mathit{E}}_{\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (c)	EMCDHF (d)	$\Delta {\mathit{E}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (e)	ERMBPT (f)	$\Delta {\mathit{E}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (g)	J	Composition in LS coupling (h)	jjCowan (i)	jjMCDHF (j)	LSMCDHF (k)
0	67	-68	0	0	0	0	2	84% 5d2 (3F) 3F + 14% 5d2 (1D) 1D	84% 5d2 (3F2)	92% 5d2 (0,2)	85% 5d2 (3F) 3F
15253	15232	21	14695	-558	15490	237	3	99% 5d2 (3F) 3F + 1% 5p55d26p (3F) 3F	99% 5d2 (3F3)	98% 5d2 (3/2,5/2)	98% 5d2 (3F) 3F
18617	18522	95	20135	1518	19174	557	0	87% 5d2 (3P) 3P + 12% 5d2 (1S) 1S	87% 5d2 (3P0)	85% 5d2 (0,0)	89% 5d2 (3P) 3P
25362	25309	53	25171	-191	25633	271	4	74% 5d2 (3F) 3F + 25% 5d2 (1G) 1G	74% 5d2 (3F4)	64% 5d2 (3/2,5/2)	77% 5d2 (3F) 3F
25575	25571	4	26377	802	26146	571	2	44% 5d2 (3P) 3P + 43% 5d2 (1D) 1D	44% 5d2 (3P2)	92% 5d2 (3/2,5/2)	46% 5d2 (3P) 3P
28517	28609	-92	29201	684	29238	721	1	99% 5d2 (3P) 3P + 1% 5p55d26p (1G) 3P	99% 5d2 (3P1)	98% 5d2 (3/2,5/2)	98% 5d2 (3P) 3P
41618	41637	-18	42357	739	41949	331	4	74% 5d2 (1G) 1G + 25% 5d2 (3F) 3F	74% 5d2 (1G4)	64% 5d2 (0,4)	77% 5d2 (1G) 1G
44997	44979	18	45676	679	45962	965	2	54% 5d2 (3P) 3P + 42% 5d2 (1D) 1D	54% 5d2 (3P2)	97% 5d2 (0,2)	52% 5d2 (3P) 3P
72535	72548	-13	78787	6252	74624	2089	0	88% 5d2 (1S) 1S + 12% 5d2 (3P) 3P	88% 5d2 (1S0)	85% 5d2 (0,0)	89% 5d2 (1S) 1S
211877	211812	65	213733	1856	211579	-298	1	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D3/2)	98% 5d6s (3/2,1/2)	98% 5d6s (2D) 3D
214275	214344	-69	216254	1979	214009	-266	2	77% 5d6s (2D) 3D + 22% 5d6s (2D) 1D	96% 5d6s (2D3/2)	94% 5d6s (3/2,1/2)	77% 5d6s (2D) 3D
230283	230299	-17	231803	1520	230364	81	3	99% 5d6s (2D) 3D + 1% 5p55d26p (3F) 3D	99% 5d6s (2D5/2)	98% 5d6s (5/2,1/2)	98% 5d6s (2D) 3D
236084	236064	20	238228	2144	236412	328	2	77% 5d6s (2D) 1D + 22% 5d6s (2D) 3D	95% 5d6s (2D5/2)	93% 5d6s (5/2,1/2)	77% 5d6s (2D) 1D
310069	310357	-288	314051	3982	310888	819	2	69% 5d6p (2D) 3Fo + 25% 5d6p (2D) 1Do	99% 5d6p (2D3/2)o	97% 5d6p (3/2,1/2)o	68% 5d6p (2D) 3Fo
314764	314469	295	318997	4233	314456	-308	1	65% 5d6p (2D) 3Do + 22% 5d6p (2D) 1Po	96% 5d6p (2D3/2)o	94% 5d6p (3/2,1/2)o	65% 5d6p (2D) 3Do
330855	330896	-41	334637	3782	331369	514	2	47% 5d6p (2D) 3Do + 33% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	94% 5d6p (5/2,1/2)o	47% 5d6p (2D) 3Do
332120	332075	45	336098	3978	333148	1028	3	55% 5d6p (2D) 3Fo + 26% 5d6p (2D) 3Do	96% 5d6p (2D5/2)o	94% 5d6p (5/2,1/2)o	55% 5d6p (2D) 3Fo
345029	344936	93	348370	3341	345942	913	2	40% 5d6p (2D) 3Do + 28% 5d6p (2D) 1Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	39% 5d6p (2D) 3Do
350085	350095	-10	353800	3715	351186	1101	3	44% 5d6p (2D) 3Fo + 30% 5d6p (2D) 1Fo	92% 5d6p (2D3/2)o	89% 5d6p (3/2,3/2)o	42% 5d6p (2D) 3Fo
350993	351077	-84	354836	3843	351634	641	1	60% 5d6p (2D) 3Po + 28% 5d6p (2D) 3Do	97% 5d6p (2D3/2)o	95% 5d6p (3/2,3/2)o	60% 5d6p (2D) 3Po
353695	353686	9	357620	3925	354580	885	0	99% 5d6p (2D) 3Po + 1% 5p55d26s (3P) 3Po	99% 5d6p (2D3/2)o	98% 5d6p (3/2,3/2)o	98% 5d6p (2D) 3Po
366094	365981	113	369376	3282	367714	1620	4	99% 5d6p (2D) 3Fo + 1% 5p55d26s (1G) 3Fo	99% 5d6p (2D5/2)o	98% 5d6p (5/2,3/2)o	98% 5d6p (2D) 3Fo
366809	366736	73	370182	3373	368050	1241	2	59% 5d6p (2D) 3Po + 30% 5d6p (2D) 1Do	96% 5d6p (2D5/2)o	94% 5d6p (5/2,3/2)o	60% 5d6p (2D) 3Po
367446	367670	-224	371128	3682	368814	1368	3	51% 5d6p (2D) 1Fo + 48% 5d6p (2D) 3Do	92% 5d6p (2D5/2)o	89% 5d6p (5/2,3/2)o	52% 5d6p (2D) 1Fo
375151	375129	22	379227	4076	375052	-99	1	65% 5d6p (2D) 1Po + 27% 5d6p (2D) 3Po	97% 5d6p (2D5/2)o	96% 5d6p (5/2,3/2)o	64% 5d6p (2D) 1Po
422093	421526	567	434305	12212	430253	8160	3	56% 5d5f (2D) 3Go + 25% 5p55d3 (2H) 3Go	61% 5d5f (2D3/2)o	64% 5d5f (3/2,5/2)o	62% 5d5f (2D) 3Go
424403	424574	-171	433360	8957	428519	4116	2	21% 5p55d3 (4P) 5So + 19% 5d5f (2D) 3Fo	27% 5d5f (2D3/2)o	54% 5d5f (3/2,5/2)o	35% 5d5f (2D) 3Fo
425349	425278	71	435736	10387	430103	4754	4	48% 5d5f (2D) 1Go + 13% 5d5f (2D) 3Fo	51% 5d5f (2D3/2)o	45% 5d5f (3/2,7/2)o	51% 5d5f (2D) 1Go
425627	427253	-1626	441092	15465	436878	11251	3	21% 5d5f (2D) 3Fo + 16% 5d5f (2D) 3Do	41% 5d5f (2D3/2)o	60% 5d5f (3/2,7/2)o	48% 5d5f (2D) 3Fo
430412	429753	659	439625	9213	434072	3660	4	52% 5d5f (2D) 3Ho + 30% 5d5f (2D) 3Go	57% 5d5f (2D3/2)o	51% 5d5f (3/2,5/2)o	58% 5d5f (2D) 3Ho
438038	431803 ★		448330	10292	443224	5186	1	36% 5d5f (2D) 3Do + 18% 5p55d3 (2F) 3Do	37% 5d5f (2D3/2)o	56% 5d5f (3/2,5/2)o	49% 5d5f (2D) 3Do
435302	435436	-134	436764	1462	440422	5120	2	30% 5d5f (2D) 3Do + 9% 5d5f (2D) 3Po	39% 5d5f (2D3/2)o	34% 5d5f (3/2,7/2)o	33% 5p55d3 (4P) 5So
436230	436460	-230	444746	8516	439680	3450	5	30% 5d5f (2D) 3Ho + 20% 5p55d3 (4F) 5Go	44% 5d5f (2D3/2)o	73% 5d5f (3/2,7/2)o	68% 5d5f (2D) 3Ho
436157	436556	-399	454557	18400	452259	16102	3	23% 5d5f (2D) 3Fo + 13% 5d5f (2D) 3Do	34% 5d5f (2D3/2)o	43% 5d5f (5/2,5/2)o	29% 5d5f (2D) 3Fo
439406	439622	-216	453756	14350	446783	7377	4	24% 5d5f (2D) 1Go + 22% 5d5f (2D) 3Ho	45% 5d5f (2D5/2)o	67% 5d5f (5/2,5/2)o	33% 5d5f (2D) 3Go
442048	442023	25	454323	12275	449925	7877	2	34% 5d5f (2D) 3Fo + 24% 5d5f (2D) 1Do	49% 5d5f (2D5/2)o	42% 5d5f (5/2,5/2)o	26% 5d5f (2D) 3Do
443691	443846	-155	456426	12735	453392	9701	5	39% 5d5f (2D) 3Go + 24% 5d5f (2D) 3Ho	37% 5d5f (2D5/2)o	43% 5d5f (5/2,7/2)o	50% 5d5f (2D) 3Go
	444923		441747		437184		0	97% 6s2 (1S) 1S + 1% 5p55d6s6p (2P) 1S	97% 6s2 (1S0)	96% 6s2 (0,0)	96% 6s2 (1S) 1S
445365	445030	335	450111	4746	449051	3686	4	63% 5d5f (2D) 3Fo + 8% 5p55d3 (2D) 3Fo	60% 5d5f (2D5/2)o	82% 5d5f (5/2,7/2)o	61% 5d5f (2D) 3Fo
	450696				453792		6	74% 5d5f (2D) 3Ho + 24% 5p55d3 (4F) 5Go	74% 5d5f (2D5/2)o
456053	455928	125	465556	9503	459678	3625	1	44% 5d5f (2D) 3Po + 19% 5p55d3 (2D) 3Po	43% 5d5f (2D5/2)o	68% 5d5f (5/2,5/2)o	48% 5d5f (2D) 3Po
456798	456104	694	464849	8051	460122	3324	2	25% 5d5f (2D) 3Po + 15% 5d5f (2D) 3Do	22% 5d5f (2D5/2)o	50% 5d5f (5/2,7/2)o	49% 5d5f (2D) 3Po
456143	456388	-245	465144	9001	460493	4350	0	66% 5d5f (2D) 3Po + 22% 5p55d3 (2D) 3Po	66% 5d5f (2D5/2)o	66% 5d5f (5/2,5/2)o	66% 5d5f (2D) 3Po
461735	462302	-567	468271	6536	464085	2350	3	19% 5d5f (2D) 1Fo + 14% 5p55d3 (2P) 3Do	23% 5d5f (2D5/2)o	43% 5d5f (5/2,7/2)o	52% 5d5f (2D) 1Fo
470214	462376 ★		481815	11601	473757	3543	5	29% 5d5f (2D) 1Ho + 16% 5p55d3 (2G) 1Ho	24% 5d5f (2D5/2)o	22% 5d5f (5/2,5/2)o	21% 5p55d3 (4F) 5Fo
	470533		485216		477574		1	50% 5d5f (2D) 1Po + 9% 5p55d3 (2D) 3Po	53% 5d5f (2D5/2)o	38% 5d5f (5/2,7/2)o	35% 5d5f (2D) 1Po
	535008		531849		527597		0	93% 6s6p (2S) 3Po + 2% 5p55d3 (4P) 5Do	93% 6s6p (2S1/2)o	97% 6s6p (1/2,1/2)o	97% 6s6p (2S) 3Po
	540991		538875		534533		1	88% 6s6p (2S) 3Po + 11% 6s6p (2S) 1Po	91% 6s6p (2S1/2)o	82% 6s6p (1/2,1/2)o	82% 6s6p (2S) 3Po
	570078		568977		565480		2	99% 6s6p (2S) 3Po + 1% 5p55d6s2 (3P) 3Po	99% 6s6p (2S1/2)o	97% 6s6p (1/2,3/2)o	97% 6s6p (2S) 3Po
	592711		593970		589085		1	83% 6s6p (2S) 1Po + 11% 6s6p (2S) 3Po	88% 6s6p (2S1/2)o	80% 6s6p (1/2,3/2)o	78% 6s6p (2S) 1Po
	609950		604745				2	65% 5d7p (2D) 3Fo + 22% 5d7p (2D) 1Do	93% 5d7p (2D3/2)o	95% 5d7p (3/2,1/2)o	66% 5d7p (2D) 3Fo
	610836		607516				1	65% 5d7p (2D) 3Do + 21% 5d7p (2D) 1Po	93% 5d7p (2D3/2)o	87% 5d7p (3/2,1/2)o	63% 5d7p (2D) 3Do
	623853		620569				2	59% 5d7p (2D) 3Do + 11% 5d7p (2D) 3Fo	70% 5d7p (2D3/2)o	69% 5d7p (3/2,3/2)o	54% 5d7p (2D) 3Do
	626063		622277				3	60% 5d7p (2D) 3Fo + 29% 5d7p (2D) 1Fo	96% 5d7p (2D3/2)o	54% 5d7p (3/2,3/2)o	60% 5d7p (2D) 3Fo
	627103		623149				1	30% 5d7p (2D) 3Po + 24% 5p55d26s (3F) 5Do	48% 5d7p (2D3/2)o	78% 5d7p (3/2,3/2)o	53% 5d7p (2D) 3Po
	628388		623875				0	96% 5d7p (2D) 3Po + 2% 5p55d26s (3F) 5Do	96% 5d7p (2D3/2)o	79% 5d7p (3/2,3/2)o	79% 5d7p (2D) 3Po
	628498		625376				3	29% 5d7p (2D) 3Do + 28% 5d7p (2D) 3Fo	80% 5d7p (2D5/2)o	73% 5d7p (5/2,1/2)o	27% 5d7p (2D) 1Fo
	629481		623517				2	19% 5d7p (2D) 3Po + 16% 5d7p (2D) 1Do	49% 5d7p (2D5/2)o	52% 5d7p (5/2,1/2)o	20% 5d7p (2D) 3Po
	643504		639651				3	36% 5d7p (2D) 3Do + 16% 5d7p (2D) 1Fo	54% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	55% 5d7p (2D) 3Do
	644419		640169				2	24% 5d7p (2D) 3Po + 22% 5d7p (2D) 1Do	51% 5d7p (2D5/2)o	94% 5d7p (5/2,3/2)o	56% 5d7p (2D) 3Po
	645295		640477				4	76% 5d7p (2D) 3Fo + 2% 5p55d3 (2G) 3Fo	76% 5d7p (2D5/2)o	77% 5d7p (5/2,3/2)o	77% 5d7p (2D) 3Fo
	648201		644644				1	62% 5d7p (2D) 1Po + 28% 5d7p (2D) 3Po	95% 5d7p (2D5/2)o	96% 5d7p (5/2,3/2)o	63% 5d7p (2D) 1Po

(a) Experimental energies from [18] and [19]; (b) Our HFR(CV) calculations where the one star symbol stands for a level not included in the fit; (c) ΔE_{HFR (CV)} = E_{HFR (CV)} − E_exp; (d) Our MCDHF-RCI calculations; (e) ΔE_MCDHF = E_MCDHF − E_exp; (f) RMBPT calculations from [21]; (g) ΔE_RMBPT = E_RMBPT − E_exp; (h) Only the first two components in LS coupling computed in our HFR(CV) model are given; (i) Only the first component in jj coupling computed in our HFR(CV) model is given; (j) The first component in jj coupling computed in our MCDHF model is given; (k) The first component in LS coupling computed with the jj2lsj program [32] is given.

After optimizing the radial parts of the 4f, 5s, 5p core orbitals and the 5d, 5f, 6s, 6p, 7p valence orbitals in the odd parity system with the MCDHF method, the square of the large radial part of the corresponding core and valence orbitals was plotted as a function of the radius in Figure 7 only for the two extreme Yb-like ions studied in this work, namely for Ta IV and Pt IX. In Figure 8, we have also plotted the radius, $\langle n_i{l}_i\left|r\right|n_i{l}_i\rangle$ (a₀), of the 4f, 5s, 5p core orbitals and the 5d, 5f, 6s, 6p, 7p valence orbitals that were obtained in the odd parity system with the MCDHF method. We first observed in both figures a collapse of all orbitals along the sequence and especially the valence orbitals move deeper and deeper into the core which explains the importance of taking into account the core-valence correlations in our calculations. We observed the same collapse in the even parity. Then, the radius of the 5f orbital decreases more rapidly along the sequence than the other orbitals moving deeper into the core, swapping with the 6p orbitals and becoming closer and closer to the 6s orbitals which explains the swap of the average energy of the 6s6p and 5d5f odd configurations beyond Re VI in Figure 2. Sugar $et$ $al.$ [15] have already discussed the collapse of the 5f orbital and the resulting difficulties encountered in the fit of the 5d5f configuration.

4. Radiative Atomic Data

We can now evaluate the accuracy of our computed radiative data by benchmarking the HFR+CPOL and the HFR (with CV correlations) methods with the MCDHF method. As already mentioned, transitions with a log($gf$) > -4 were retained. Then, each transition computed with the HFR or the HFR+CPOL method was associated with a cancellation factor ($CF$) which gives the quality of the computed transition probabilities or oscillator strengths. The cancellation factor is defined by [22]

$$\begin{array}{c}\hfill C{F}_{ij}={\left({\displaystyle \frac{|{\sum }_b{\sum }_c{y}_j^b{y}_i^c{\Phi }_c{\mathrm{P}}^{\left(1\right)}{\Phi }_b|}{{\sum }_b{\sum }_c\left|y_j^b{y}_i^c{\Phi }_c{\mathrm{P}}^{\left(1\right)}{\Phi }_b\right|}}\right)}^2,\end{array}$$

(2)

where P⁽¹⁾ is the electric dipole operator for a E1 transition between two pure basis configuration state functions ${\Phi }_b$ and ${\Phi }_c$ and ${\mathrm{y}}_j^b$, ${\mathrm{y}}_i^c$ are the mixing coefficients.

In Figure 9, the $CF$-values of the remaining 221 transitions with log($gf$) > -4 among the 229 transitions observed in experiments in Ta IV are represented as a function of the logarithm of the transition probabilities. The 193, 112, 147 and 129 transitions observed in W V, Re VI, Os VII and Ir VIII, respectively, have all a log($gf$)-value higher than -4 but two of the 131 observed transitions in Pt IX had a computed log($gf$)-value lower than -4.

The $CF$-values smaller than 0.05 [22] indicate severe destructive interference which may lead to significant errors in the computations of the line strengths especially due to important mixing in the composition of the levels involved in the corresponding transitions. In this case, the transition probabilities (or oscillator strengths) are much lower than expected and are thus unreliable. In general, weak transitions are much smaller in the computations due to strong cancellation effects characterized by a $CF$-value below than 0.05. Therefore, strong transitions that have more chance to be observed in the ITER Tokamak are more reliable because they are less affected by cancellation effects due to less mixing in the composition of the levels involved in these strong transitions.

In the same idea, we can define an uncertainty parameter, $dT$ or $dS$, which gives the reliability of the $gA$- (or $gf$-) or S-values computed with the MCDHF method and defined by Ekman $et$ $al.$ [33] , $dT={\displaystyle \frac{|A^B-A^C|}{max(A^B;A^C)}}$ or $dS={\displaystyle \frac{|S^B-S^C|}{max(S^B;S^C)}}$ where $A^B$, $S^B$ and $A^C$, $S^C$ stand for the transition probabilities and line strengths computed in the Babushkin (length) and Coulomb (velocity) gauges, respectively. Actually, the dipole transition moment would be the same whatever the gauge because of the gauge invariance of the electromagnetism theory [34]. If the discrepancy between both gauges is too large for a specific transition, the corresponding computed Einstein coefficient and line strength are thus less accurate. It is preferred to choose the uncertainty parameter $dS$ to describe the discrepancy between both gauges because it is less dependent on the transition energy [35]. The gauge disagreement in the line strengths, $dS$, of all the 355 transitions computed between the configurations of interest with the MCDHF method in Ta IV are plotted as a function of the logarithm of the transitions probabilities in Figure 10. In this figure, one can see the decreasing of the numerical uncertainties for higher transition probabilities as expected. Figure 9 shows an equivalent trend with the $CF$-values for our HFR+CPOL calculation.

Only the transition probabilities computed with the HFR+CPOL, HFR(CV) and MCDHF methods, associated with the lines experimentally identified for which the $CF$-values were higher than 0.05 and the $dS$-values were lower than 0.2 are listed in Table 10, Table 11, Table 12, Table 13, Table 14 and Table 15. In these tables, the transitions are classified in ascending order of measured wavelengths and the measured intensity are also given. The extended tables with all transitions computed with the HFR+CPOL model for Ta IV and W V or with the HFR(CV) model for Re VI, Os VII, Ir VIII and Pt IX are available in DESIRE Database.

4.1. Tantalum and tungsten Yb-like ions

This first part is about evaluating the good quality of the atomic data set computed with the HFR+CPOL and MCDHF methods for Ta IV and W V. Firstly, in the MCDHF calculations (see Section 3.4), we have used two different interaction Hamiltonians namely the Dirac-Coulomb (DC) and the Dirac-Coulomb-Breit (DCB) Hamiltonians to reduce the set of CSFs in the expansion of the ASF. For reminder, 373 720 CSFs and 2 602 097 CSFs were remained for the even and odd parities by using a DC Hamiltonian, respectively, while there were a little bit more CSFs retained with a DCB Hamiltonian, namely 379 960 CSFs and 2 641 560 CSFs for the even and odd parities, respectively. However, we have compared the transition probabilities computed with both sets of CSFs obtained after the reduction and we were able to conclude that the set of CSFs obtained with the DCB Hamiltonian had not significant impact on the transition probabilities computed with the one by considering the DC Hamiltonian. We have represented 354 of the 355 transitions computed by the MCDHF method with both sets of CSFs in Figure 11 where the logarithm of the ratio between the transition probabilities obtained with the DC and DCB reduced CSF sets, $log(g{A}_{MCDHF\left(DC\right)}/g{A}_{MCDHF\left(DCB\right)})$, are plotted as a function of the logarithm of the line strength computed with the DCB reduced CSF set, $log\left(S_{MCDHF\left(DCB\right)}(a.u.)\right)$. The resulting mean ratio, $g{A}_{MCDHF\left(DCB\right)}/g{A}_{MCDHF\left(DC\right)}$ is equal to 1.003 ± 0.074. One transition was not taken into account in Figure 11 and in the calculation of the mean ratio because the corresponding ratio was too high (1163) and the corresponding $dS$-value was equal to 0.999 in both calculations. For the following comparisons with the MCDHF method for all ions studied in this work, we thus used the MCDHF(DC) calculations where the set of CSFs is the smaller one. Indeed, we have seen that the additional CSFs introduced by using a DCB interaction Hamiltonian in the reduction procedure had not significant effects on the transition probabilities as compared to the ones computed with the set of CSFs by using a DC Hamiltonian instead and did not improve the agreement with the HFR+CPOL method.

Secondly, as suggested by Kramida [28], the logarithm of the ratio between the transition probabilities computed by the less accurate MCDHF method and the reference HFR+CPOL method, $log(g{A}_{MCDHF}/g{A}_{HFR+CPOL})$, are plotted as a function of the logarithm of the line strength computed with the HFR+CPOL method, $log\left(S_{HFR+CPOL}(a.u.)\right)$, in Figure 12. Our MCDHF model is expected to be the less accurate because it is purely $ab$ $initio$ with a more limited treatment of the core correlation while our HFR+CPOL model is based on a semi-empirical adjustment of the observed energy levels with a more complete treatment of the core correlation through a core polarization potential and a correction to the dipole transition operator. All the 221 and 193 transitions with log($gf$) > -4 are represented in this figure for Ta IV and W V, respectively.

It still remains 170 transitions among the 221 transitions observed between 551.422 and 3076.058 Å in Ta IV and 158 transitions among the 193 transitions observed in the range 391.566-2187.270 Å for W V associated with a $CF$-value higher than 0.05 and a $dS$-value lower than 0.2. In these two ions, we have already shown that the HFR+CPOL method well reproduced the radiative decay parameters computed with the HFR(CV) method (see Section 3.3) where in the latter the core-valence correlations were introduced explicitly in the calculations while in the former, the core correlation effects were described with a core polarization pseudo-potential. Indeed, the mean ratio $g{A}_{HFR\left(CV\right)}/g{A}_{HFR+CPOL}$ = 1.08 ± 0.42 and 1.02 ± 0.36 for Ta IV and W V, respectively.

In order to quantify the agreement between our two models, i.e., HFR+CPOL and MCDHF, and the uncertainties of our radiative decay rates, we have computed the ratio $g{A}_{MCDHF}/g{A}_{HFR+CPOL}$ and the relative deviation $\Delta gA$/max($g{A}_{HFR+CPOL},g{A}_{MCDHF}$) where $\Delta gA=|g{A}_{HFR+CPOL}-g{A}_{MCDHF}|$. In Table 10 and Table 11 are tabulated the 170 and 158 transitions for Ta IV and W V, respectively, where the transitions with one star ’*’ presented a ratio in the range [0.2,5] but a relative deviation bigger than 50%, the transitions with a double star ’**’ have a ratio outside the range [0.2,5] but a relative deviation lower than 50% and the transitions with a triple star ’***’ presented a ratio outside the range [0.2,5] as well as a relative deviation bigger than 50%. Actually, all transitions in Ta IV with a ratio lower than 0.2 or higher than 5 have also a relative deviation bigger than 50% while in W V all transitions have a ratio in the range [0.2,5] but only three have a relative deviation slightly higher than 50%. It means that even though these transitions are reliable in the sense that the $CF$- and $dS$-values are higher than 0.05 and lower than 0.2, respectively, the radiative decay rates (and oscillator strengths) with at least one star should be treated with care. Among these 170 and 158 transitions, we observed that it still remains 150 and 155 transitions which have a mean ratio in the range [0.2,5] and also a mean relative deviation lower than 50% for Ta IV and W V, respectively. In Ta IV, the mean ratio, $g{A}_{MCDHF}/g{A}_{HFR+CPOL}$, and the mean relative deviation $\Delta gA$/max($g{A}_{HFR+CPOL},g{A}_{MCDHF}$) (%) for the remaining 150 transitions are found to be 1.18 ± 0.25 and 19.9 ± 10.6 %, respectively. For the remaining 155 transitions in W V, the same parameters are equal to 1.08 ± 0.23 and 15.8 ± 11.1 %, respectively. Notice that we have obtained the same results by using a DCB Hamiltonian. Even though the MCDHF approach is purely $ab$ $initio$, we observed a very good agreement between our two models, namely HFR+CPOL and MCDHF, for a large number of transitions outlined by a mean ratio near to one. It highlights the importance of considering CV and CC correlations in the MCDHF method to well reproduce the realistic level structure and so to minimize the uncertainty on the transition probabilities which is estimated on average at 20% and 16% for Ta IV and W V, respectively.

Table 10. Transition probabilities for the selected 170 experimentally observed lines in Ta IV.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
551.422	10555.3	2	191903	1	2	8.94	7.69	6.55	10.98
554.029	0	2	180496	3	20	42.20	27.10	25.00	38.37
555.423	8576.4	4	188618	3	8	19.50	15.30	8.47	14.98
556.435	8576.4	4	188291	4	13	31.90	23.40	15.90	20.56
556.888	0	2	179568	1	17	41.80	30.50	26.40	28.69
558.799	4542.9	3	183499	2	15	42.30	31.20***	33.40	3.68
562.891	4542.9	3	182200	3	8	27.70	21.50*	2.63	53.05
565.499	4542.9	3	181380	2	17	27.20	19.00	13.70	28.94
567.691	8576.4	4	184728	3	12	45.50	32.60	28.70	37.05
568.340	4542.9	3	180496	3	77	136.00	87.30	98.60	62.37
569.222	4542.9	3	180222	4	99	740.00	488.00	486.00	545.90
570.688	0	3	175230	3	99	123.00	83.90	93.00	103.35
573.739	17607.8	2	191903	1	6	15.10	11.70	10.50	13.42
574.556	10555.3	2	184605	1	15	15.90	13.20	14.80	21.63
575.063	4542.9	3	178438	4	77	73.20	47.00	61.20	62.82
575.293	0	2	173827	3	90	307.00	209.00	241.00	247.23
575.583	10555.3	2	184290	2	7	14.60	11.30*	10.50	29.49
576.576	11166.5	0	184605	1	4	11.00	6.67	8.56	6.15
577.641	0	2	173119	2	80	243.00	160.00	164.00	151.90
578.221	10555.3	2	183499	2	30	76.30	51.00*	36.20	16.44
579.875	8576.4	4	181028	5	99	1320.00	870.00	910.00	1044.56
580.408	13599.1	1	185885	1	28	46.50	28.60	16.70	17.47
580.889	10555.3	2	182706	3	28	110.00	74.90	60.40	58.35
582.592	8576.4	4	180222	4	85	289.00	191.00	203.00	215.90
582.867	13599.1	1	184290	2	30	38.60	26.30	16.80	45.53
584.206	17607.8	2	188780	2	24	77.50	54.80	44.70	65.36
584.768	13599.1	1	184605	1	75	82.40	60.20	65.00	84.54
584.769	17607.8	2	188618	3	30	48.10	35.10	28.00	63.92
585.394	10555.3	2	181380	2	20	61.50	39.30	23.30	68.68
585.872	4542.9	3	175230	3	80	123.00	83.90	93.00	103.35
586.453	11166.5	0	181681	1	7	18.20	12.70	5.72	18.49
586.851	18217.5	4	188618	3	20	51.70	38.40	37.00	47.52
588.433	10555.3	2	180496	3	90	354.00	234.00	260.00	167.22
588.575	13599.1	1	183499	2	18	48.30	35.20*	32.70	15.03
588.715	8576.4	4	178438	4	80	127.00	82.30	78.50	104.62
589.685	10555.3	2	180137	2	70	79.80	53.70*	76.90	22.30
590.726	4542.9	3	173827	3	75	105.00	67.00	59.90	72.03
591.961	4542.9	3	173475	4	85	324.00	217.00	217.00	240.53
592.775	13599.1	1	182297	0	6	13.70	8.66***	12.00	1.58
593.227	4542.9	3	173119	2	23	10.70	6.87	6.12	7.39
593.817	11166.5	0	179568	1	30	127.00	88.90	81.00	107.17
594.948	13599.1	1	181681	1	25	43.60	28.10	34.90	14.09
595.791	4542.9	3	172386	4	30	91.10	59.60	78.80	100.36
596.012	13599.1	1	181380	2	24	41.50	25.90*	16.80	72.84
598.711	18217.5	4	185243	5	90	1450.00	983.00	1100.00	1173.57
598.810	17607.8	2	184605	1	55	66.50	44.10	47.50	52.14
600.456	13599.1	1	180137	2	70	74.20	51.30*	68.90	22.10
601.484	8576.4	4	174832	5	85	214.00	143.00	162.00	178.70
602.519	13599.1	1	179568	1	12	7.50	5.38*	6.80	11.75
602.799	17607.8	2	183499	2	70	232.00	157.00***	180.00	13.87
602.842	10555.3	2	176438	2	70	114.00	76.70***	81.90	11.34
605.698	17607.8	2	182706	3	37	299.00	221.00	105.00	370.57
605.831	11166.5	0	176228	1	30	85.30	55.60	73.00	33.54
606.429	8576.4	4	173475	4	35	19.80	13.10	8.99	8.26
607.251	10555.3	2	175230	3	70	124.00	83.50	98.70	93.99
607.555	17607.8	2	182200	3	75	274.00	164.00*	310.00	55.67
609.480	17607.8	2	181681	1	5	4.94	3.36***	6.30	0.67
610.462	8576.4	4	172386	4	30	63.40	41.60	44.00	43.24
610.606	17607.8	2	181380	2	30	94.40	62.90	56.70	44.49
610.847	13599.1	1	177309	2	7	8.52	5.42***	1.55	141.46
612.467	10555.3	2	173827	3	80	116.00	75.80	76.90	86.34
614.101	13599.1	1	176438	2	85	220.00	148.00***	168.00	29.59
614.207	18217.5	4	181028	5	30	17.70	11.60	13.70	14.01
614.892	13599.1	1	176228	1	16	10.90	7.06	9.27	5.39
615.141	10555.3	2	173119	2	40	16.60	11.70	14.10	16.69
624.132	18217.5	4	178438	4	85	163.00	110.00	105.00	98.15
626.884	13599.1	1	173119	2	40	11.10	7.30	8.42	8.46
635.616	34573.8	0	191903	1	45	52.40	40.40	36.50	53.91
636.889	18217.5	4	175230	3	6	5.58	4.08	6.44	4.02
638.512	18217.5	4	174832	5	80	75.10	51.50	55.60	68.30
640.133	17607.8	2	173827	3	40	14.40	9.66	11.30	12.46
644.100	18217.5	4	173475	4	10	8.92	6.21	3.71	3.59
648.637	18217.5	4	172386	4	30	84.70	56.20	60.60	67.82
648.656	18217.5	4	172386	4	75	84.70	56.20	60.60	67.82
660.891	34573.8	0	185885	1	13	84.60	58.20	74.70	47.61
666.536	34573.8	0	184605	1	12	30.00	16.80*	11.30	4.14
679.775	34573.8	0	181681	1	18	6.93	4.49	4.52	3.56
710.862	41528.4	2	182200	3	25	4.55	3.78***	9.09	0.34
718.976	34390.9	3	173475	4	30	0.12	0.06	0.07	0.07
719.587	41528.4	2	180496	3	30	5.88	5.35	5.07	5.02
724.427	41528.4	2	179568	1	35	1.07	0.78	1.04	0.83
766.720	11166.5	0	141593.2	1	2	1.32	1.01	1.37	0.75
855.191	68952.3	0	185885	1	54	4.73	4.72	8.86	7.12
864.646	68952.3	0	184605	1	60	0.55	0.51*	0.41	0.25
904.045	68952.3	0	179568	1	40	1.33	1.20	1.43	1.37
934.410	34573.8	0	141593.2	1	32	13.50	10.60*	17.00	21.80
999.340	41528.4	2	141593.2	1	67	95.90	81.70	79.70	98.06
1045.310	28324.6	1	123989.2	2	25	1.53	1.28	1.08	1.21
1048.310	4542.9	3	99934.6	3	61	3.51	3.12	3.00	2.41
1063.530	29962.3	2	123989.2	2	65	20.00	16.60	14.20	16.72
1067.170	4542.9	3	98248.7	2	68	6.50	5.78	5.68	5.08
1074.470	0	2	93068.5	1	71	9.17	8.05	7.98	7.86
1079.190	0	2	92661.5	3	16	0.37	0.37	0.32	0.31
1086.390	4542.9	3	96591.2	4	71	4.87	4.23	4.06	4.57
1094.600	8576.4	4	99934.6	3	72	10.00	9.43	8.79	8.63
1100.130	10555.3	2	101452.8	1	68	4.75	4.61	4.11	3.90
1107.590	11166.5	0	101452.8	1	66	2.88	2.53	2.47	3.37
1116.100	34390.9	3	123989.2	2	79	98.80	82.90	71.90	91.29
1118.830	10555.3	2	99934.6	3	71	5.62	4.20	4.83	5.71
1136.170	8576.4	4	96591.2	4	78	60.00	52.10	50.40	60.61
1138.260	13599.1	1	101452.8	1	66	2.27	1.95	1.87	2.20
1149.720	0	2	86977.8	3	75	3.19	2.72	2.65	3.36
1150.420	28324.6	1	115249.4	1	75	18.10	15.00	12.50	16.83
1172.510	29962.3	2	115249.4	1	76	47.20	39.50	33.70	47.34
1175.510	4542.9	3	89612.1	2	85	48.20	42.70	42.40	50.83
1181.340	13599.1	1	98248.7	2	12	7.57	6.59	6.44	8.03
1189.280	8576.4	4	92661.5	3	80	96.10	84.50	83.40	104.13
1192.530	28324.6	1	112180.1	0	78	22.40	18.50	15.40	22.06
1192.670	17607.8	2	101452.8	1	80	11.30	10.30	9.64	11.45
1211.940	10555.3	2	93068.5	1	78	13.50	12.20	11.60	13.50
1212.680	41528.4	2	123989.2	2	80	1.19	0.97	0.75	0.86
1213.090	4542.9	3	86977.8	3	85	42.20	36.80	35.80	45.35
1215.530	4542.9	3	86811.6	2	85	25.90	22.60	21.70	28.55
1220.730	0	2	81917.4	1	80	36.20	32.10	31.20	40.94
1220.960	11166.5	0	93068.5	1	80	4.93	4.33	4.25	4.91
1223.730	18217.5	4	99934.6	3	90	133.00	117.00	116.00	138.17
1238.120	13599.1	1	94366.8	0	88	11.90	10.60	10.50	12.50
1240.060	17607.8	2	98248.7	2	95	55.00	48.40	47.70	57.08
1258.340	13599.1	1	93068.5	1	87	8.97	8.06	8.05	9.55
1264.910	10555.3	2	89612.1	2	94	27.50	23.50	22.80	27.74
1272.420	0	2	78590.5	2	98	33.60	29.10	28.30	34.13
1275.480	8576.4	4	86977.8	3	94	9.41	8.17	8.11	10.01
1275.940	18217.5	4	96591.2	4	86	2.62	2.27	2.24	2.23
1308.510	10555.3	2	86977.8	3	92	1.25	1.18	1.15	1.34
1311.350	10555.3	2	86811.6	2	85	29.50	25.60	25.50	29.81
1315.580	13599.1	1	89612.1	2	87	1.42	1.33	1.44	1.56
1329.190	17607.8	2	93068.5	1	81	3.37	2.95	3.17	3.84
1332.380	17607.8	2	92661.5	3	92	8.48	7.25	7.72	9.57
1343.300	18217.5	4	92661.5	3	86	10.60	10.00	9.56	8.91
1365.880	13599.1	1	86811.6	2	92	10.20	9.18	9.11	10.65
1376.620	68952.3	0	141593.2	1	79	79.20	62.70	64.30	74.08
1398.780	29962.3	2	101452.8	1	91	6.47	5.16	5.80	7.58
1413.400	11166.5	0	81917.4	1	93	5.60	5.06	5.06	5.96
1430.110	28324.6	1	98248.7	2	79	0.74	0.60	0.63	0.76
1441.540	17607.8	2	86977.8	3	83	0.80	0.70	0.74	1.06
1454.320	18217.5	4	86977.8	3	91	3.42	3.06	2.91	2.75
1464.410	29962.3	2	98248.7	2	92	18.10	14.70	15.80	19.54
1469.820	10555.3	2	78590.5	2	93	7.00	5.78	6.09	9.82
1495.250	34573.8	0	101452.8	1	90	9.23	8.18	8.25	9.08
1514.190	28324.6	1	94366.8	0	95	10.40	8.45	9.71	11.11
1525.690	34390.9	3	99934.6	3	70	26.30	21.40	20.30	19.69
1544.540	28324.6	1	93068.5	1	60	24.00	19.40	20.10	22.84
1565.970	34390.9	3	98248.7	2	82	21.50	17.40	19.70	26.91
1584.650	29962.3	2	93068.5	1	82	6.11	5.05	6.12	7.55
1594.910	29962.3	2	92661.5	3	84	54.00	43.00	42.20	52.66
1607.700	34390.9	3	96591.2	4	85	107.00	85.20	85.40	109.09
1631.650	28324.6	1	89612.1	2	84	31.10	24.70	24.50	32.12
1639.820	17607.8	2	78590.5	2	79	0.90	0.70	0.75	1.24
1668.760	41528.4	2	101452.8	1	84	22.80	18.70	19.80	23.64
1676.450	29962.3	2	89612.1	2	84	14.20	11.50	11.00	12.60
1709.570	34573.8	0	93068.5	1	54	0.64	0.54	0.54	0.81
1712.160	41528.4	2	99934.6	3	85	46.30	37.40	38.50	52.55
1716.130	34390.9	3	92661.5	3	85	20.90	16.50	16.10	23.95
1753.900	29962.3	2	86977.8	3	82	22.80	18.30	18.40	25.26
1759.040	29962.3	2	86811.6	2	82	6.29	4.88	4.61	7.67
1763.030	41528.4	2	98248.7	2	79	11.60	9.28	8.75	9.15
1810.900	34390.9	3	89612.1	2	69	0.85	0.69	0.68	0.84
1865.930	28324.6	1	81917.4	1	83	8.75	6.92	6.57	10.00
1901.630	34390.9	3	86977.8	3	84	24.70	19.50	19.40	27.18
1907.660	34390.9	3	86811.6	2	84	18.30	14.80	15.20	18.57
1924.750	29962.3	2	81917.4	1	84	11.60	9.35	9.51	12.02
1940.250	41528.4	2	93068.5	1	77	1.32	1.05	1.06	1.58
1989.450	28324.6	1	78590.5	2	82	14.70	11.80	11.60	14.98
2055.750	29962.3	2	78590.5	2	85	10.80	8.55	8.36	11.16
2079.010	41528.4	2	89612.1	2	83	3.26	2.55	2.30	3.25
2111.530	34573.8	0	81917.4	1	75	0.30	0.27	0.26	0.32
2207.640	41528.4	2	86811.6	2	90	7.07	5.59	5.25	6.96
2475.310	41528.4	2	81917.4	1	35	0.44	0.37	0.41	0.47
2697.420	41528.4	2	78590.5	2	68	1.28	1.00	0.94	1.58
3076.060	68952.3	0	101452.8	1	10	0.48	0.35	0.26	0.32

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [8], [9] and [10]; (e) Our HFR, HFR+CPOL, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 10. Transition probabilities for the selected 170 experimentally observed lines in Ta IV.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
551.422	10555.3	2	191903	1	2	8.94	7.69	6.55	10.98
554.029	0	2	180496	3	20	42.20	27.10	25.00	38.37
555.423	8576.4	4	188618	3	8	19.50	15.30	8.47	14.98
556.435	8576.4	4	188291	4	13	31.90	23.40	15.90	20.56
556.888	0	2	179568	1	17	41.80	30.50	26.40	28.69
558.799	4542.9	3	183499	2	15	42.30	31.20***	33.40	3.68
562.891	4542.9	3	182200	3	8	27.70	21.50*	2.63	53.05
565.499	4542.9	3	181380	2	17	27.20	19.00	13.70	28.94
567.691	8576.4	4	184728	3	12	45.50	32.60	28.70	37.05
568.340	4542.9	3	180496	3	77	136.00	87.30	98.60	62.37
569.222	4542.9	3	180222	4	99	740.00	488.00	486.00	545.90
570.688	0	3	175230	3	99	123.00	83.90	93.00	103.35
573.739	17607.8	2	191903	1	6	15.10	11.70	10.50	13.42
574.556	10555.3	2	184605	1	15	15.90	13.20	14.80	21.63
575.063	4542.9	3	178438	4	77	73.20	47.00	61.20	62.82
575.293	0	2	173827	3	90	307.00	209.00	241.00	247.23
575.583	10555.3	2	184290	2	7	14.60	11.30*	10.50	29.49
576.576	11166.5	0	184605	1	4	11.00	6.67	8.56	6.15
577.641	0	2	173119	2	80	243.00	160.00	164.00	151.90
578.221	10555.3	2	183499	2	30	76.30	51.00*	36.20	16.44
579.875	8576.4	4	181028	5	99	1320.00	870.00	910.00	1044.56
580.408	13599.1	1	185885	1	28	46.50	28.60	16.70	17.47
580.889	10555.3	2	182706	3	28	110.00	74.90	60.40	58.35
582.592	8576.4	4	180222	4	85	289.00	191.00	203.00	215.90
582.867	13599.1	1	184290	2	30	38.60	26.30	16.80	45.53
584.206	17607.8	2	188780	2	24	77.50	54.80	44.70	65.36
584.768	13599.1	1	184605	1	75	82.40	60.20	65.00	84.54
584.769	17607.8	2	188618	3	30	48.10	35.10	28.00	63.92
585.394	10555.3	2	181380	2	20	61.50	39.30	23.30	68.68
585.872	4542.9	3	175230	3	80	123.00	83.90	93.00	103.35
586.453	11166.5	0	181681	1	7	18.20	12.70	5.72	18.49
586.851	18217.5	4	188618	3	20	51.70	38.40	37.00	47.52
588.433	10555.3	2	180496	3	90	354.00	234.00	260.00	167.22
588.575	13599.1	1	183499	2	18	48.30	35.20*	32.70	15.03
588.715	8576.4	4	178438	4	80	127.00	82.30	78.50	104.62
589.685	10555.3	2	180137	2	70	79.80	53.70*	76.90	22.30
590.726	4542.9	3	173827	3	75	105.00	67.00	59.90	72.03
591.961	4542.9	3	173475	4	85	324.00	217.00	217.00	240.53
592.775	13599.1	1	182297	0	6	13.70	8.66***	12.00	1.58
593.227	4542.9	3	173119	2	23	10.70	6.87	6.12	7.39
593.817	11166.5	0	179568	1	30	127.00	88.90	81.00	107.17
594.948	13599.1	1	181681	1	25	43.60	28.10	34.90	14.09
595.791	4542.9	3	172386	4	30	91.10	59.60	78.80	100.36
596.012	13599.1	1	181380	2	24	41.50	25.90*	16.80	72.84
598.711	18217.5	4	185243	5	90	1450.00	983.00	1100.00	1173.57
598.810	17607.8	2	184605	1	55	66.50	44.10	47.50	52.14
600.456	13599.1	1	180137	2	70	74.20	51.30*	68.90	22.10
601.484	8576.4	4	174832	5	85	214.00	143.00	162.00	178.70
602.519	13599.1	1	179568	1	12	7.50	5.38*	6.80	11.75
602.799	17607.8	2	183499	2	70	232.00	157.00***	180.00	13.87
602.842	10555.3	2	176438	2	70	114.00	76.70***	81.90	11.34
605.698	17607.8	2	182706	3	37	299.00	221.00	105.00	370.57
605.831	11166.5	0	176228	1	30	85.30	55.60	73.00	33.54
606.429	8576.4	4	173475	4	35	19.80	13.10	8.99	8.26
607.251	10555.3	2	175230	3	70	124.00	83.50	98.70	93.99
607.555	17607.8	2	182200	3	75	274.00	164.00*	310.00	55.67
609.480	17607.8	2	181681	1	5	4.94	3.36***	6.30	0.67
610.462	8576.4	4	172386	4	30	63.40	41.60	44.00	43.24
610.606	17607.8	2	181380	2	30	94.40	62.90	56.70	44.49
610.847	13599.1	1	177309	2	7	8.52	5.42***	1.55	141.46
612.467	10555.3	2	173827	3	80	116.00	75.80	76.90	86.34
614.101	13599.1	1	176438	2	85	220.00	148.00***	168.00	29.59
614.207	18217.5	4	181028	5	30	17.70	11.60	13.70	14.01
614.892	13599.1	1	176228	1	16	10.90	7.06	9.27	5.39
615.141	10555.3	2	173119	2	40	16.60	11.70	14.10	16.69
624.132	18217.5	4	178438	4	85	163.00	110.00	105.00	98.15
626.884	13599.1	1	173119	2	40	11.10	7.30	8.42	8.46
635.616	34573.8	0	191903	1	45	52.40	40.40	36.50	53.91
636.889	18217.5	4	175230	3	6	5.58	4.08	6.44	4.02
638.512	18217.5	4	174832	5	80	75.10	51.50	55.60	68.30
640.133	17607.8	2	173827	3	40	14.40	9.66	11.30	12.46
644.100	18217.5	4	173475	4	10	8.92	6.21	3.71	3.59
648.637	18217.5	4	172386	4	30	84.70	56.20	60.60	67.82
648.656	18217.5	4	172386	4	75	84.70	56.20	60.60	67.82
660.891	34573.8	0	185885	1	13	84.60	58.20	74.70	47.61
666.536	34573.8	0	184605	1	12	30.00	16.80*	11.30	4.14
679.775	34573.8	0	181681	1	18	6.93	4.49	4.52	3.56
710.862	41528.4	2	182200	3	25	4.55	3.78***	9.09	0.34
718.976	34390.9	3	173475	4	30	0.12	0.06	0.07	0.07
719.587	41528.4	2	180496	3	30	5.88	5.35	5.07	5.02
724.427	41528.4	2	179568	1	35	1.07	0.78	1.04	0.83
766.720	11166.5	0	141593.2	1	2	1.32	1.01	1.37	0.75
855.191	68952.3	0	185885	1	54	4.73	4.72	8.86	7.12
864.646	68952.3	0	184605	1	60	0.55	0.51*	0.41	0.25
904.045	68952.3	0	179568	1	40	1.33	1.20	1.43	1.37
934.410	34573.8	0	141593.2	1	32	13.50	10.60*	17.00	21.80
999.340	41528.4	2	141593.2	1	67	95.90	81.70	79.70	98.06
1045.310	28324.6	1	123989.2	2	25	1.53	1.28	1.08	1.21
1048.310	4542.9	3	99934.6	3	61	3.51	3.12	3.00	2.41
1063.530	29962.3	2	123989.2	2	65	20.00	16.60	14.20	16.72
1067.170	4542.9	3	98248.7	2	68	6.50	5.78	5.68	5.08
1074.470	0	2	93068.5	1	71	9.17	8.05	7.98	7.86
1079.190	0	2	92661.5	3	16	0.37	0.37	0.32	0.31
1086.390	4542.9	3	96591.2	4	71	4.87	4.23	4.06	4.57
1094.600	8576.4	4	99934.6	3	72	10.00	9.43	8.79	8.63
1100.130	10555.3	2	101452.8	1	68	4.75	4.61	4.11	3.90
1107.590	11166.5	0	101452.8	1	66	2.88	2.53	2.47	3.37
1116.100	34390.9	3	123989.2	2	79	98.80	82.90	71.90	91.29
1118.830	10555.3	2	99934.6	3	71	5.62	4.20	4.83	5.71
1136.170	8576.4	4	96591.2	4	78	60.00	52.10	50.40	60.61
1138.260	13599.1	1	101452.8	1	66	2.27	1.95	1.87	2.20
1149.720	0	2	86977.8	3	75	3.19	2.72	2.65	3.36
1150.420	28324.6	1	115249.4	1	75	18.10	15.00	12.50	16.83
1172.510	29962.3	2	115249.4	1	76	47.20	39.50	33.70	47.34
1175.510	4542.9	3	89612.1	2	85	48.20	42.70	42.40	50.83
1181.340	13599.1	1	98248.7	2	12	7.57	6.59	6.44	8.03
1189.280	8576.4	4	92661.5	3	80	96.10	84.50	83.40	104.13
1192.530	28324.6	1	112180.1	0	78	22.40	18.50	15.40	22.06
1192.670	17607.8	2	101452.8	1	80	11.30	10.30	9.64	11.45
1211.940	10555.3	2	93068.5	1	78	13.50	12.20	11.60	13.50
1212.680	41528.4	2	123989.2	2	80	1.19	0.97	0.75	0.86
1213.090	4542.9	3	86977.8	3	85	42.20	36.80	35.80	45.35
1215.530	4542.9	3	86811.6	2	85	25.90	22.60	21.70	28.55
1220.730	0	2	81917.4	1	80	36.20	32.10	31.20	40.94
1220.960	11166.5	0	93068.5	1	80	4.93	4.33	4.25	4.91
1223.730	18217.5	4	99934.6	3	90	133.00	117.00	116.00	138.17
1238.120	13599.1	1	94366.8	0	88	11.90	10.60	10.50	12.50
1240.060	17607.8	2	98248.7	2	95	55.00	48.40	47.70	57.08
1258.340	13599.1	1	93068.5	1	87	8.97	8.06	8.05	9.55
1264.910	10555.3	2	89612.1	2	94	27.50	23.50	22.80	27.74
1272.420	0	2	78590.5	2	98	33.60	29.10	28.30	34.13
1275.480	8576.4	4	86977.8	3	94	9.41	8.17	8.11	10.01
1275.940	18217.5	4	96591.2	4	86	2.62	2.27	2.24	2.23
1308.510	10555.3	2	86977.8	3	92	1.25	1.18	1.15	1.34
1311.350	10555.3	2	86811.6	2	85	29.50	25.60	25.50	29.81
1315.580	13599.1	1	89612.1	2	87	1.42	1.33	1.44	1.56
1329.190	17607.8	2	93068.5	1	81	3.37	2.95	3.17	3.84
1332.380	17607.8	2	92661.5	3	92	8.48	7.25	7.72	9.57
1343.300	18217.5	4	92661.5	3	86	10.60	10.00	9.56	8.91
1365.880	13599.1	1	86811.6	2	92	10.20	9.18	9.11	10.65
1376.620	68952.3	0	141593.2	1	79	79.20	62.70	64.30	74.08
1398.780	29962.3	2	101452.8	1	91	6.47	5.16	5.80	7.58
1413.400	11166.5	0	81917.4	1	93	5.60	5.06	5.06	5.96
1430.110	28324.6	1	98248.7	2	79	0.74	0.60	0.63	0.76
1441.540	17607.8	2	86977.8	3	83	0.80	0.70	0.74	1.06
1454.320	18217.5	4	86977.8	3	91	3.42	3.06	2.91	2.75
1464.410	29962.3	2	98248.7	2	92	18.10	14.70	15.80	19.54
1469.820	10555.3	2	78590.5	2	93	7.00	5.78	6.09	9.82
1495.250	34573.8	0	101452.8	1	90	9.23	8.18	8.25	9.08
1514.190	28324.6	1	94366.8	0	95	10.40	8.45	9.71	11.11
1525.690	34390.9	3	99934.6	3	70	26.30	21.40	20.30	19.69
1544.540	28324.6	1	93068.5	1	60	24.00	19.40	20.10	22.84
1565.970	34390.9	3	98248.7	2	82	21.50	17.40	19.70	26.91
1584.650	29962.3	2	93068.5	1	82	6.11	5.05	6.12	7.55
1594.910	29962.3	2	92661.5	3	84	54.00	43.00	42.20	52.66
1607.700	34390.9	3	96591.2	4	85	107.00	85.20	85.40	109.09
1631.650	28324.6	1	89612.1	2	84	31.10	24.70	24.50	32.12
1639.820	17607.8	2	78590.5	2	79	0.90	0.70	0.75	1.24
1668.760	41528.4	2	101452.8	1	84	22.80	18.70	19.80	23.64
1676.450	29962.3	2	89612.1	2	84	14.20	11.50	11.00	12.60
1709.570	34573.8	0	93068.5	1	54	0.64	0.54	0.54	0.81
1712.160	41528.4	2	99934.6	3	85	46.30	37.40	38.50	52.55
1716.130	34390.9	3	92661.5	3	85	20.90	16.50	16.10	23.95
1753.900	29962.3	2	86977.8	3	82	22.80	18.30	18.40	25.26
1759.040	29962.3	2	86811.6	2	82	6.29	4.88	4.61	7.67
1763.030	41528.4	2	98248.7	2	79	11.60	9.28	8.75	9.15
1810.900	34390.9	3	89612.1	2	69	0.85	0.69	0.68	0.84
1865.930	28324.6	1	81917.4	1	83	8.75	6.92	6.57	10.00
1901.630	34390.9	3	86977.8	3	84	24.70	19.50	19.40	27.18
1907.660	34390.9	3	86811.6	2	84	18.30	14.80	15.20	18.57
1924.750	29962.3	2	81917.4	1	84	11.60	9.35	9.51	12.02
1940.250	41528.4	2	93068.5	1	77	1.32	1.05	1.06	1.58
1989.450	28324.6	1	78590.5	2	82	14.70	11.80	11.60	14.98
2055.750	29962.3	2	78590.5	2	85	10.80	8.55	8.36	11.16
2079.010	41528.4	2	89612.1	2	83	3.26	2.55	2.30	3.25
2111.530	34573.8	0	81917.4	1	75	0.30	0.27	0.26	0.32
2207.640	41528.4	2	86811.6	2	90	7.07	5.59	5.25	6.96
2475.310	41528.4	2	81917.4	1	35	0.44	0.37	0.41	0.47
2697.420	41528.4	2	78590.5	2	68	1.28	1.00	0.94	1.58
3076.060	68952.3	0	101452.8	1	10	0.48	0.35	0.26	0.32

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [8], [9] and [10]; (e) Our HFR, HFR+CPOL, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 11. Transition probabilities for the selected 155 experimentally observed lines in W V.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
391.566	13742	2	269124	1	7	12.40	9.65	8.97	11.98
392.941	11519	4	266010	4	27	34.70	27.00	27.20	34.83
393.375	11519	4	265733	3	11	36.60	25.90	13.40	22.00
393.480	6245	3	260388	3	12	18.10	14.20	13.30	10.30
395.575	0	2	252797	1	30	61.50	43.50	28.40	24.44
397.379	6245	3	257895	3	15	12.20	9.95	11.90	14.83
398.234	0	2	251112	2	23	26.90	21.00	21.70	17.48
399.295	6245	3	256688	2	35	73.70	52.30	37.60	47.99
400.095	16331	1	266271	2	6	7.15	5.47	4.77	6.11
401.824	11519	4	260388	3	25	69.70	51.10	37.40	42.07
405.441	13742	2	260388	3	17	45.30	29.20	13.00	27.57
405.666	22615	2	269124	1	13	27.90	20.80	18.40	25.32
405.882	11519	4	257895	3	23	37.20	26.00	20.70	22.30
406.017	13742	2	260035	2	15	27.10	20.20	21.30	16.18
406.600	12839	0	258778	1	6	6.46	5.20	5.03	4.70
408.106	13742	2	258778	1	20	40.20	28.30	22.50	30.59
410.338	16331	1	260035	2	15	39.30	26.50	13.50	16.76
410.415	22615	2	266271	2	25	73.50	52.00	40.30	52.61
410.869	22346	4	265733	3	20	112.00	82.00	70.00	83.69
411.320	22615	2	265733	3	20	57.40	36.50	16.10	32.17
411.605	13742	2	256688	2	17	28.20	18.90	11.60	17.32
411.914	16331	1	259100	0	16	23.70	16.80	12.00	17.67
412.464	16331	1	258778	1	16	30.50	20.50	12.20	18.58
416.050	16331	1	256688	2	10	20.20	12.20	4.59	7.96
420.092	22346	4	260388	3	14	25.20	19.30	15.10	14.03
421.278	13742	2	251112	2	11	14.80	8.85	5.41	5.61
422.891	16331	1	252797	1	4	11.40	6.43*	1.24	2.89
423.612	0	2	236062	1	10	43.60	26.20	37.10	33.06
423.770	12839	0	248815	1	17	29.30	16.80	14.10	30.13
427.220	22615	2	256688	2	5	8.20	4.82	0.99	2.72
428.787	6245	3	239456	3	60	310.00	172.00	157.00	141.03
430.643	0	2	232210	3	80	1430.00	821.00	772.00	840.48
431.045	6245	3	238239	4	80	1720.00	986.00	1040.00	1146.24
435.012	0	2	229873	3	90	751.00	423.00	523.00	510.76
436.001	6245	3	235598	4	75	228.00	133.00	135.00	145.70
436.277	13742	2	242953	2	33	150.00	88.00	95.30	109.16
436.880	13742	2	242636	3	25	156.00	91.70	104.00	111.07
437.250	0	2	228702	2	80	610.00	345.00	344.00	328.80
438.408	11519	4	239614	5	90	3050.00	1750.00	1900.00	2149.69
439.991	16331	1	243609	1	65	326.00	190.00	216.00	204.36
441.074	11519	4	238239	4	75	677.00	383.00	390.00	408.68
442.457	43110	0	269124	1	17	54.80	37.40	36.20	43.36
442.547	6245	3	232210	3	70	366.00	208.00	245.00	261.10
443.030	13742	2	239456	3	77	1070.00	619.00	701.00	709.35
444.474	13742	2	238727	2	40	255.00	144.00	140.00	105.17
444.854	22346	4	247139	5	90	3530.00	2080.00	2490.00	2681.67
446.272	11519	4	235598	4	77	245.00	136.00	141.00	188.16
447.173	6245	3	229873	3	70	245.00	139.00	120.00	143.76
447.989	12839	0	236062	1	77	491.00	287.00	318.00	307.50
448.505	6245	3	229205	4	80	764.00	431.00	453.00	476.30
449.527	6245	3	228702	2	10	26.00	14.20	12.70	14.42
449.649	16331	1	238727	2	70	449.00	264.00	283.00	326.60
451.889	6245	3	227536	4	75	104.00	55.90*	100.00	133.47
452.501	22615	2	243609	1	30	119.00	69.00	74.70	74.85
453.854	22615	2	242953	2	75	735.00	427.00	478.00	476.26
454.415	13742	2	233804	2	70	351.00	203.00	213.00	231.50
454.502	22615	2	242636	3	75	1430.00	830.00	957.00	1022.26
455.099	16331	1	236062	1	25	72.90	42.50	40.80	45.67
455.408	11519	4	231099	5	77	415.00	234.00	290.00	311.98
457.733	13742	2	232210	3	60	206.00	119.00	154.00	148.16
459.385	11519	4	229205	4	45	81.10	46.60	33.40	28.02
459.830	16331	1	233804	2	80	470.00	271.00	308.00	299.93
460.268	22346	4	239614	5	25	102.00	56.00	61.40	55.64
462.692	13742	2	229873	3	60	255.00	146.00	144.00	165.16
462.933	11519	4	227536	4	60	134.00	75.00	90.30	88.20
463.680	43110	0	258778	1	11	22.50	13.70	13.00	18.92
465.203	13742	2	228702	2	18	45.50	26.80	28.00	33.60
468.937	22346	4	235598	4	80	392.00	222.00	213.00	194.32
470.863	16331	1	228702	2	5	20.10	11.60	12.80	13.55
476.906	43110	0	252797	1	27	70.60	44.10*	59.30	96.82
479.044	22346	4	231099	5	55	84.50	49.70	61.20	82.07
483.423	22346	4	229205	4	10	40.20	24.50	13.70	13.15
486.138	43110	0	248815	1	50	284.00	174.00	191.00	113.07
638.173	58514	1	215213	1	18	3.28	2.89	2.53	1.62
702.963	72959	2	215213	1	41	159.00	141.00	133.00	151.94
716.727	6245	3	145768	3	25	8.78	7.85	7.48	5.95
723.876	6245	3	144390	2	29	14.70	13.20	12.80	10.86
725.616	60296	2	198108	2	25	36.10	31.30	28.30	29.68
726.162	0	2	137709	1	29	19.40	17.10	16.60	15.12
730.524	0	2	136888	3	25	2.16	2.15	1.98	1.64
731.725	6245	3	142908	4	22	11.40	9.92	9.51	9.57
733.560	12839	0	149160	1	8	6.04	5.37	5.40	6.44
738.453	13742	2	149160	1	16	12.80	12.30	10.80	9.41
744.887	11519	4	145768	3	35	24.20	21.50	19.10	19.85
752.847	16331	1	149160	1	16	4.57	4.03	3.96	3.96
757.424	13742	2	145768	3	8	6.63	4.80	5.25	5.00
760.740	66658	3	198108	2	76	195.00	169.00	153.00	171.96
761.103	11519	4	142908	4	41	137.00	120.00	116.00	126.25
765.441	6245	3	136888	3	22	5.72	4.83	4.66	4.18
772.324	0	2	129480	3	67	6.46	5.42	5.23	6.23
775.212	0	2	128997	2	34	6.46	5.86	5.95	8.79
780.884	16331	1	144390	2	52	17.40	15.30	15.00	16.57
785.897	58514	1	185757	1	44	31.30	27.10	24.50	29.22
786.254	6245	3	133430	2	86	104.00	92.60	91.20	98.39
797.057	60296	2	185757	1	57	93.00	80.90	73.90	90.70
797.645	11519	4	136888	3	80	213.00	190.00	186.00	209.26
799.053	72959	2	198108	2	19	3.59	3.11	2.71	2.79
800.832	12839	0	137709	1	37	12.80	11.30	10.90	11.51
806.659	13742	2	137709	1	62	41.00	37.30	36.10	38.60
809.569	58514	1	182037	0	40	40.40	35.10	31.60	39.05
810.225	22346	4	145768	3	79	311.00	279.00	276.00	297.45
811.460	6245	3	129480	3	77	96.30	84.60	81.90	94.99
812.008	22615	2	145768	3	29	4.98	5.86	5.22	3.31
812.045	13742	2	136888	3	59	2.31	2.87	2.65	2.90
813.528	16331	1	139252	0	58	30.10	26.90	26.50	28.58
814.653	6245	3	128997	2	76	70.20	62.80	59.80	71.55
817.492	0	2	122326	1	78	88.20	79.00	76.40	90.15
821.188	22615	2	144390	2	76	132.00	117.00	114.00	122.74
823.875	16331	1	137709	1	83	23.50	21.30	21.00	22.59
829.450	22346	4	142908	4	47	10.30	9.02	8.81	7.94
835.501	13742	2	133430	2	84	59.80	52.10	49.90	54.44
842.733	0	2	118663	2	81	79.70	69.50	67.20	74.50
847.749	11519	4	129480	3	80	35.30	31.80	31.60	34.33
853.980	16331	1	133430	2	50	2.04	2.01	2.27	2.16
864.024	13742	2	129480	3	40	4.62	4.63	4.54	4.76
867.633	13742	2	128997	2	74	56.20	48.80	48.10	50.90
868.858	22615	2	137709	1	25	4.22	3.64	3.73	3.97
873.045	22346	4	136888	3	68	28.00	25.20	22.70	22.27
875.102	22615	2	136888	3	48	10.00	8.58	9.21	11.09
887.567	16331	1	128997	2	69	28.60	26.30	25.70	28.03
913.347	12839	0	122326	1	78	14.90	13.70	13.60	14.66
933.410	22346	4	129480	3	62	12.30	11.00	10.30	10.05
935.767	22615	2	129480	3	57	2.07	1.82	2.00	2.49
942.961	43110	0	149160	1	58	21.00	19.40	19.10	18.66
953.096	13742	2	118663	2	66	10.30	8.80	9.46	13.36
1041.140	22615	2	118663	2	82	1.54	1.23	1.34	2.20
1057.090	43110	0	137709	1	62	0.86	0.83	0.85	1.03
1125.300	60296	2	149160	1	82	6.23	4.77	4.99	6.16
1164.466	58514	1	144390	2	67	0.96	0.74	0.79	0.89
1189.151	60296	2	144390	2	84	19.90	15.50	16.70	20.23
1238.574	58514	1	139252	0	73	19.40	15.00	15.90	18.00
1262.358	43110	0	122326	1	46	0.62	0.57	0.55	0.59
1262.707	58514	1	137709	1	76	40.40	31.30	31.80	34.68
1264.066	66658	3	145768	3	75	46.80	36.20	34.50	33.25
1286.456	66658	3	144390	2	75	35.00	27.10	29.60	37.24
1291.759	60296	2	137709	1	73	13.80	10.70	11.70	14.26
1305.611	60296	2	136888	3	76	96.80	75.50	76.20	86.30
1311.465	66658	3	142908	4	76	162.00	126.00	129.00	150.94
1312.319	72959	2	149160	1	75	44.90	35.20	37.10	42.06
1334.841	58514	1	133430	2	75	47.10	36.50	37.10	44.01
1367.341	60296	2	133430	2	74	26.20	20.20	19.40	20.60
1373.439	72959	2	145768	3	74	70.70	56.20	59.00	73.48
1399.933	72959	2	144390	2	72	30.10	23.20	22.10	22.61
1423.889	66658	3	136888	3	74	20.70	16.00	16.00	22.23
1445.413	60296	2	129480	3	74	22.60	17.50	17.80	23.38
1455.559	60296	2	128997	2	75	6.39	4.95	4.86	7.13
1544.377	72959	2	137709	1	56	1.14	0.90	0.97	1.29
1564.223	72959	2	136888	3	69	3.14	2.57	2.42	2.23
1567.095	58514	1	122326	1	74	11.70	9.06	8.83	11.83
1591.804	66658	3	129480	3	75	37.30	28.90	29.40	36.99
1604.126	66658	3	128997	2	75	28.80	22.30	22.70	26.08
1612.132	60296	2	122326	1	73	18.20	14.20	14.40	16.84
1653.662	72959	2	133430	2	73	6.20	4.78	4.53	5.87
1662.540	58514	1	118663	2	73	20.80	16.10	16.10	18.99
1713.270	60296	2	118663	2	71	18.30	14.20	14.20	17.16
1769.249	72959	2	129480	3	72	12.30	9.71	9.94	10.19
1784.499	72959	2	128997	2	74	12.20	9.41	9.23	11.00
2187.270	72959	2	118663	2	81	1.70	1.31	1.33	1.93

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [12]; (e) Our HFR, HFR+CPOL, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 11. Transition probabilities for the selected 155 experimentally observed lines in W V.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR+CPOL (e)	HFR(CV) (e)	MCDHF (e)
391.566	13742	2	269124	1	7	12.40	9.65	8.97	11.98
392.941	11519	4	266010	4	27	34.70	27.00	27.20	34.83
393.375	11519	4	265733	3	11	36.60	25.90	13.40	22.00
393.480	6245	3	260388	3	12	18.10	14.20	13.30	10.30
395.575	0	2	252797	1	30	61.50	43.50	28.40	24.44
397.379	6245	3	257895	3	15	12.20	9.95	11.90	14.83
398.234	0	2	251112	2	23	26.90	21.00	21.70	17.48
399.295	6245	3	256688	2	35	73.70	52.30	37.60	47.99
400.095	16331	1	266271	2	6	7.15	5.47	4.77	6.11
401.824	11519	4	260388	3	25	69.70	51.10	37.40	42.07
405.441	13742	2	260388	3	17	45.30	29.20	13.00	27.57
405.666	22615	2	269124	1	13	27.90	20.80	18.40	25.32
405.882	11519	4	257895	3	23	37.20	26.00	20.70	22.30
406.017	13742	2	260035	2	15	27.10	20.20	21.30	16.18
406.600	12839	0	258778	1	6	6.46	5.20	5.03	4.70
408.106	13742	2	258778	1	20	40.20	28.30	22.50	30.59
410.338	16331	1	260035	2	15	39.30	26.50	13.50	16.76
410.415	22615	2	266271	2	25	73.50	52.00	40.30	52.61
410.869	22346	4	265733	3	20	112.00	82.00	70.00	83.69
411.320	22615	2	265733	3	20	57.40	36.50	16.10	32.17
411.605	13742	2	256688	2	17	28.20	18.90	11.60	17.32
411.914	16331	1	259100	0	16	23.70	16.80	12.00	17.67
412.464	16331	1	258778	1	16	30.50	20.50	12.20	18.58
416.050	16331	1	256688	2	10	20.20	12.20	4.59	7.96
420.092	22346	4	260388	3	14	25.20	19.30	15.10	14.03
421.278	13742	2	251112	2	11	14.80	8.85	5.41	5.61
422.891	16331	1	252797	1	4	11.40	6.43*	1.24	2.89
423.612	0	2	236062	1	10	43.60	26.20	37.10	33.06
423.770	12839	0	248815	1	17	29.30	16.80	14.10	30.13
427.220	22615	2	256688	2	5	8.20	4.82	0.99	2.72
428.787	6245	3	239456	3	60	310.00	172.00	157.00	141.03
430.643	0	2	232210	3	80	1430.00	821.00	772.00	840.48
431.045	6245	3	238239	4	80	1720.00	986.00	1040.00	1146.24
435.012	0	2	229873	3	90	751.00	423.00	523.00	510.76
436.001	6245	3	235598	4	75	228.00	133.00	135.00	145.70
436.277	13742	2	242953	2	33	150.00	88.00	95.30	109.16
436.880	13742	2	242636	3	25	156.00	91.70	104.00	111.07
437.250	0	2	228702	2	80	610.00	345.00	344.00	328.80
438.408	11519	4	239614	5	90	3050.00	1750.00	1900.00	2149.69
439.991	16331	1	243609	1	65	326.00	190.00	216.00	204.36
441.074	11519	4	238239	4	75	677.00	383.00	390.00	408.68
442.457	43110	0	269124	1	17	54.80	37.40	36.20	43.36
442.547	6245	3	232210	3	70	366.00	208.00	245.00	261.10
443.030	13742	2	239456	3	77	1070.00	619.00	701.00	709.35
444.474	13742	2	238727	2	40	255.00	144.00	140.00	105.17
444.854	22346	4	247139	5	90	3530.00	2080.00	2490.00	2681.67
446.272	11519	4	235598	4	77	245.00	136.00	141.00	188.16
447.173	6245	3	229873	3	70	245.00	139.00	120.00	143.76
447.989	12839	0	236062	1	77	491.00	287.00	318.00	307.50
448.505	6245	3	229205	4	80	764.00	431.00	453.00	476.30
449.527	6245	3	228702	2	10	26.00	14.20	12.70	14.42
449.649	16331	1	238727	2	70	449.00	264.00	283.00	326.60
451.889	6245	3	227536	4	75	104.00	55.90*	100.00	133.47
452.501	22615	2	243609	1	30	119.00	69.00	74.70	74.85
453.854	22615	2	242953	2	75	735.00	427.00	478.00	476.26
454.415	13742	2	233804	2	70	351.00	203.00	213.00	231.50
454.502	22615	2	242636	3	75	1430.00	830.00	957.00	1022.26
455.099	16331	1	236062	1	25	72.90	42.50	40.80	45.67
455.408	11519	4	231099	5	77	415.00	234.00	290.00	311.98
457.733	13742	2	232210	3	60	206.00	119.00	154.00	148.16
459.385	11519	4	229205	4	45	81.10	46.60	33.40	28.02
459.830	16331	1	233804	2	80	470.00	271.00	308.00	299.93
460.268	22346	4	239614	5	25	102.00	56.00	61.40	55.64
462.692	13742	2	229873	3	60	255.00	146.00	144.00	165.16
462.933	11519	4	227536	4	60	134.00	75.00	90.30	88.20
463.680	43110	0	258778	1	11	22.50	13.70	13.00	18.92
465.203	13742	2	228702	2	18	45.50	26.80	28.00	33.60
468.937	22346	4	235598	4	80	392.00	222.00	213.00	194.32
470.863	16331	1	228702	2	5	20.10	11.60	12.80	13.55
476.906	43110	0	252797	1	27	70.60	44.10*	59.30	96.82
479.044	22346	4	231099	5	55	84.50	49.70	61.20	82.07
483.423	22346	4	229205	4	10	40.20	24.50	13.70	13.15
486.138	43110	0	248815	1	50	284.00	174.00	191.00	113.07
638.173	58514	1	215213	1	18	3.28	2.89	2.53	1.62
702.963	72959	2	215213	1	41	159.00	141.00	133.00	151.94
716.727	6245	3	145768	3	25	8.78	7.85	7.48	5.95
723.876	6245	3	144390	2	29	14.70	13.20	12.80	10.86
725.616	60296	2	198108	2	25	36.10	31.30	28.30	29.68
726.162	0	2	137709	1	29	19.40	17.10	16.60	15.12
730.524	0	2	136888	3	25	2.16	2.15	1.98	1.64
731.725	6245	3	142908	4	22	11.40	9.92	9.51	9.57
733.560	12839	0	149160	1	8	6.04	5.37	5.40	6.44
738.453	13742	2	149160	1	16	12.80	12.30	10.80	9.41
744.887	11519	4	145768	3	35	24.20	21.50	19.10	19.85
752.847	16331	1	149160	1	16	4.57	4.03	3.96	3.96
757.424	13742	2	145768	3	8	6.63	4.80	5.25	5.00
760.740	66658	3	198108	2	76	195.00	169.00	153.00	171.96
761.103	11519	4	142908	4	41	137.00	120.00	116.00	126.25
765.441	6245	3	136888	3	22	5.72	4.83	4.66	4.18
772.324	0	2	129480	3	67	6.46	5.42	5.23	6.23
775.212	0	2	128997	2	34	6.46	5.86	5.95	8.79
780.884	16331	1	144390	2	52	17.40	15.30	15.00	16.57
785.897	58514	1	185757	1	44	31.30	27.10	24.50	29.22
786.254	6245	3	133430	2	86	104.00	92.60	91.20	98.39
797.057	60296	2	185757	1	57	93.00	80.90	73.90	90.70
797.645	11519	4	136888	3	80	213.00	190.00	186.00	209.26
799.053	72959	2	198108	2	19	3.59	3.11	2.71	2.79
800.832	12839	0	137709	1	37	12.80	11.30	10.90	11.51
806.659	13742	2	137709	1	62	41.00	37.30	36.10	38.60
809.569	58514	1	182037	0	40	40.40	35.10	31.60	39.05
810.225	22346	4	145768	3	79	311.00	279.00	276.00	297.45
811.460	6245	3	129480	3	77	96.30	84.60	81.90	94.99
812.008	22615	2	145768	3	29	4.98	5.86	5.22	3.31
812.045	13742	2	136888	3	59	2.31	2.87	2.65	2.90
813.528	16331	1	139252	0	58	30.10	26.90	26.50	28.58
814.653	6245	3	128997	2	76	70.20	62.80	59.80	71.55
817.492	0	2	122326	1	78	88.20	79.00	76.40	90.15
821.188	22615	2	144390	2	76	132.00	117.00	114.00	122.74
823.875	16331	1	137709	1	83	23.50	21.30	21.00	22.59
829.450	22346	4	142908	4	47	10.30	9.02	8.81	7.94
835.501	13742	2	133430	2	84	59.80	52.10	49.90	54.44
842.733	0	2	118663	2	81	79.70	69.50	67.20	74.50
847.749	11519	4	129480	3	80	35.30	31.80	31.60	34.33
853.980	16331	1	133430	2	50	2.04	2.01	2.27	2.16
864.024	13742	2	129480	3	40	4.62	4.63	4.54	4.76
867.633	13742	2	128997	2	74	56.20	48.80	48.10	50.90
868.858	22615	2	137709	1	25	4.22	3.64	3.73	3.97
873.045	22346	4	136888	3	68	28.00	25.20	22.70	22.27
875.102	22615	2	136888	3	48	10.00	8.58	9.21	11.09
887.567	16331	1	128997	2	69	28.60	26.30	25.70	28.03
913.347	12839	0	122326	1	78	14.90	13.70	13.60	14.66
933.410	22346	4	129480	3	62	12.30	11.00	10.30	10.05
935.767	22615	2	129480	3	57	2.07	1.82	2.00	2.49
942.961	43110	0	149160	1	58	21.00	19.40	19.10	18.66
953.096	13742	2	118663	2	66	10.30	8.80	9.46	13.36
1041.140	22615	2	118663	2	82	1.54	1.23	1.34	2.20
1057.090	43110	0	137709	1	62	0.86	0.83	0.85	1.03
1125.300	60296	2	149160	1	82	6.23	4.77	4.99	6.16
1164.466	58514	1	144390	2	67	0.96	0.74	0.79	0.89
1189.151	60296	2	144390	2	84	19.90	15.50	16.70	20.23
1238.574	58514	1	139252	0	73	19.40	15.00	15.90	18.00
1262.358	43110	0	122326	1	46	0.62	0.57	0.55	0.59
1262.707	58514	1	137709	1	76	40.40	31.30	31.80	34.68
1264.066	66658	3	145768	3	75	46.80	36.20	34.50	33.25
1286.456	66658	3	144390	2	75	35.00	27.10	29.60	37.24
1291.759	60296	2	137709	1	73	13.80	10.70	11.70	14.26
1305.611	60296	2	136888	3	76	96.80	75.50	76.20	86.30
1311.465	66658	3	142908	4	76	162.00	126.00	129.00	150.94
1312.319	72959	2	149160	1	75	44.90	35.20	37.10	42.06
1334.841	58514	1	133430	2	75	47.10	36.50	37.10	44.01
1367.341	60296	2	133430	2	74	26.20	20.20	19.40	20.60
1373.439	72959	2	145768	3	74	70.70	56.20	59.00	73.48
1399.933	72959	2	144390	2	72	30.10	23.20	22.10	22.61
1423.889	66658	3	136888	3	74	20.70	16.00	16.00	22.23
1445.413	60296	2	129480	3	74	22.60	17.50	17.80	23.38
1455.559	60296	2	128997	2	75	6.39	4.95	4.86	7.13
1544.377	72959	2	137709	1	56	1.14	0.90	0.97	1.29
1564.223	72959	2	136888	3	69	3.14	2.57	2.42	2.23
1567.095	58514	1	122326	1	74	11.70	9.06	8.83	11.83
1591.804	66658	3	129480	3	75	37.30	28.90	29.40	36.99
1604.126	66658	3	128997	2	75	28.80	22.30	22.70	26.08
1612.132	60296	2	122326	1	73	18.20	14.20	14.40	16.84
1653.662	72959	2	133430	2	73	6.20	4.78	4.53	5.87
1662.540	58514	1	118663	2	73	20.80	16.10	16.10	18.99
1713.270	60296	2	118663	2	71	18.30	14.20	14.20	17.16
1769.249	72959	2	129480	3	72	12.30	9.71	9.94	10.19
1784.499	72959	2	128997	2	74	12.20	9.41	9.23	11.00
2187.270	72959	2	118663	2	81	1.70	1.31	1.33	1.93

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [12]; (e) Our HFR, HFR+CPOL, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

4.2. Rhenium, Osmium, Iridium and Platinum Yb-like Ions

For these four ions, we have already explained the need to use the HFR(CV) method instead of the HFR+CPOL method because of the increasing configuration interactions in the odd parity between the core-excited configurations especially the 5p⁵5d³ configuration and the configurations of interest (see Figure 2). We have thus evaluated the uncertainty of the set of transition probabilities computed by the HFR(CV) and the MCDHF methods by plotting the logarithm of the ratio between the transition probabilities computed with the less accurate MCDHF method and the reference HFR(CV) model, $log(g{A}_{MCDHF}/g{A}_{HFR\left(CV\right)})$, as a function of the logarithm of the line strength computed by the HFR(CV) model, $log\left(S_{HFR\left(CV\right)}(a.u.)\right)$. In Figure 13, all the 112 and 147 observed lines in Re VI and Os VII are plotted, respectively. In Figure 14, only 125 and 126 of the 129 observed transitions in Ir VIII and in Pt IX, respectively, are plotted because one levels in Ir VIII measured at 406 542 cm⁻¹ and two levels in Pt IX observed at 438 038 cm⁻¹ and 470 214 cm⁻¹ have been removed from the fit as already explained previously and thus the transitions involving these levels were also removed.

In Table 12, Table 13, Table 14 and Table 15, as for the Ta IV and W V ions, we have selected only the reliable atomic data namely the transitions for which the $CF$-value was higher than 0.05 and the $dS$-value was lower than 0.2. It remains 90 transitions among the 112 transitions observed between 332.044 and 1513.957 Å in Re VI, 92 transitions among the 147 transitions observed between 288.274 and 1319.811 Å in Os VII, 77 transitions among the 125 transitions observed between 237.098 and 1172.084 Å in Ir VIII and 63 transitions among the 126 transitions observed between 216.575 and 1055.171 Å in Pt IX. The transitions with one, double or triple stars stand for the same conditions on the ratio and the relative deviation as defined for Ta VI and W V. Actually, three transitions in Re VI have a ratio lower than 0.2 and a relative deviation higher than 50% associated with a triple star ’***’, one transition in Os VII have one star namely a ratio in the range [0.2,5] but a relative deviation higher than 50% and another have a triple star namely a ratio outside the range [0.2,5] and a relative deviation higher than 50%, two transitions have one star in Ir VIII and also in Pt IX and one more transition in Pt IX have a triple star.

Among these 90, 92, 77 and 63 selected transitions we observed that it still remains 87, 90, 75 and 60 transitions which have a mean ratio in the range [0.2,5] and also a mean relative deviation lower than 50% for Re VI, Os VII, Ir VIII and Pt IX, respectively. The mean ratio, $g{A}_{MCDHF}$/$g{A}_{HFR\left(CV\right)}$, and the mean relative deviation, $\Delta gA$/max($g{A}_{HFR\left(CV\right)},g{A}_{MCDHF}$) (%), for the remaining 87, 90, 75 and 65 transitions in Re VI, Os VII, Ir VIII and Pt IX, respectively, are found to be 1.07 ± 0.13 and 9.6 ± 7.5 % in Re VI, 1.06 ± 0.18 and 12.9 ± 10.5 % in Os VII, 1.01 ± 0.13 and 8.4 ± 7.8 % in Ir VIII and 1.02 ± 0.09 and 6.5 ± 5.7 % in Pt IX.

Safronova $et$ $al.$ [21] have only tabulated in their work the line strengths computed with the RMBPT method in length (L) and velocity (V) gauges for the 35 transitions between the 5d², 5d6s even configurations and the 5d6p odd configuration in Re VI. We were able to identify these transitions in our MCDHF method for which the line strengths in the Babushkin (B) and the Coulomb (C) gauges are presented in Table 16 with the corresponding line strengths computed by Safronova $et$ $al.$ [21]. The mean ratios S_RMBPT(L)/S_MCDHF(B) and S_RMBPT(V)/S_MCDHF(C) which are respectively equal to 0.85 ± 0.29 and 0.86 ± 0.34 indicate that on average our computed line strengths were lower than the ones computed by the RMBPT method by 15%.

Table 12. Transition probabilities for the selected 90 experimentally observed lines in Re VI.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
341.578	14679.4	4	307440	5	10	337.00	174.00	107.25
341.736	8166.6	3	300794	3	1	61.00	22.50	24.08
344.570	0	2	290208	1	5	107.00	57.20***	0.25
349.003	8166.6	3	294688	2	8	207.00	105.00	105.77
349.120	0	2	286426	3	60	2140.00	935.00	1102.95
350.165	8166.6	3	293741	4	200	2540.00	1490.00	1688.47
351.363	16576.7	2	301178	2	10	390.00	187.00	226.86
352.641	0	2	283559	3	200	1880.00	978.00	923.17
353.174	8166.6	3	290824	4	20	1040.00	284.00	269.71
354.714	0	2	281906	2	80	1060.00	516.00	498.04
355.548	14679.4	4	295928	5	100	5340.00	2870.00	3279.54
356.144	26657.1	4	307440	5	80	6600.00	4230.00	4647.83
358.091	16576.7	2	295836	3	50	1690.00	1120.00	1164.46
358.349	14679.4	4	293741	4	40	1440.00	589.00	609.15
359.376	8166.6	3	286426	3	30	841.00	467.00	484.40
362.139	14679.4	4	290824	4	20	198.00	159.00	235.65
362.547	14379.3	0	290208	1	40	867.00	354.00***	3.38
362.926	19141.6	1	294688	2	40	1010.00	523.00	612.06
364.061	8166.6	3	282853	4	80	1300.00	703.00	753.31
365.713	27722.9	2	301178	2	7	1320.00	727.00	725.53
366.230	27722.9	2	300794	3	60	2520.00	1550.00	1680.41
367.104	8166.6	3	280575	4	20	241.00	144.00	175.91
367.282	16576.7	2	288853	2	30	540.00	328.00	352.29
368.923	19141.6	1	290208	1	5	181.00	45.40***	0.32
369.462	14679.4	4	285346	5	80	831.00	457.00	485.13
370.591	16576.7	2	286426	3	20	406.00	217.00	200.01
370.767	19141.6	1	288853	2	30	764.00	406.00	386.53
371.382	26657.1	4	295928	5	20	357.00	176.00	158.04
374.550	16576.7	2	283559	3	30	466.00	196.00	236.16
376.080	14679.4	4	280575	4	30	266.00	151.00	144.63
380.831	16576.7	2	279156	2	3	23.00	20.20	18.53
386.559	26657.1	4	285346	5	20	92.70	56.50	84.87
536.550	8166.6	3	194539.1	2	5	27.00	23.80	19.88
537.462	14379.3	0	200436.6	1	1	10.50	9.55	10.99
537.738	0	2	185962.9	1	10	34.90	30.20	26.94
551.579	19141.6	1	200436.6	1	1	8.51	7.35	6.90
559.977	14679.4	4	193260	4	200	252.00	213.00	222.19
565.438	8166.6	3	185021.6	3	10	18.20	15.20	13.51
566.753	102712.2	3	279156	2	20	329.00	261.00	274.84
569.794	0	2	175501.8	3	10	10.60	8.32	9.77
570.141	19141.6	1	194539.1	2	15	32.10	27.60	28.77
578.051	8166.6	3	181154.9	2	100	191.00	169.00	174.28
578.993	27722.9	2	200436.6	1	40	80.80	71.10	73.21
582.803	14379.3	0	185962.9	1	20	24.90	20.90	20.97
587.053	14679.4	4	185021.6	3	200	393.00	343.00	365.16
590.385	16576.7	2	185962.9	1	20	86.60	76.90	78.91
591.596	26657.1	4	195691.3	3	200	601.00	528.00	542.98
592.993	19141.6	1	187780.4	0	20	58.70	51.90	53.63
593.671	16576.7	2	185021.6	3	1	5.88	6.90	7.36
595.352	27722.9	2	195691.3	3	4	13.40	15.20	11.46
597.599	8166.6	3	175501.8	3	100	176.00	150.00	167.66
599.476	27722.9	2	194539.1	2	200	249.00	218.00	222.27
600.254	8166.6	3	174761.5	2	200	140.00	119.00	135.09
602.132	0	2	166076.9	1	100	168.00	146.00	164.56
607.618	16576.7	2	181154.9	2	50	112.00	93.50	96.68
616.778	0	2	162134.4	2	100	154.00	130.00	139.38
621.805	14679.4	4	175501.8	3	50	90.70	80.30	82.92
629.221	16576.7	2	175501.8	3	8	11.70	11.80	11.96
631.454	26657.1	4	185021.6	3	10	47.40	40.40	42.19
632.173	16576.7	2	174761.5	2	20	99.00	85.70	87.95
635.730	27722.9	2	185021.6	3	5	12.90	11.80	13.68
642.589	19141.6	1	174761.5	2	20	58.90	54.00	57.16
659.206	14379.3	0	166076.9	1	20	30.50	28.30	29.54
666.912	50491.7	0	200436.6	1	10	42.40	39.00	36.41
671.846	26657.1	4	175501.8	3	10	27.10	23.30	23.98
676.687	27722.9	2	175501.8	3	3	3.51	3.37	4.01
997.245	94262	2	194539.1	2	50	21.90	18.30	21.81
1047.444	92312.3	1	187780.4	0	50	28.70	22.70	24.98
1067.393	92312.3	1	185962.9	1	100	59.20	45.70	48.45
1075.472	102712.2	3	195691.3	3	100	71.10	52.70	51.00
1089.016	102712.2	3	194539.1	2	200	48.60	39.80	47.67
1090.185	108709.2	2	200436.6	1	100	69.30	56.90	62.59
1090.535	94262	2	185962.9	1	50	20.90	17.00	19.94
1101.804	94262	2	185021.6	3	200	149.00	117.00	126.40
1104.368	102712.2	3	193260	4	300	230.00	182.00	202.81
1125.525	92312.3	1	181154.9	2	2	66.80	52.20	58.44
1149.599	108709.2	2	195691.3	3	200	99.40	81.30	95.26
1150.831	94262	2	181154.9	2	300	41.20	30.20	31.12
1165.093	108709.2	2	194539.1	2	100	53.50	39.10	39.32
1214.930	102712.2	3	185021.6	3	100	21.20	15.80	20.95
1230.928	94262	2	175501.8	3	200	21.80	17.10	21.86
1355.655	92312.3	1	166076.9	1	200	14.80	11.00	13.63
1373.837	102712.2	3	175501.8	3	300	51.40	39.80	46.99
1380.310	108709.2	2	181154.9	2	100	8.32	6.09	7.51
1387.963	102712.2	3	174761.5	2	500	39.90	31.00	34.16
1392.531	94262	2	166076.9	1	200	25.10	19.70	21.98
1432.221	92312.3	1	162134.4	2	200	27.50	21.30	23.74
1473.437	94262	2	162134.4	2	300	26.50	20.40	23.08
1497.166	108709.2	2	175501.8	3	300	21.00	17.00	17.14
1513.957	108709.2	2	174761.5	2	200	17.10	12.90	14.59
289.012	10308	3	356322	3	2	69.90	29.10	28.88
290.288	19444	2	363927	1	45	94.80	93.30	151.09
296.345	0	2	337436	3	60	3500.00	497.00	786.35
296.663	10308	3	347386	2	40	243.00	129.00	128.89
297.759	10308	3	346144	4	75	4540.00	1180.00	1709.49
298.725	22098	1	356849	1	50	849.00	231.00	146.29
298.890	19444	2	354012	2	50	611.00	236.00	292.43
299.182	0	2	334240	3	75	2820.00	1620.00	1577.63
299.687	31274	4	364949	5	75	10400.00	5450.00	6409.01
299.765	10308	3	343897	4	70	907.00	747.00	514.21
301.862	18049	4	349324	5	70	8050.00	3320.00	3931.69
302.296	33127	2	363927	1	30	135.00	129.00	152.35
303.299	19444	2	349155	3	75	3270.00	1230.00	1445.79
304.795	18049	4	346144	4	75	1950.00	802.00	804.92
306.749	15837	0	341844	1	80	563.00	586.00	350.33
307.425	22098	1	347386	2	75	1440.00	539.00	694.66
308.648	10308	3	334302	4	85	2290.00	990.00	1049.93
309.695	10308	3	337436	3	60	1470.00	688.00	752.56
311.385	10308	3	331454	4	85	267.00	156.00	245.18
311.643	19444	2	340330	2	90	1020.00	379.00	446.48
313.007	18049	4	337535	5	80	1280.00	642.00	718.07
314.236	22098	1	340330	2	90	1200.00	613.00	578.40
314.418	31274	4	349324	5	85	849.00	324.00	329.80
314.476	19444	2	337436	3	85	383.00	391.00	323.00
317.594	31274	4	346144	4	65	120.00	172.00	97.91
317.670	19444	2	334240	3	80	677.00	172.00	240.88
322.158	22098	1	332501	2	20	42.30	20.30	20.28
417.700	15837	0	255246	1	60	16.70	14.80	17.19
418.242	10308	3	249401	3	65	28.90	24.90	20.33
419.945	10308	3	248430	2	70	44.80	39.30	32.86
420.723	0	2	237682	1	70	57.90	49.60	44.25
421.860	10308	3	247354	4	60	36.20	30.30	28.26
422.439	0	2	236726	3	55	11.80	11.40	9.22
424.073	19444	2	255246	1	60	38.50	33.10	27.47
428.898	22098	1	255246	1	55	14.40	12.00	11.28
436.096	18049	4	247354	4	70	405.00	342.00	351.39
441.655	10308	3	236726	3	70	41.80	34.80	31.27
441.826	22098	1	248430	2	70	52.10	44.30	45.16
444.964	0	2	224741	3	70	15.60	11.80	13.98
446.849	0	2	223790	2	70	16.30	14.90	20.33
450.170	10308	3	232453	2	75	323.00	283.00	286.84
450.209	33127	2	255246	1	70	147.00	129.00	131.19
450.758	15837	0	237682	1	75	41.20	34.60	33.83
457.297	18049	4	236726	3	80	646.00	563.00	585.81
458.208	19444	2	237682	1	78	155.00	137.00	139.06
458.437	31274	4	249401	3	80	1010.00	886.00	895.98
459.364	22098	1	239794	0	70	99.60	88.30	89.97
460.234	19444	2	236726	3	60	9.54	12.00	12.76
462.380	33127	2	249401	3	60	25.80	31.10	25.09
462.799	31274	4	247354	4	60	68.00	57.90	50.01
463.851	22098	1	237682	1	70	78.50	71.70	72.72
464.454	33127	2	248430	2	70	414.00	365.00	366.10
466.358	10308	3	224741	3	70	285.00	243.00	267.38
468.435	10308	3	223790	2	70	231.00	199.00	222.21
469.467	19444	2	232453	2	70	180.00	155.00	156.97
469.797	0	2	212862	1	70	280.00	244.00	269.69
472.031	142163	3	354012	2	10	44.20	6.64*	19.38
475.213	131416	2	341844	1	28	157.00	10.80***	93.17
479.260	0	2	208659	2	70	261.00	221.00	234.72
483.819	18049	4	224741	3	70	185.00	163.00	166.13
486.734	31274	4	236726	3	70	72.60	61.70	67.13
487.117	19444	2	224741	3	65	22.70	23.80	23.83
489.371	19444	2	223790	2	70	165.00	141.00	145.05
491.165	33127	2	236726	3	50	16.10	14.50	16.68
495.805	22098	1	223790	2	70	103.00	95.80	101.12
506.221	57710	0	255246	1	70	73.30	68.80	63.68
507.563	15837	0	212862	1	70	53.90	50.50	52.41
516.885	31274	4	224741	3	65	48.20	41.10	44.73
521.865	33127	2	224741	3	60	5.07	4.83	5.75
528.505	19444	2	208659	2	60	20.10	18.80	24.89
854.600	131416	2	248430	2	45	23.20	20.60	23.62
905.036	129301	1	239794	0	50	37.70	32.40	33.39
922.672	129301	1	237682	1	50	80.70	64.20	65.81
932.508	142163	3	249401	3	30	104.00	76.10	74.13
932.636	148023	2	255246	1	55	98.60	81.60	87.43
941.023	142163	3	248430	2	45	60.80	54.20	60.00
949.584	131416	2	236726	3	50	214.00	166.00	176.75
950.655	142163	3	247354	4	70	313.00	246.00	268.83
969.440	129301	1	232453	2	40	90.50	70.20	76.72
986.390	148023	2	249401	3	30	131.00	106.00	121.42
989.742	131416	2	232453	2	50	60.60	44.50	45.18
995.946	148023	2	248430	2	50	82.60	61.20	60.94
1057.496	142163	3	236726	3	20	20.80	15.30	20.16
1071.537	131416	2	224741	3	40	20.80	16.30	20.82
1196.743	129301	1	212862	1	15	18.00	13.10	15.71
1210.984	142163	3	224741	3	50	65.80	50.60	58.11
1225.082	142163	3	223790	2	50	51.30	41.30	43.82
1227.815	131416	2	212862	1	30	32.70	26.00	28.15
1260.119	129301	1	208659	2	50	35.00	27.10	29.60
1294.622	131416	2	208659	2	60	35.30	27.00	29.86
1303.446	148023	2	224741	3	55	31.50	25.30	25.70
1319.811	148023	2	223790	2	40	22.60	16.70	18.52

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [15]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 12. Transition probabilities for the selected 90 experimentally observed lines in Re VI.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
341.578	14679.4	4	307440	5	10	337.00	174.00	107.25
341.736	8166.6	3	300794	3	1	61.00	22.50	24.08
344.570	0	2	290208	1	5	107.00	57.20***	0.25
349.003	8166.6	3	294688	2	8	207.00	105.00	105.77
349.120	0	2	286426	3	60	2140.00	935.00	1102.95
350.165	8166.6	3	293741	4	200	2540.00	1490.00	1688.47
351.363	16576.7	2	301178	2	10	390.00	187.00	226.86
352.641	0	2	283559	3	200	1880.00	978.00	923.17
353.174	8166.6	3	290824	4	20	1040.00	284.00	269.71
354.714	0	2	281906	2	80	1060.00	516.00	498.04
355.548	14679.4	4	295928	5	100	5340.00	2870.00	3279.54
356.144	26657.1	4	307440	5	80	6600.00	4230.00	4647.83
358.091	16576.7	2	295836	3	50	1690.00	1120.00	1164.46
358.349	14679.4	4	293741	4	40	1440.00	589.00	609.15
359.376	8166.6	3	286426	3	30	841.00	467.00	484.40
362.139	14679.4	4	290824	4	20	198.00	159.00	235.65
362.547	14379.3	0	290208	1	40	867.00	354.00***	3.38
362.926	19141.6	1	294688	2	40	1010.00	523.00	612.06
364.061	8166.6	3	282853	4	80	1300.00	703.00	753.31
365.713	27722.9	2	301178	2	7	1320.00	727.00	725.53
366.230	27722.9	2	300794	3	60	2520.00	1550.00	1680.41
367.104	8166.6	3	280575	4	20	241.00	144.00	175.91
367.282	16576.7	2	288853	2	30	540.00	328.00	352.29
368.923	19141.6	1	290208	1	5	181.00	45.40***	0.32
369.462	14679.4	4	285346	5	80	831.00	457.00	485.13
370.591	16576.7	2	286426	3	20	406.00	217.00	200.01
370.767	19141.6	1	288853	2	30	764.00	406.00	386.53
371.382	26657.1	4	295928	5	20	357.00	176.00	158.04
374.550	16576.7	2	283559	3	30	466.00	196.00	236.16
376.080	14679.4	4	280575	4	30	266.00	151.00	144.63
380.831	16576.7	2	279156	2	3	23.00	20.20	18.53
386.559	26657.1	4	285346	5	20	92.70	56.50	84.87
536.550	8166.6	3	194539.1	2	5	27.00	23.80	19.88
537.462	14379.3	0	200436.6	1	1	10.50	9.55	10.99
537.738	0	2	185962.9	1	10	34.90	30.20	26.94
551.579	19141.6	1	200436.6	1	1	8.51	7.35	6.90
559.977	14679.4	4	193260	4	200	252.00	213.00	222.19
565.438	8166.6	3	185021.6	3	10	18.20	15.20	13.51
566.753	102712.2	3	279156	2	20	329.00	261.00	274.84
569.794	0	2	175501.8	3	10	10.60	8.32	9.77
570.141	19141.6	1	194539.1	2	15	32.10	27.60	28.77
578.051	8166.6	3	181154.9	2	100	191.00	169.00	174.28
578.993	27722.9	2	200436.6	1	40	80.80	71.10	73.21
582.803	14379.3	0	185962.9	1	20	24.90	20.90	20.97
587.053	14679.4	4	185021.6	3	200	393.00	343.00	365.16
590.385	16576.7	2	185962.9	1	20	86.60	76.90	78.91
591.596	26657.1	4	195691.3	3	200	601.00	528.00	542.98
592.993	19141.6	1	187780.4	0	20	58.70	51.90	53.63
593.671	16576.7	2	185021.6	3	1	5.88	6.90	7.36
595.352	27722.9	2	195691.3	3	4	13.40	15.20	11.46
597.599	8166.6	3	175501.8	3	100	176.00	150.00	167.66
599.476	27722.9	2	194539.1	2	200	249.00	218.00	222.27
600.254	8166.6	3	174761.5	2	200	140.00	119.00	135.09
602.132	0	2	166076.9	1	100	168.00	146.00	164.56
607.618	16576.7	2	181154.9	2	50	112.00	93.50	96.68
616.778	0	2	162134.4	2	100	154.00	130.00	139.38
621.805	14679.4	4	175501.8	3	50	90.70	80.30	82.92
629.221	16576.7	2	175501.8	3	8	11.70	11.80	11.96
631.454	26657.1	4	185021.6	3	10	47.40	40.40	42.19
632.173	16576.7	2	174761.5	2	20	99.00	85.70	87.95
635.730	27722.9	2	185021.6	3	5	12.90	11.80	13.68
642.589	19141.6	1	174761.5	2	20	58.90	54.00	57.16
659.206	14379.3	0	166076.9	1	20	30.50	28.30	29.54
666.912	50491.7	0	200436.6	1	10	42.40	39.00	36.41
671.846	26657.1	4	175501.8	3	10	27.10	23.30	23.98
676.687	27722.9	2	175501.8	3	3	3.51	3.37	4.01
997.245	94262	2	194539.1	2	50	21.90	18.30	21.81
1047.444	92312.3	1	187780.4	0	50	28.70	22.70	24.98
1067.393	92312.3	1	185962.9	1	100	59.20	45.70	48.45
1075.472	102712.2	3	195691.3	3	100	71.10	52.70	51.00
1089.016	102712.2	3	194539.1	2	200	48.60	39.80	47.67
1090.185	108709.2	2	200436.6	1	100	69.30	56.90	62.59
1090.535	94262	2	185962.9	1	50	20.90	17.00	19.94
1101.804	94262	2	185021.6	3	200	149.00	117.00	126.40
1104.368	102712.2	3	193260	4	300	230.00	182.00	202.81
1125.525	92312.3	1	181154.9	2	2	66.80	52.20	58.44
1149.599	108709.2	2	195691.3	3	200	99.40	81.30	95.26
1150.831	94262	2	181154.9	2	300	41.20	30.20	31.12
1165.093	108709.2	2	194539.1	2	100	53.50	39.10	39.32
1214.930	102712.2	3	185021.6	3	100	21.20	15.80	20.95
1230.928	94262	2	175501.8	3	200	21.80	17.10	21.86
1355.655	92312.3	1	166076.9	1	200	14.80	11.00	13.63
1373.837	102712.2	3	175501.8	3	300	51.40	39.80	46.99
1380.310	108709.2	2	181154.9	2	100	8.32	6.09	7.51
1387.963	102712.2	3	174761.5	2	500	39.90	31.00	34.16
1392.531	94262	2	166076.9	1	200	25.10	19.70	21.98
1432.221	92312.3	1	162134.4	2	200	27.50	21.30	23.74
1473.437	94262	2	162134.4	2	300	26.50	20.40	23.08
1497.166	108709.2	2	175501.8	3	300	21.00	17.00	17.14
1513.957	108709.2	2	174761.5	2	200	17.10	12.90	14.59
289.012	10308	3	356322	3	2	69.90	29.10	28.88
290.288	19444	2	363927	1	45	94.80	93.30	151.09
296.345	0	2	337436	3	60	3500.00	497.00	786.35
296.663	10308	3	347386	2	40	243.00	129.00	128.89
297.759	10308	3	346144	4	75	4540.00	1180.00	1709.49
298.725	22098	1	356849	1	50	849.00	231.00	146.29
298.890	19444	2	354012	2	50	611.00	236.00	292.43
299.182	0	2	334240	3	75	2820.00	1620.00	1577.63
299.687	31274	4	364949	5	75	10400.00	5450.00	6409.01
299.765	10308	3	343897	4	70	907.00	747.00	514.21
301.862	18049	4	349324	5	70	8050.00	3320.00	3931.69
302.296	33127	2	363927	1	30	135.00	129.00	152.35
303.299	19444	2	349155	3	75	3270.00	1230.00	1445.79
304.795	18049	4	346144	4	75	1950.00	802.00	804.92
306.749	15837	0	341844	1	80	563.00	586.00	350.33
307.425	22098	1	347386	2	75	1440.00	539.00	694.66
308.648	10308	3	334302	4	85	2290.00	990.00	1049.93
309.695	10308	3	337436	3	60	1470.00	688.00	752.56
311.385	10308	3	331454	4	85	267.00	156.00	245.18
311.643	19444	2	340330	2	90	1020.00	379.00	446.48
313.007	18049	4	337535	5	80	1280.00	642.00	718.07
314.236	22098	1	340330	2	90	1200.00	613.00	578.40
314.418	31274	4	349324	5	85	849.00	324.00	329.80
314.476	19444	2	337436	3	85	383.00	391.00	323.00
317.594	31274	4	346144	4	65	120.00	172.00	97.91
317.670	19444	2	334240	3	80	677.00	172.00	240.88
322.158	22098	1	332501	2	20	42.30	20.30	20.28
417.700	15837	0	255246	1	60	16.70	14.80	17.19
418.242	10308	3	249401	3	65	28.90	24.90	20.33
419.945	10308	3	248430	2	70	44.80	39.30	32.86
420.723	0	2	237682	1	70	57.90	49.60	44.25
421.860	10308	3	247354	4	60	36.20	30.30	28.26
422.439	0	2	236726	3	55	11.80	11.40	9.22
424.073	19444	2	255246	1	60	38.50	33.10	27.47
428.898	22098	1	255246	1	55	14.40	12.00	11.28
436.096	18049	4	247354	4	70	405.00	342.00	351.39
441.655	10308	3	236726	3	70	41.80	34.80	31.27
441.826	22098	1	248430	2	70	52.10	44.30	45.16
444.964	0	2	224741	3	70	15.60	11.80	13.98
446.849	0	2	223790	2	70	16.30	14.90	20.33
450.170	10308	3	232453	2	75	323.00	283.00	286.84
450.209	33127	2	255246	1	70	147.00	129.00	131.19
450.758	15837	0	237682	1	75	41.20	34.60	33.83
457.297	18049	4	236726	3	80	646.00	563.00	585.81
458.208	19444	2	237682	1	78	155.00	137.00	139.06
458.437	31274	4	249401	3	80	1010.00	886.00	895.98
459.364	22098	1	239794	0	70	99.60	88.30	89.97
460.234	19444	2	236726	3	60	9.54	12.00	12.76
462.380	33127	2	249401	3	60	25.80	31.10	25.09
462.799	31274	4	247354	4	60	68.00	57.90	50.01
463.851	22098	1	237682	1	70	78.50	71.70	72.72
464.454	33127	2	248430	2	70	414.00	365.00	366.10
466.358	10308	3	224741	3	70	285.00	243.00	267.38
468.435	10308	3	223790	2	70	231.00	199.00	222.21
469.467	19444	2	232453	2	70	180.00	155.00	156.97
469.797	0	2	212862	1	70	280.00	244.00	269.69
472.031	142163	3	354012	2	10	44.20	6.64*	19.38
475.213	131416	2	341844	1	28	157.00	10.80***	93.17
479.260	0	2	208659	2	70	261.00	221.00	234.72
483.819	18049	4	224741	3	70	185.00	163.00	166.13
486.734	31274	4	236726	3	70	72.60	61.70	67.13
487.117	19444	2	224741	3	65	22.70	23.80	23.83
489.371	19444	2	223790	2	70	165.00	141.00	145.05
491.165	33127	2	236726	3	50	16.10	14.50	16.68
495.805	22098	1	223790	2	70	103.00	95.80	101.12
506.221	57710	0	255246	1	70	73.30	68.80	63.68
507.563	15837	0	212862	1	70	53.90	50.50	52.41
516.885	31274	4	224741	3	65	48.20	41.10	44.73
521.865	33127	2	224741	3	60	5.07	4.83	5.75
528.505	19444	2	208659	2	60	20.10	18.80	24.89
854.600	131416	2	248430	2	45	23.20	20.60	23.62
905.036	129301	1	239794	0	50	37.70	32.40	33.39
922.672	129301	1	237682	1	50	80.70	64.20	65.81
932.508	142163	3	249401	3	30	104.00	76.10	74.13
932.636	148023	2	255246	1	55	98.60	81.60	87.43
941.023	142163	3	248430	2	45	60.80	54.20	60.00
949.584	131416	2	236726	3	50	214.00	166.00	176.75
950.655	142163	3	247354	4	70	313.00	246.00	268.83
969.440	129301	1	232453	2	40	90.50	70.20	76.72
986.390	148023	2	249401	3	30	131.00	106.00	121.42
989.742	131416	2	232453	2	50	60.60	44.50	45.18
995.946	148023	2	248430	2	50	82.60	61.20	60.94
1057.496	142163	3	236726	3	20	20.80	15.30	20.16
1071.537	131416	2	224741	3	40	20.80	16.30	20.82
1196.743	129301	1	212862	1	15	18.00	13.10	15.71
1210.984	142163	3	224741	3	50	65.80	50.60	58.11
1225.082	142163	3	223790	2	50	51.30	41.30	43.82
1227.815	131416	2	212862	1	30	32.70	26.00	28.15
1260.119	129301	1	208659	2	50	35.00	27.10	29.60
1294.622	131416	2	208659	2	60	35.30	27.00	29.86
1303.446	148023	2	224741	3	55	31.50	25.30	25.70
1319.811	148023	2	223790	2	40	22.60	16.70	18.52

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [15]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 13. Transition probabilities for the selected 92 experimentally observed lines in Os VII.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
289.012	10308	3	356322	3	2	69.90	29.10	28.88
290.288	19444	2	363927	1	45	94.80	93.30	151.09
296.345	0	2	337436	3	60	3500.00	497.00	786.35
296.663	10308	3	347386	2	40	243.00	129.00	128.89
297.759	10308	3	346144	4	75	4540.00	1180.00	1709.49
298.725	22098	1	356849	1	50	849.00	231.00	146.29
298.890	19444	2	354012	2	50	611.00	236.00	292.43
299.182	0	2	334240	3	75	2820.00	1620.00	1577.63
299.687	31274	4	364949	5	75	10400.00	5450.00	6409.01
299.765	10308	3	343897	4	70	907.00	747.00	514.21
301.862	18049	4	349324	5	70	8050.00	3320.00	3931.69
302.296	33127	2	363927	1	30	135.00	129.00	152.35
303.299	19444	2	349155	3	75	3270.00	1230.00	1445.79
304.795	18049	4	346144	4	75	1950.00	802.00	804.92
306.749	15837	0	341844	1	80	563.00	586.00	350.33
307.425	22098	1	347386	2	75	1440.00	539.00	694.66
308.648	10308	3	334302	4	85	2290.00	990.00	1049.93
309.695	10308	3	337436	3	60	1470.00	688.00	752.56
311.385	10308	3	331454	4	85	267.00	156.00	245.18
311.643	19444	2	340330	2	90	1020.00	379.00	446.48
313.007	18049	4	337535	5	80	1280.00	642.00	718.07
314.236	22098	1	340330	2	90	1200.00	613.00	578.40
314.418	31274	4	349324	5	85	849.00	324.00	329.80
314.476	19444	2	337436	3	85	383.00	391.00	323.00
317.594	31274	4	346144	4	65	120.00	172.00	97.91
317.670	19444	2	334240	3	80	677.00	172.00	240.88
322.158	22098	1	332501	2	20	42.30	20.30	20.28
417.700	15837	0	255246	1	60	16.70	14.80	17.19
418.242	10308	3	249401	3	65	28.90	24.90	20.33
419.945	10308	3	248430	2	70	44.80	39.30	32.86
420.723	0	2	237682	1	70	57.90	49.60	44.25
421.860	10308	3	247354	4	60	36.20	30.30	28.26
422.439	0	2	236726	3	55	11.80	11.40	9.22
424.073	19444	2	255246	1	60	38.50	33.10	27.47
428.898	22098	1	255246	1	55	14.40	12.00	11.28
436.096	18049	4	247354	4	70	405.00	342.00	351.39
441.655	10308	3	236726	3	70	41.80	34.80	31.27
441.826	22098	1	248430	2	70	52.10	44.30	45.16
444.964	0	2	224741	3	70	15.60	11.80	13.98
446.849	0	2	223790	2	70	16.30	14.90	20.33
450.170	10308	3	232453	2	75	323.00	283.00	286.84
450.209	33127	2	255246	1	70	147.00	129.00	131.19
450.758	15837	0	237682	1	75	41.20	34.60	33.83
457.297	18049	4	236726	3	80	646.00	563.00	585.81
458.208	19444	2	237682	1	78	155.00	137.00	139.06
458.437	31274	4	249401	3	80	1010.00	886.00	895.98
459.364	22098	1	239794	0	70	99.60	88.30	89.97
460.234	19444	2	236726	3	60	9.54	12.00	12.76
462.380	33127	2	249401	3	60	25.80	31.10	25.09
462.799	31274	4	247354	4	60	68.00	57.90	50.01
463.851	22098	1	237682	1	70	78.50	71.70	72.72
464.454	33127	2	248430	2	70	414.00	365.00	366.10
466.358	10308	3	224741	3	70	285.00	243.00	267.38
468.435	10308	3	223790	2	70	231.00	199.00	222.21
469.467	19444	2	232453	2	70	180.00	155.00	156.97
469.797	0	2	212862	1	70	280.00	244.00	269.69
472.031	142163	3	354012	2	10	44.20	6.64*	19.38
475.213	131416	2	341844	1	28	157.00	10.80***	93.17
479.260	0	2	208659	2	70	261.00	221.00	234.72
483.819	18049	4	224741	3	70	185.00	163.00	166.13
486.734	31274	4	236726	3	70	72.60	61.70	67.13
487.117	19444	2	224741	3	65	22.70	23.80	23.83
489.371	19444	2	223790	2	70	165.00	141.00	145.05
491.165	33127	2	236726	3	50	16.10	14.50	16.68
495.805	22098	1	223790	2	70	103.00	95.80	101.12
506.221	57710	0	255246	1	70	73.30	68.80	63.68
507.563	15837	0	212862	1	70	53.90	50.50	52.41
516.885	31274	4	224741	3	65	48.20	41.10	44.73
521.865	33127	2	224741	3	60	5.07	4.83	5.75
528.505	19444	2	208659	2	60	20.10	18.80	24.89
854.600	131416	2	248430	2	45	23.20	20.60	23.62
905.036	129301	1	239794	0	50	37.70	32.40	33.39
922.672	129301	1	237682	1	50	80.70	64.20	65.81
932.508	142163	3	249401	3	30	104.00	76.10	74.13
932.636	148023	2	255246	1	55	98.60	81.60	87.43
941.023	142163	3	248430	2	45	60.80	54.20	60.00
949.584	131416	2	236726	3	50	214.00	166.00	176.75
950.655	142163	3	247354	4	70	313.00	246.00	268.83
969.440	129301	1	232453	2	40	90.50	70.20	76.72
986.390	148023	2	249401	3	30	131.00	106.00	121.42
989.742	131416	2	232453	2	50	60.60	44.50	45.18
995.946	148023	2	248430	2	50	82.60	61.20	60.94
1057.496	142163	3	236726	3	20	20.80	15.30	20.16
1071.537	131416	2	224741	3	40	20.80	16.30	20.82
1196.743	129301	1	212862	1	15	18.00	13.10	15.71
1210.984	142163	3	224741	3	50	65.80	50.60	58.11
1225.082	142163	3	223790	2	50	51.30	41.30	43.82
1227.815	131416	2	212862	1	30	32.70	26.00	28.15
1260.119	129301	1	208659	2	50	35.00	27.10	29.60
1294.622	131416	2	208659	2	60	35.30	27.00	29.86
1303.446	148023	2	224741	3	55	31.50	25.30	25.70
1319.811	148023	2	223790	2	40	22.60	16.70	18.52

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [16] and [17]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 13. Transition probabilities for the selected 92 experimentally observed lines in Os VII.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
289.012	10308	3	356322	3	2	69.90	29.10	28.88
290.288	19444	2	363927	1	45	94.80	93.30	151.09
296.345	0	2	337436	3	60	3500.00	497.00	786.35
296.663	10308	3	347386	2	40	243.00	129.00	128.89
297.759	10308	3	346144	4	75	4540.00	1180.00	1709.49
298.725	22098	1	356849	1	50	849.00	231.00	146.29
298.890	19444	2	354012	2	50	611.00	236.00	292.43
299.182	0	2	334240	3	75	2820.00	1620.00	1577.63
299.687	31274	4	364949	5	75	10400.00	5450.00	6409.01
299.765	10308	3	343897	4	70	907.00	747.00	514.21
301.862	18049	4	349324	5	70	8050.00	3320.00	3931.69
302.296	33127	2	363927	1	30	135.00	129.00	152.35
303.299	19444	2	349155	3	75	3270.00	1230.00	1445.79
304.795	18049	4	346144	4	75	1950.00	802.00	804.92
306.749	15837	0	341844	1	80	563.00	586.00	350.33
307.425	22098	1	347386	2	75	1440.00	539.00	694.66
308.648	10308	3	334302	4	85	2290.00	990.00	1049.93
309.695	10308	3	337436	3	60	1470.00	688.00	752.56
311.385	10308	3	331454	4	85	267.00	156.00	245.18
311.643	19444	2	340330	2	90	1020.00	379.00	446.48
313.007	18049	4	337535	5	80	1280.00	642.00	718.07
314.236	22098	1	340330	2	90	1200.00	613.00	578.40
314.418	31274	4	349324	5	85	849.00	324.00	329.80
314.476	19444	2	337436	3	85	383.00	391.00	323.00
317.594	31274	4	346144	4	65	120.00	172.00	97.91
317.670	19444	2	334240	3	80	677.00	172.00	240.88
322.158	22098	1	332501	2	20	42.30	20.30	20.28
417.700	15837	0	255246	1	60	16.70	14.80	17.19
418.242	10308	3	249401	3	65	28.90	24.90	20.33
419.945	10308	3	248430	2	70	44.80	39.30	32.86
420.723	0	2	237682	1	70	57.90	49.60	44.25
421.860	10308	3	247354	4	60	36.20	30.30	28.26
422.439	0	2	236726	3	55	11.80	11.40	9.22
424.073	19444	2	255246	1	60	38.50	33.10	27.47
428.898	22098	1	255246	1	55	14.40	12.00	11.28
436.096	18049	4	247354	4	70	405.00	342.00	351.39
441.655	10308	3	236726	3	70	41.80	34.80	31.27
441.826	22098	1	248430	2	70	52.10	44.30	45.16
444.964	0	2	224741	3	70	15.60	11.80	13.98
446.849	0	2	223790	2	70	16.30	14.90	20.33
450.170	10308	3	232453	2	75	323.00	283.00	286.84
450.209	33127	2	255246	1	70	147.00	129.00	131.19
450.758	15837	0	237682	1	75	41.20	34.60	33.83
457.297	18049	4	236726	3	80	646.00	563.00	585.81
458.208	19444	2	237682	1	78	155.00	137.00	139.06
458.437	31274	4	249401	3	80	1010.00	886.00	895.98
459.364	22098	1	239794	0	70	99.60	88.30	89.97
460.234	19444	2	236726	3	60	9.54	12.00	12.76
462.380	33127	2	249401	3	60	25.80	31.10	25.09
462.799	31274	4	247354	4	60	68.00	57.90	50.01
463.851	22098	1	237682	1	70	78.50	71.70	72.72
464.454	33127	2	248430	2	70	414.00	365.00	366.10
466.358	10308	3	224741	3	70	285.00	243.00	267.38
468.435	10308	3	223790	2	70	231.00	199.00	222.21
469.467	19444	2	232453	2	70	180.00	155.00	156.97
469.797	0	2	212862	1	70	280.00	244.00	269.69
472.031	142163	3	354012	2	10	44.20	6.64*	19.38
475.213	131416	2	341844	1	28	157.00	10.80***	93.17
479.260	0	2	208659	2	70	261.00	221.00	234.72
483.819	18049	4	224741	3	70	185.00	163.00	166.13
486.734	31274	4	236726	3	70	72.60	61.70	67.13
487.117	19444	2	224741	3	65	22.70	23.80	23.83
489.371	19444	2	223790	2	70	165.00	141.00	145.05
491.165	33127	2	236726	3	50	16.10	14.50	16.68
495.805	22098	1	223790	2	70	103.00	95.80	101.12
506.221	57710	0	255246	1	70	73.30	68.80	63.68
507.563	15837	0	212862	1	70	53.90	50.50	52.41
516.885	31274	4	224741	3	65	48.20	41.10	44.73
521.865	33127	2	224741	3	60	5.07	4.83	5.75
528.505	19444	2	208659	2	60	20.10	18.80	24.89
854.600	131416	2	248430	2	45	23.20	20.60	23.62
905.036	129301	1	239794	0	50	37.70	32.40	33.39
922.672	129301	1	237682	1	50	80.70	64.20	65.81
932.508	142163	3	249401	3	30	104.00	76.10	74.13
932.636	148023	2	255246	1	55	98.60	81.60	87.43
941.023	142163	3	248430	2	45	60.80	54.20	60.00
949.584	131416	2	236726	3	50	214.00	166.00	176.75
950.655	142163	3	247354	4	70	313.00	246.00	268.83
969.440	129301	1	232453	2	40	90.50	70.20	76.72
986.390	148023	2	249401	3	30	131.00	106.00	121.42
989.742	131416	2	232453	2	50	60.60	44.50	45.18
995.946	148023	2	248430	2	50	82.60	61.20	60.94
1057.496	142163	3	236726	3	20	20.80	15.30	20.16
1071.537	131416	2	224741	3	40	20.80	16.30	20.82
1196.743	129301	1	212862	1	15	18.00	13.10	15.71
1210.984	142163	3	224741	3	50	65.80	50.60	58.11
1225.082	142163	3	223790	2	50	51.30	41.30	43.82
1227.815	131416	2	212862	1	30	32.70	26.00	28.15
1260.119	129301	1	208659	2	50	35.00	27.10	29.60
1294.622	131416	2	208659	2	60	35.30	27.00	29.86
1303.446	148023	2	224741	3	55	31.50	25.30	25.70
1319.811	148023	2	223790	2	40	22.60	16.70	18.52

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [16] and [17]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 14. Transition probabilities for the selected 77 experimentally observed lines in Ir VIII.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
255.173	0	2	391888	1	8	252.00	88.90	95.24
259.822	12672	3	397557	2	20	518.00	109.00	100.81
260.391	36253	4	420291	5	90	14200.00	2360.00*	6552.40
264.892	21615	4	399128	5	75	9500.00	2860.00	3666.30
266.929	17254	0	391888	1	90	2020.00	503.00	645.18
266.978	22436	2	385282	3	90	1290.00	508.00	538.65
268.374	12672	3	385282	3	65	2380.00	718.00	870.16
268.572	25221	1	397557	2	55	2230.00	452.00	439.74
269.657	12672	3	383508	4	85	3260.00	1120.00	1284.05
270.603	38878	2	408418	3	80	5320.00	969.00*	2390.59
271.988	12672	3	380334	4	90	1070.00	242.00	369.60
272.494	38878	2	405867	2	70	2610.00	875.00	761.96
273.285	21615	4	387545	5	80	2800.00	777.00	1005.92
275.576	36253	4	399128	5	65	1830.00	521.00	529.04
275.594	22436	2	385282	3	65	1290.00	508.00	538.65
279.783	36253	4	396001	4	60	1080.00	305.00	386.47
280.302	65022	0	421774	1	55	638.00	575.00	783.82
337.532	17254	0	313520	1	15	23.80	20.20	24.82
340.105	12672	3	306697	3	25	44.20	38.30	31.58
341.036	12672	3	305894	2	20	68.00	59.30	49.69
341.610	0	2	292734	1	30	88.50	74.90	66.90
342.071	12672	3	305005	4	30	56.20	46.80	42.81
342.704	0	2	291792	3	30	19.80	20.20	16.22
343.538	22436	2	313520	1	25	56.80	49.50	39.78
346.855	25221	1	313520	1	15	22.60	18.60	17.09
352.862	21615	4	305005	4	75	594.00	502.00	506.81
356.281	25221	1	305894	2	40	78.90	65.80	65.27
358.267	12672	3	291792	3	45	80.50	65.60	59.48
361.018	0	2	276994	3	30	21.80	15.60	18.59
362.492	0	2	275872	2	30	21.50	20.00	26.52
363.009	17254	0	292734	1	40	63.70	52.70	49.78
364.105	38878	2	313520	1	65	237.00	209.00	208.16
364.365	12672	3	287122	2	80	503.00	438.00	436.90
369.747	36253	4	306697	3	85	1560.00	1370.00	1354.54
369.959	22436	2	292734	1	60	248.00	221.00	219.83
370.130	21615	4	291792	3	85	980.00	859.00	871.12
370.482	25221	1	295142	0	60	155.00	137.00	137.51
371.256	22436	2	291792	3	20	11.90	18.00	18.39
372.087	36253	4	305005	4	65	136.00	116.00	100.00
373.384	38878	2	306697	3	45	39.90	52.80	43.85
373.812	25221	1	292734	1	65	121.00	112.00	111.51
374.497	38878	2	305894	2	80	635.00	561.00	553.56
377.800	22436	2	287122	2	80	270.00	235.00	233.84
378.330	12672	3	276994	3	85	422.00	362.00	391.12
379.948	12672	3	275872	2	85	348.00	302.00	330.07
381.001	0	2	262461	1	85	427.00	373.00	403.57
387.581	0	2	258017	2	90	404.00	344.00	360.05
391.332	36253	4	291792	3	70	101.00	80.30	92.86
391.584	21615	4	276994	3	85	329.00	289.00	290.26
392.845	22436	2	276994	3	65	37.10	41.20	40.45
394.582	22436	2	275872	2	80	256.00	217.00	222.55
395.395	38878	2	291792	3	40	18.90	17.40	19.63
398.967	25221	1	275872	2	85	161.00	153.00	159.89
402.428	65022	0	313520	1	70	115.00	114.00	100.29
407.816	17254	0	262461	1	80	85.50	81.80	83.47
415.388	36253	4	276994	3	75	73.90	60.90	69.63
424.496	22436	2	258017	2	75	25.00	24.10	31.19
743.999	171485	2	305894	2	80	24.50	22.20	24.78
794.159	169223	1	295142	0	70	49.70	42.30	42.34
809.641	169223	1	292734	1	80	108.00	84.80	84.81
813.228	190553	2	313520	1	85	135.00	109.00	114.09
820.016	184748	3	306697	3	70	144.00	104.00	100.41
824.748	171485	2	292734	1	70	34.50	30.80	32.14
825.452	184748	3	305894	2	70	76.70	68.10	72.35
831.204	171485	2	291792	3	85	290.00	225.00	231.80
831.552	184748	3	305005	4	85	412.00	322.00	340.15
848.179	169223	1	287122	2	80	119.00	91.60	96.27
860.999	190553	2	306697	3	80	167.00	136.00	148.07
864.771	171485	2	287122	2	80	85.20	61.80	61.31
867.000	190553	2	305894	2	75	120.00	87.80	85.70
1084.055	184748	3	276994	3	85	80.50	62.00	67.73
1097.392	184748	3	275872	2	30	64.80	51.70	52.97
1099.197	171485	2	262461	1	15	41.30	32.50	33.99
1126.192	169223	1	258017	2	30	43.50	33.40	35.08
1155.627	171485	2	258017	2	25	44.70	34.20	36.04
1156.853	190553	2	276994	3	25	43.50	34.50	34.46
1172.084	190553	2	275872	2	15	28.20	20.60	21.94
233.848	28517	1	456143	0	55	1070.00	148.00	164.06
239.044	25362	4	443691	5	95	11100.00	1170.00*	531.46
242.825	44997	2	456798	2	55	3690.00	337.00*	868.89
248.707	41618	4	443691	5	65	2900.00	551.00***	51.22
249.960	25575	2	425627	3	65	1460.00	522.00	642.22
280.474	18617	0	375151	1	30	33.30	30.40	34.38
283.946	15253	3	367446	3	55	63.40	55.10	46.13
284.456	15253	3	366809	2	55	96.60	83.80	71.35
284.911	0	2	350993	1	75	127.00	107.00	96.34
285.034	15253	3	366094	4	95	83.90	68.50	62.30
285.648	0	2	350085	3	40	27.30	30.70	25.90
286.066	25575	2	375151	1	45	78.50	63.70	54.38
288.487	28517	1	375151	1	60	31.50	27.20	24.72
293.485	25362	4	366094	4	95	825.00	690.00	693.37
295.609	28517	1	366809	2	50	109.00	93.70	90.20
298.664	15253	3	350085	3	80	139.00	110.00	101.64
300.865	18617	0	350993	1	50	89.00	74.90	69.60
301.092	0	2	332120	3	35	30.70	20.30	23.86
302.896	44997	2	375151	1	70	344.00	306.00	308.06
303.239	15253	3	345029	2	90	736.00	638.00	635.10
306.910	41618	4	367446	3	99	2250.00	1980.00	1944.17
307.297	25575	2	350993	1	85	363.00	330.00	326.56
307.528	28517	1	353695	0	70	220.00	201.00	199.29
307.956	25362	4	350085	3	99	1410.00	1230.00	1239.87
308.157	25575	2	350085	3	27	11.00	22.10	23.84
308.191	41618	4	366094	4	70	247.00	208.00	181.67
310.106	28517	1	350993	1	70	171.00	163.00	161.75
310.133	44997	2	367446	3	50	47.60	75.00	67.55
310.746	44997	2	366809	2	90	900.00	814.00	796.48
313.040	25575	2	345029	2	90	379.00	336.00	331.38
315.598	15253	3	332120	3	99	594.00	508.00	544.55
316.863	15253	3	330855	2	90	492.00	429.00	463.15
317.711	0	2	314764	1	97	611.00	533.00	572.96
322.514	0	2	310069	2	99	589.00	501.00	522.62
324.193	41618	4	350085	3	55	122.00	95.40	117.80
325.994	25362	4	332120	3	95	531.00	464.00	467.05
326.221	25575	2	332120	3	60	53.20	62.80	62.47
330.457	72535	0	375151	1	55	156.00	158.00	147.81
330.764	28517	1	330855	2	80	231.00	226.00	236.64
337.681	18617	0	314764	1	75	124.00	121.00	124.63
344.232	41618	4	332120	3	90	98.80	80.60	97.10
351.503	25575	2	310069	2	144	29.70	29.20	37.75
655.592	214275	2	366809	2	197	27.50	23.10	26.10
705.129	211877	1	353695	0	275	69.20	53.00	53.09
718.828	211877	1	350993	1	588	145.00	109.00	108.03
719.101	236084	2	375151	1	794	180.00	139.00	145.97
729.051	230283	3	367446	3	700	191.00	136.00	132.83
731.438	214275	2	350993	1	192	48.00	37.50	39.07
732.464	230283	3	366809	2	456	104.00	82.20	87.04
736.320	214275	2	350085	3	1313	380.00	293.00	298.58
751.022	211877	1	345029	2	637	152.00	117.00	120.13
761.261	236084	2	367446	3	606	210.00	170.00	180.10
764.800	214275	2	345029	2	552	116.00	82.70	81.40
764.969	236084	2	366809	2	536	167.00	120.00	116.32
834.731	230283	3	350085	3	125	19.80	15.30	18.07
971.945	211877	1	314764	1	244	23.80	17.60	19.28
981.958	230283	3	332120	3	485	96.10	73.70	78.48
994.309	230283	3	330855	2	243	82.50	62.60	63.59
995.136	214275	2	314764	1	231	51.80	39.50	40.74
1018.405	211877	1	310069	2	242	52.50	40.30	41.49
1041.273	236084	2	332120	3	221	56.60	44.80	44.53
1043.913	214275	2	310069	2	324	55.00	41.80	43.03
1055.171	236084	2	330855	2	774	33.60	24.70	25.75

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [16] and [17]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 14. Transition probabilities for the selected 77 experimentally observed lines in Ir VIII.

${\lambda }_{Exp}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$gA$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
255.173	0	2	391888	1	8	252.00	88.90	95.24
259.822	12672	3	397557	2	20	518.00	109.00	100.81
260.391	36253	4	420291	5	90	14200.00	2360.00*	6552.40
264.892	21615	4	399128	5	75	9500.00	2860.00	3666.30
266.929	17254	0	391888	1	90	2020.00	503.00	645.18
266.978	22436	2	385282	3	90	1290.00	508.00	538.65
268.374	12672	3	385282	3	65	2380.00	718.00	870.16
268.572	25221	1	397557	2	55	2230.00	452.00	439.74
269.657	12672	3	383508	4	85	3260.00	1120.00	1284.05
270.603	38878	2	408418	3	80	5320.00	969.00*	2390.59
271.988	12672	3	380334	4	90	1070.00	242.00	369.60
272.494	38878	2	405867	2	70	2610.00	875.00	761.96
273.285	21615	4	387545	5	80	2800.00	777.00	1005.92
275.576	36253	4	399128	5	65	1830.00	521.00	529.04
275.594	22436	2	385282	3	65	1290.00	508.00	538.65
279.783	36253	4	396001	4	60	1080.00	305.00	386.47
280.302	65022	0	421774	1	55	638.00	575.00	783.82
337.532	17254	0	313520	1	15	23.80	20.20	24.82
340.105	12672	3	306697	3	25	44.20	38.30	31.58
341.036	12672	3	305894	2	20	68.00	59.30	49.69
341.610	0	2	292734	1	30	88.50	74.90	66.90
342.071	12672	3	305005	4	30	56.20	46.80	42.81
342.704	0	2	291792	3	30	19.80	20.20	16.22
343.538	22436	2	313520	1	25	56.80	49.50	39.78
346.855	25221	1	313520	1	15	22.60	18.60	17.09
352.862	21615	4	305005	4	75	594.00	502.00	506.81
356.281	25221	1	305894	2	40	78.90	65.80	65.27
358.267	12672	3	291792	3	45	80.50	65.60	59.48
361.018	0	2	276994	3	30	21.80	15.60	18.59
362.492	0	2	275872	2	30	21.50	20.00	26.52
363.009	17254	0	292734	1	40	63.70	52.70	49.78
364.105	38878	2	313520	1	65	237.00	209.00	208.16
364.365	12672	3	287122	2	80	503.00	438.00	436.90
369.747	36253	4	306697	3	85	1560.00	1370.00	1354.54
369.959	22436	2	292734	1	60	248.00	221.00	219.83
370.130	21615	4	291792	3	85	980.00	859.00	871.12
370.482	25221	1	295142	0	60	155.00	137.00	137.51
371.256	22436	2	291792	3	20	11.90	18.00	18.39
372.087	36253	4	305005	4	65	136.00	116.00	100.00
373.384	38878	2	306697	3	45	39.90	52.80	43.85
373.812	25221	1	292734	1	65	121.00	112.00	111.51
374.497	38878	2	305894	2	80	635.00	561.00	553.56
377.800	22436	2	287122	2	80	270.00	235.00	233.84
378.330	12672	3	276994	3	85	422.00	362.00	391.12
379.948	12672	3	275872	2	85	348.00	302.00	330.07
381.001	0	2	262461	1	85	427.00	373.00	403.57
387.581	0	2	258017	2	90	404.00	344.00	360.05
391.332	36253	4	291792	3	70	101.00	80.30	92.86
391.584	21615	4	276994	3	85	329.00	289.00	290.26
392.845	22436	2	276994	3	65	37.10	41.20	40.45
394.582	22436	2	275872	2	80	256.00	217.00	222.55
395.395	38878	2	291792	3	40	18.90	17.40	19.63
398.967	25221	1	275872	2	85	161.00	153.00	159.89
402.428	65022	0	313520	1	70	115.00	114.00	100.29
407.816	17254	0	262461	1	80	85.50	81.80	83.47
415.388	36253	4	276994	3	75	73.90	60.90	69.63
424.496	22436	2	258017	2	75	25.00	24.10	31.19
743.999	171485	2	305894	2	80	24.50	22.20	24.78
794.159	169223	1	295142	0	70	49.70	42.30	42.34
809.641	169223	1	292734	1	80	108.00	84.80	84.81
813.228	190553	2	313520	1	85	135.00	109.00	114.09
820.016	184748	3	306697	3	70	144.00	104.00	100.41
824.748	171485	2	292734	1	70	34.50	30.80	32.14
825.452	184748	3	305894	2	70	76.70	68.10	72.35
831.204	171485	2	291792	3	85	290.00	225.00	231.80
831.552	184748	3	305005	4	85	412.00	322.00	340.15
848.179	169223	1	287122	2	80	119.00	91.60	96.27
860.999	190553	2	306697	3	80	167.00	136.00	148.07
864.771	171485	2	287122	2	80	85.20	61.80	61.31
867.000	190553	2	305894	2	75	120.00	87.80	85.70
1084.055	184748	3	276994	3	85	80.50	62.00	67.73
1097.392	184748	3	275872	2	30	64.80	51.70	52.97
1099.197	171485	2	262461	1	15	41.30	32.50	33.99
1126.192	169223	1	258017	2	30	43.50	33.40	35.08
1155.627	171485	2	258017	2	25	44.70	34.20	36.04
1156.853	190553	2	276994	3	25	43.50	34.50	34.46
1172.084	190553	2	275872	2	15	28.20	20.60	21.94
233.848	28517	1	456143	0	55	1070.00	148.00	164.06
239.044	25362	4	443691	5	95	11100.00	1170.00*	531.46
242.825	44997	2	456798	2	55	3690.00	337.00*	868.89
248.707	41618	4	443691	5	65	2900.00	551.00***	51.22
249.960	25575	2	425627	3	65	1460.00	522.00	642.22
280.474	18617	0	375151	1	30	33.30	30.40	34.38
283.946	15253	3	367446	3	55	63.40	55.10	46.13
284.456	15253	3	366809	2	55	96.60	83.80	71.35
284.911	0	2	350993	1	75	127.00	107.00	96.34
285.034	15253	3	366094	4	95	83.90	68.50	62.30
285.648	0	2	350085	3	40	27.30	30.70	25.90
286.066	25575	2	375151	1	45	78.50	63.70	54.38
288.487	28517	1	375151	1	60	31.50	27.20	24.72
293.485	25362	4	366094	4	95	825.00	690.00	693.37
295.609	28517	1	366809	2	50	109.00	93.70	90.20
298.664	15253	3	350085	3	80	139.00	110.00	101.64
300.865	18617	0	350993	1	50	89.00	74.90	69.60
301.092	0	2	332120	3	35	30.70	20.30	23.86
302.896	44997	2	375151	1	70	344.00	306.00	308.06
303.239	15253	3	345029	2	90	736.00	638.00	635.10
306.910	41618	4	367446	3	99	2250.00	1980.00	1944.17
307.297	25575	2	350993	1	85	363.00	330.00	326.56
307.528	28517	1	353695	0	70	220.00	201.00	199.29
307.956	25362	4	350085	3	99	1410.00	1230.00	1239.87
308.157	25575	2	350085	3	27	11.00	22.10	23.84
308.191	41618	4	366094	4	70	247.00	208.00	181.67
310.106	28517	1	350993	1	70	171.00	163.00	161.75
310.133	44997	2	367446	3	50	47.60	75.00	67.55
310.746	44997	2	366809	2	90	900.00	814.00	796.48
313.040	25575	2	345029	2	90	379.00	336.00	331.38
315.598	15253	3	332120	3	99	594.00	508.00	544.55
316.863	15253	3	330855	2	90	492.00	429.00	463.15
317.711	0	2	314764	1	97	611.00	533.00	572.96
322.514	0	2	310069	2	99	589.00	501.00	522.62
324.193	41618	4	350085	3	55	122.00	95.40	117.80
325.994	25362	4	332120	3	95	531.00	464.00	467.05
326.221	25575	2	332120	3	60	53.20	62.80	62.47
330.457	72535	0	375151	1	55	156.00	158.00	147.81
330.764	28517	1	330855	2	80	231.00	226.00	236.64
337.681	18617	0	314764	1	75	124.00	121.00	124.63
344.232	41618	4	332120	3	90	98.80	80.60	97.10
351.503	25575	2	310069	2	144	29.70	29.20	37.75
655.592	214275	2	366809	2	197	27.50	23.10	26.10
705.129	211877	1	353695	0	275	69.20	53.00	53.09
718.828	211877	1	350993	1	588	145.00	109.00	108.03
719.101	236084	2	375151	1	794	180.00	139.00	145.97
729.051	230283	3	367446	3	700	191.00	136.00	132.83
731.438	214275	2	350993	1	192	48.00	37.50	39.07
732.464	230283	3	366809	2	456	104.00	82.20	87.04
736.320	214275	2	350085	3	1313	380.00	293.00	298.58
751.022	211877	1	345029	2	637	152.00	117.00	120.13
761.261	236084	2	367446	3	606	210.00	170.00	180.10
764.800	214275	2	345029	2	552	116.00	82.70	81.40
764.969	236084	2	366809	2	536	167.00	120.00	116.32
834.731	230283	3	350085	3	125	19.80	15.30	18.07
971.945	211877	1	314764	1	244	23.80	17.60	19.28
981.958	230283	3	332120	3	485	96.10	73.70	78.48
994.309	230283	3	330855	2	243	82.50	62.60	63.59
995.136	214275	2	314764	1	231	51.80	39.50	40.74
1018.405	211877	1	310069	2	242	52.50	40.30	41.49
1041.273	236084	2	332120	3	221	56.60	44.80	44.53
1043.913	214275	2	310069	2	324	55.00	41.80	43.03
1055.171	236084	2	330855	2	774	33.60	24.70	25.75

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [16] and [17]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 15. Transition probabilities for the selected 63 experimentally observed lines in Pt IX.

${\mathit{\lambda }}_{\mathit{E}\mathit{x}\mathit{p}}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$\mathit{g}\mathit{A}$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
233.848	28517	1	456143	0	55	1070.00	148.00	164.06
239.044	25362	4	443691	5	95	11100.00	1170.00*	531.46
242.825	44997	2	456798	2	55	3690.00	337.00*	868.89
248.707	41618	4	443691	5	65	2900.00	551.00***	51.22
249.960	25575	2	425627	3	65	1460.00	522.00	642.22
280.474	18617	0	375151	1	30	33.30	30.40	34.38
283.946	15253	3	367446	3	55	63.40	55.10	46.13
284.456	15253	3	366809	2	55	96.60	83.80	71.35
284.911	0	2	350993	1	75	127.00	107.00	96.34
285.034	15253	3	366094	4	95	83.90	68.50	62.30
285.648	0	2	350085	3	40	27.30	30.70	25.90
286.066	25575	2	375151	1	45	78.50	63.70	54.38
288.487	28517	1	375151	1	60	31.50	27.20	24.72
293.485	25362	4	366094	4	95	825.00	690.00	693.37
295.609	28517	1	366809	2	50	109.00	93.70	90.20
298.664	15253	3	350085	3	80	139.00	110.00	101.64
300.865	18617	0	350993	1	50	89.00	74.90	69.60
301.092	0	2	332120	3	35	30.70	20.30	23.86
302.896	44997	2	375151	1	70	344.00	306.00	308.06
303.239	15253	3	345029	2	90	736.00	638.00	635.10
306.910	41618	4	367446	3	99	2250.00	1980.00	1944.17
307.297	25575	2	350993	1	85	363.00	330.00	326.56
307.528	28517	1	353695	0	70	220.00	201.00	199.29
307.956	25362	4	350085	3	99	1410.00	1230.00	1239.87
308.157	25575	2	350085	3	27	11.00	22.10	23.84
308.191	41618	4	366094	4	70	247.00	208.00	181.67
310.106	28517	1	350993	1	70	171.00	163.00	161.75
310.133	44997	2	367446	3	50	47.60	75.00	67.55
310.746	44997	2	366809	2	90	900.00	814.00	796.48
313.040	25575	2	345029	2	90	379.00	336.00	331.38
315.598	15253	3	332120	3	99	594.00	508.00	544.55
316.863	15253	3	330855	2	90	492.00	429.00	463.15
317.711	0	2	314764	1	97	611.00	533.00	572.96
322.514	0	2	310069	2	99	589.00	501.00	522.62
324.193	41618	4	350085	3	55	122.00	95.40	117.80
325.994	25362	4	332120	3	95	531.00	464.00	467.05
326.221	25575	2	332120	3	60	53.20	62.80	62.47
330.457	72535	0	375151	1	55	156.00	158.00	147.81
330.764	28517	1	330855	2	80	231.00	226.00	236.64
337.681	18617	0	314764	1	75	124.00	121.00	124.63
344.232	41618	4	332120	3	90	98.80	80.60	97.10
351.503	25575	2	310069	2	144	29.70	29.20	37.75
655.592	214275	2	366809	2	197	27.50	23.10	26.10
705.129	211877	1	353695	0	275	69.20	53.00	53.09
718.828	211877	1	350993	1	588	145.00	109.00	108.03
719.101	236084	2	375151	1	794	180.00	139.00	145.97
729.051	230283	3	367446	3	700	191.00	136.00	132.83
731.438	214275	2	350993	1	192	48.00	37.50	39.07
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
732.464	230283	3	366809	2	456	104.00	82.20	87.04
736.320	214275	2	350085	3	1313	380.00	293.00	298.58
751.022	211877	1	345029	2	637	152.00	117.00	120.13
761.261	236084	2	367446	3	606	210.00	170.00	180.10
764.800	214275	2	345029	2	552	116.00	82.70	81.40
764.969	236084	2	366809	2	536	167.00	120.00	116.32
834.731	230283	3	350085	3	125	19.80	15.30	18.07
971.945	211877	1	314764	1	244	23.80	17.60	19.28
981.958	230283	3	332120	3	485	96.10	73.70	78.48
994.309	230283	3	330855	2	243	82.50	62.60	63.59
995.136	214275	2	314764	1	231	51.80	39.50	40.74
1018.405	211877	1	310069	2	242	52.50	40.30	41.49
1041.273	236084	2	332120	3	221	56.60	44.80	44.53
1043.913	214275	2	310069	2	324	55.00	41.80	43.03
1055.171	236084	2	330855	2	774	33.60	24.70	25.75

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [18] and [19]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 15. Transition probabilities for the selected 63 experimentally observed lines in Pt IX.

${\mathit{\lambda }}_{\mathit{E}\mathit{x}\mathit{p}}$ (Å) (a)	Lower Level (b)		Upper Level (c)		Int (d)	$\mathit{g}\mathit{A}$ (108 s−1)
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
233.848	28517	1	456143	0	55	1070.00	148.00	164.06
239.044	25362	4	443691	5	95	11100.00	1170.00*	531.46
242.825	44997	2	456798	2	55	3690.00	337.00*	868.89
248.707	41618	4	443691	5	65	2900.00	551.00***	51.22
249.960	25575	2	425627	3	65	1460.00	522.00	642.22
280.474	18617	0	375151	1	30	33.30	30.40	34.38
283.946	15253	3	367446	3	55	63.40	55.10	46.13
284.456	15253	3	366809	2	55	96.60	83.80	71.35
284.911	0	2	350993	1	75	127.00	107.00	96.34
285.034	15253	3	366094	4	95	83.90	68.50	62.30
285.648	0	2	350085	3	40	27.30	30.70	25.90
286.066	25575	2	375151	1	45	78.50	63.70	54.38
288.487	28517	1	375151	1	60	31.50	27.20	24.72
293.485	25362	4	366094	4	95	825.00	690.00	693.37
295.609	28517	1	366809	2	50	109.00	93.70	90.20
298.664	15253	3	350085	3	80	139.00	110.00	101.64
300.865	18617	0	350993	1	50	89.00	74.90	69.60
301.092	0	2	332120	3	35	30.70	20.30	23.86
302.896	44997	2	375151	1	70	344.00	306.00	308.06
303.239	15253	3	345029	2	90	736.00	638.00	635.10
306.910	41618	4	367446	3	99	2250.00	1980.00	1944.17
307.297	25575	2	350993	1	85	363.00	330.00	326.56
307.528	28517	1	353695	0	70	220.00	201.00	199.29
307.956	25362	4	350085	3	99	1410.00	1230.00	1239.87
308.157	25575	2	350085	3	27	11.00	22.10	23.84
308.191	41618	4	366094	4	70	247.00	208.00	181.67
310.106	28517	1	350993	1	70	171.00	163.00	161.75
310.133	44997	2	367446	3	50	47.60	75.00	67.55
310.746	44997	2	366809	2	90	900.00	814.00	796.48
313.040	25575	2	345029	2	90	379.00	336.00	331.38
315.598	15253	3	332120	3	99	594.00	508.00	544.55
316.863	15253	3	330855	2	90	492.00	429.00	463.15
317.711	0	2	314764	1	97	611.00	533.00	572.96
322.514	0	2	310069	2	99	589.00	501.00	522.62
324.193	41618	4	350085	3	55	122.00	95.40	117.80
325.994	25362	4	332120	3	95	531.00	464.00	467.05
326.221	25575	2	332120	3	60	53.20	62.80	62.47
330.457	72535	0	375151	1	55	156.00	158.00	147.81
330.764	28517	1	330855	2	80	231.00	226.00	236.64
337.681	18617	0	314764	1	75	124.00	121.00	124.63
344.232	41618	4	332120	3	90	98.80	80.60	97.10
351.503	25575	2	310069	2	144	29.70	29.20	37.75
655.592	214275	2	366809	2	197	27.50	23.10	26.10
705.129	211877	1	353695	0	275	69.20	53.00	53.09
718.828	211877	1	350993	1	588	145.00	109.00	108.03
719.101	236084	2	375151	1	794	180.00	139.00	145.97
729.051	230283	3	367446	3	700	191.00	136.00	132.83
731.438	214275	2	350993	1	192	48.00	37.50	39.07
	E(cm−1)	J	E(cm−1)	J		HFR (e)	HFR(CV) (e)	MCDHF (e)
732.464	230283	3	366809	2	456	104.00	82.20	87.04
736.320	214275	2	350085	3	1313	380.00	293.00	298.58
751.022	211877	1	345029	2	637	152.00	117.00	120.13
761.261	236084	2	367446	3	606	210.00	170.00	180.10
764.800	214275	2	345029	2	552	116.00	82.70	81.40
764.969	236084	2	366809	2	536	167.00	120.00	116.32
834.731	230283	3	350085	3	125	19.80	15.30	18.07
971.945	211877	1	314764	1	244	23.80	17.60	19.28
981.958	230283	3	332120	3	485	96.10	73.70	78.48
994.309	230283	3	330855	2	243	82.50	62.60	63.59
995.136	214275	2	314764	1	231	51.80	39.50	40.74
1018.405	211877	1	310069	2	242	52.50	40.30	41.49
1041.273	236084	2	332120	3	221	56.60	44.80	44.53
1043.913	214275	2	310069	2	324	55.00	41.80	43.03
1055.171	236084	2	330855	2	774	33.60	24.70	25.75

(a),(b),(c),(d) Experimental wavelengths, even and odd energy levels and intensities, respectively, from [18] and [19]; (e) Our HFR, HFR(CV) and MCDHF $gA$-values with $CF$-value higher than 0.05 and $dS$-value lower than 0.2.

Table 16. Line strengths computed previously with the RMBPT method in the length and velocity forms as well as with our MCDHF method in the Babushkin and Coulomb gauges for the 35 transitions between the 5d², 5d6s even configurations and the 5d6p odd configuration in Re VI.

${\mathit{\lambda }}_{\mathit{R}\mathit{i}\mathit{t}\mathit{z},\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (Å) (a)	${\mathit{\lambda }}_{\mathit{E}\mathit{x}\mathit{p}}$ (Å) (b)	Lower Level (c)		Upper Level (d)		${\mathit{S}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (a.u.)		${\mathit{S}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (a.u.)		$\mathit{d}\mathit{S}$ (e)
		E(cm−1)	J	E(cm−1)	J	Length	Velocity	Babushkin	Coulomb
536.560	536.550	8166.6	3	194539.1	2	0.138	0.144	0.139	0.135	0.032
537.469	537.462	14379.3	0	200436.6	1	0.065	0.065	0.078	0.075	0.044
537.742	537.738	0	2	185962.9	1	0.165	0.164	0.190	0.183	0.034
540.268		8166.6	3	193260.0	4	0.137	0.129	0.123	0.120	0.022
551.587	551.579	19141.6	1	200436.6	1	0.036	0.034	0.053	0.051	0.030
552.450		14679.4	4	195691.3	3	0.144	0.156	0.266	0.252	0.055
559.971	559.977	14679.4	4	193260.0	4	1.954	1.901	1.766	1.718	0.027
565.435	565.438	8166.6	3	185021.6	3	0.053	0.056	0.110	0.106	0.036
570.134	570.141	19141.6	1	194539.1	2	0.280	0.257	0.244	0.237	0.029
572.208		0	2	174761.5	2	0.115	0.115	0.120	0.118	0.018
578.074	578.051	8166.6	3	181154.9	2	1.615	1.611	1.517	1.467	0.033
582.806	582.803	14379.3	0	185962.9	1	0.242	0.227	0.190	0.185	0.030
587.054	587.053	14679.4	4	185021.6	3	3.696	3.645	3.315	3.216	0.030
591.596	591.596	26657.1	4	195691.3	3	5.643	5.582	5.150	5.067	0.016
592.983	592.993	19141.6	1	187780.4	0	0.504	0.501	0.507	0.489	0.037
597.603	597.599	8166.6	3	175501.8	3	1.688	1.533	1.596	1.568	0.017
599.444		19141.6	1	185962.9	1	0.414	0.413	0.421	0.404	0.039
600.230		26657.1	4	193260.0	4	0.154	0.157	0.216	0.209	0.036
617.233		19141.6	1	181154.9	2	0.027	0.030	0.033	0.031	0.060
621.804	621.805	14679.4	4	175501.8	3	0.590	0.520	0.887	0.871	0.017
629.227	629.221	16576.7	2	175501.8	3	0.038	0.036	0.135	0.124	0.084
631.455	631.454	26657.1	4	185021.6	3	0.312	0.303	0.486	0.484	0.004
659.206	659.206	14379.3	0	166076.9	1	0.263	0.231	0.383	0.363	0.052
666.912	666.912	50491.7	0	200436.6	1	0.326	0.343	0.532	0.506	0.048
680.572		19141.6	1	166076.9	1	0.008	0.008	0.008	0.007	0.133
738.164		50491.7	0	185962.9	1	0.005	0.005	0.031	0.029	0.056
865.163		50491.7	0	166076.9	1	0.004	0.003	0.036	0.034	0.070
997.237	997.245	94262.0	2	194539.1	2	1.214	1.260	0.970	0.907	0.065
1047.470	1047.444	92312.3	1	187780.4	0	1.166	1.179	1.264	1.176	0.070
1067.799	1067.393	92312.3	1	185962.9	1	2.186	2.276	2.596	2.479	0.045
1075.511	1075.472	102712.2	3	195691.3	3	1.732	1.833	2.771	2.728	0.015
1089.006	1089.016	102712.2	3	194539.1	2	2.720	2.967	2.713	2.494	0.081
1104.389	1104.368	102712.2	3	193260.0	4	11.135	11.502	12.053	11.649	0.034
1230.924	1230.928	94262.0	2	175501.8	3	2.449	2.710	1.767	1.729	0.021
1682.873		102712.2	3	162134.4	2	0.002	0.003	0.002	0.002	0.304

(a) Ritz wavelengths obtained using the energy levels computed by our HFR(CV) calculations; (b),(c),(d) Experimental wavelengths, even and odd energy levels, respectively, from [15]; (e) MCDHF uncertainty parameter as defined in [33].

Table 16. Line strengths computed previously with the RMBPT method in the length and velocity forms as well as with our MCDHF method in the Babushkin and Coulomb gauges for the 35 transitions between the 5d², 5d6s even configurations and the 5d6p odd configuration in Re VI.

${\mathit{\lambda }}_{\mathit{R}\mathit{i}\mathit{t}\mathit{z},\mathit{H}\mathit{F}\mathit{R}\left(\mathit{C}\mathit{V}\right)}$ (Å) (a)	${\mathit{\lambda }}_{\mathit{E}\mathit{x}\mathit{p}}$ (Å) (b)	Lower Level (c)		Upper Level (d)		${\mathit{S}}_{\mathit{R}\mathit{M}\mathit{B}\mathit{P}\mathit{T}}$ (a.u.)		${\mathit{S}}_{\mathit{M}\mathit{C}\mathit{D}\mathit{H}\mathit{F}}$ (a.u.)		$\mathit{d}\mathit{S}$ (e)
		E(cm−1)	J	E(cm−1)	J	Length	Velocity	Babushkin	Coulomb
536.560	536.550	8166.6	3	194539.1	2	0.138	0.144	0.139	0.135	0.032
537.469	537.462	14379.3	0	200436.6	1	0.065	0.065	0.078	0.075	0.044
537.742	537.738	0	2	185962.9	1	0.165	0.164	0.190	0.183	0.034
540.268		8166.6	3	193260.0	4	0.137	0.129	0.123	0.120	0.022
551.587	551.579	19141.6	1	200436.6	1	0.036	0.034	0.053	0.051	0.030
552.450		14679.4	4	195691.3	3	0.144	0.156	0.266	0.252	0.055
559.971	559.977	14679.4	4	193260.0	4	1.954	1.901	1.766	1.718	0.027
565.435	565.438	8166.6	3	185021.6	3	0.053	0.056	0.110	0.106	0.036
570.134	570.141	19141.6	1	194539.1	2	0.280	0.257	0.244	0.237	0.029
572.208		0	2	174761.5	2	0.115	0.115	0.120	0.118	0.018
578.074	578.051	8166.6	3	181154.9	2	1.615	1.611	1.517	1.467	0.033
582.806	582.803	14379.3	0	185962.9	1	0.242	0.227	0.190	0.185	0.030
587.054	587.053	14679.4	4	185021.6	3	3.696	3.645	3.315	3.216	0.030
591.596	591.596	26657.1	4	195691.3	3	5.643	5.582	5.150	5.067	0.016
592.983	592.993	19141.6	1	187780.4	0	0.504	0.501	0.507	0.489	0.037
597.603	597.599	8166.6	3	175501.8	3	1.688	1.533	1.596	1.568	0.017
599.444		19141.6	1	185962.9	1	0.414	0.413	0.421	0.404	0.039
600.230		26657.1	4	193260.0	4	0.154	0.157	0.216	0.209	0.036
617.233		19141.6	1	181154.9	2	0.027	0.030	0.033	0.031	0.060
621.804	621.805	14679.4	4	175501.8	3	0.590	0.520	0.887	0.871	0.017
629.227	629.221	16576.7	2	175501.8	3	0.038	0.036	0.135	0.124	0.084
631.455	631.454	26657.1	4	185021.6	3	0.312	0.303	0.486	0.484	0.004
659.206	659.206	14379.3	0	166076.9	1	0.263	0.231	0.383	0.363	0.052
666.912	666.912	50491.7	0	200436.6	1	0.326	0.343	0.532	0.506	0.048
680.572		19141.6	1	166076.9	1	0.008	0.008	0.008	0.007	0.133
738.164		50491.7	0	185962.9	1	0.005	0.005	0.031	0.029	0.056
865.163		50491.7	0	166076.9	1	0.004	0.003	0.036	0.034	0.070
997.237	997.245	94262.0	2	194539.1	2	1.214	1.260	0.970	0.907	0.065
1047.470	1047.444	92312.3	1	187780.4	0	1.166	1.179	1.264	1.176	0.070
1067.799	1067.393	92312.3	1	185962.9	1	2.186	2.276	2.596	2.479	0.045
1075.511	1075.472	102712.2	3	195691.3	3	1.732	1.833	2.771	2.728	0.015
1089.006	1089.016	102712.2	3	194539.1	2	2.720	2.967	2.713	2.494	0.081
1104.389	1104.368	102712.2	3	193260.0	4	11.135	11.502	12.053	11.649	0.034
1230.924	1230.928	94262.0	2	175501.8	3	2.449	2.710	1.767	1.729	0.021
1682.873		102712.2	3	162134.4	2	0.002	0.003	0.002	0.002	0.304

(a) Ritz wavelengths obtained using the energy levels computed by our HFR(CV) calculations; (b),(c),(d) Experimental wavelengths, even and odd energy levels, respectively, from [15]; (e) MCDHF uncertainty parameter as defined in [33].

4.3. Discussions

Although we have selected the transitions that were in a sense more reliable with a corresponding $C{F}_{HFR+CPOL}$- or $C{F}_{HFR\left(CV\right)}$-value higher than 0.05 and $d{S}_{MCDHF}$-value lower than 0.2, we still observed discrepancies between the Einstein coefficients computed with our two independent approaches (with ratio>5 or ratio<0.2 or with relative difference > 50%), namely the HFR+CPOL or HFR(CV) methods and the MCDHF method. We have seen that after applying the selection criteria on the $CF$- and $dS$-values, the percentages of the remaining transitions were 74%, 82%, 80%, 63%, 60% and 48% for Ta IV, W V, Re VI, Os VII, Ir VIII and Pt IX, respectively. After selecting only the most reliable transitions with a ratio in the range [0.2,5] and with a relative deviation lower than 50%, these percentages decreased to 66%, 80%, 78%, 60%, 58% and 46% for Ta IV, W V, Re VI, Os VII, Ir VIII and Pt IX, respectively. We explain the larger number of remaining transitions in W V than in Ta IV by the fact that the line strengths and thus the $gA$’s computed with the HFR+CPOL and the MCDHF methods were a little bit less affected by the cancellation effects (having higher $CF$-values) because of less important mixing in the level composition in W V than in Ta IV. We have already shown in Table 2 that the mean purity in W V is slightly higher than in Ta IV in the three coupling schemes presented in this work, i.e., $LS$, $j{j}_{Cowan}$ and $j{j}_{MCDHF}$, especially for the odd parity. However, for the four other Yb-like ions, the number of transitions computed with the HFR(CV) and the MCDHF methods that present some discrepancies become bigger and bigger along the Yb isoelectronic sequence which could be explained as being due to the increasing overlap between the core-excited configurations and the configurations of interest as already discussed (see Figure 2). This overlap gives rise to more and more mixing in the level composition (see Table 2) and to increasing cancellation effects in the computation of the line strengths represented by lower $CF$-values in particular lower than 0.05 [22]. Despite a smaller fraction of reliable transitions along the sequence, one can observe that the agreement between the HFR(CV) and the MCDHF methods is getting better and better as illustrated by a decreasing mean ratio, $g{A}_{MCDHF}$/$g{A}_{HFR\left(CV\right)}$. This shows again the importance of introducing a large number of core-excited configurations in the HFR(CV) calculations and by considering a large number of electronic correlation effects in the MCDHF calculations to have first a good reproduction of the observed level structure with both methods and to have then a wide set of high-quality computed radiative parameters characterized by small uncertainties. We have also seen that the reproduction of the observed level structure and the contributions of the eigenvector components in the line strengths are thus very sensitive to the models and the methods (semi-empirical or $ab$ $initio$).

5. Conclusions

In the present work, we have carried out a systematic investigation of the Yb-like ions Ta IV, W V, Re VI, Os VII, Ir VIII, and Pt IX using complementary pseudo-relativistic Hartree–Fock and fully relativistic multiconfiguration Dirac–Hartree–Fock approaches. New sets of energy levels, level compositions, oscillator strengths, and transition probabilities have been obtained for ions of direct interest to fusion-plasma diagnostics and to the spectroscopic characterization of tungsten transmutation products expected in future fusion reactors.

A special attention was devoted to the treatment of electron-correlation effects. The comparison between the HFR+CPOL and HFR(CV) approaches demonstrates that the core polarization model provides an adequate description of core–valence interactions in the lower members of the sequence, namely Ta IV and W V. For these ions, both approaches lead to similar transition probabilities and comparable agreement with experimental observations.

As the nuclear charge increases, however, the situation changes significantly. The progressive lowering of the 5p⁵5d³ core-excited configuration leads to increasingly strong interactions with the 5d5f and 5d7p configurations. These interactions become particularly important from Re VI onwards and cannot be described satisfactorily within a simple core polarization framework. The explicit inclusion of core-excited configurations in the HFR(CV) model results in a substantial improvement of the agreement with experimental energy levels, reducing the standard deviation of the odd-parity fits from 779 to 139 cm⁻¹ in Os VII, from 1216 to 571 cm⁻¹ in Ir VIII, and from 3363 to 422 cm⁻¹ in Pt IX. These results clearly demonstrate the increasing importance of core–valence correlations along the sequence.

The comparison with independent MCDHF calculations further supports the reliability of the radiative data reported in this work. The consistency observed between the different theoretical approaches provides confidence in the resulting dataset and highlights the robustness of the adopted modeling strategy.

Beyond the atomic-structure aspects, the present study contributes to the growing body of atomic data required for fusion-energy applications. In particular, the ions investigated here include W V together with several species corresponding to the principal neutron-induced transmutation products of tungsten, namely Ta, Re, Os, Ir, and Pt. The radiative parameters reported in this work are therefore expected to be useful for future spectroscopic diagnostics, impurity transport studies, and radiation modeling in ITER, DEMO, and related fusion devices.

Future work will be devoted to extending these investigations to other transmutation products and ionization stages, as well as to the calculation of complementary collisional data required for comprehensive plasma modeling.