REVIEW | doi:10.20944/preprints201808.0355.v1
Subject: Engineering, Electrical & Electronic Engineering Keywords: Orbital angular momentum; free-space optical communications; turbulence mitigation
Online: 20 August 2018 (12:34:41 CEST)
We review recent progress in high-speed orbital angular momentum (OAM) multiplexed free-space optical communication systems. The outdoor atmospheric turbulence is emulated by an indoor turbulence emulator, which is based on split-step beam propagation method. Adaptive optics, channel coding, Huffman coding combined with LDPC coding, and spatial offset are used for turbulence mitigation; while OAM multiplexing and wavelength-division multiplexing (WDM) are applied to boost aggregate capacity.
ARTICLE | doi:10.20944/preprints202110.0114.v1
Subject: Physical Sciences, Optics Keywords: Photon; Relativistic Energy Wave; Abraham Momentum; Minkonwski Momentum; Relativistic Photon Ignition; Apparent Doppler; Orbital Angular Momentum; OAM
Online: 7 October 2021 (10:45:58 CEST)
An analysis of the consistency of the Abraham and Minkowski momenta in the determination of the photon trajectory was carried out considering a new principle of conservation of the photon's mechanical energy, in which the photon conserves translational energy in orbital angular momentum when transiting between two media, introducing the relativistic energy wave (REW). The confrontation between REW and the recent theory of space-time waves (ST) was considered, pondering your differences. Throughout this study it was possible to verify that the Abraham momentum appears a relativistic photon ignition device in the transition between two media, acting as the hidden momentum of the Minkowski’s relativistic momentum. The wavy behavior in the matter is relativistic, and the relativistic trajectory appears with delays and advances, with points of synchronization between source-observer. The classical or relativistic trajectories are determined as a function of the angle of incidence and the relative refractive index, by one of two distinct non-additive torques, the classic by Abraham or the relativistic by Minkowski. It was found that the same analysis conducted under the principle of conservation of the mechanical energy of the photon can be treated by an new Doppler, Relativistic Apparent, that can be confused with other Dopplers in the treatment of redshift from distant sources. It was found that the conservation of energy in Orbital Angular Momentum (OAM), in the interaction with matter, explains that the synchronization instants are found in the inversion of the OAM, where the advances and delays of REW occur under negligible variations of the OAM, however, opposites.
ARTICLE | doi:10.20944/preprints201807.0234.v1
Online: 13 July 2018 (11:21:14 CEST)
We investigate on the plasmons of monolayer MoS2 in the presence of spin-orbit interactions (SOIs) under the random phase approximation. The theoretical study shows that two new and novel plasmonic modes can be achieved via inter spin sub-band transitions around the Fermi level duo to the SOIs. The plasmon modes are optic-like, which are very different from the plasmon modes reported recently in monolayer MoS2, and the other two-dimensional systems. The frequency of such plasmons increases with the increasing of the electron density or the spin polarizability, and decreases with the increasing of the wave vectors q. Our results exhibit some interesting features which can be utilized to the plasmonic and terahertz devices based on monolayer MoS2.
ARTICLE | doi:10.20944/preprints202202.0279.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: Manganite; Charge/Orbital ordering; Dielectric property; Polaron
Online: 22 February 2022 (14:30:41 CET)
Low temperature dielectric property of charge/orbital ordered manganite, Pr1-xCaxMnO3 for 0.40≤x≤0.50 is investigated systematically as a function of Ca-content, x. The Ca-content dependence of dielectric permittivity and dissipation factor exhibit distinct maxima around x=0.45. The overall dielectric response of charge ordered Pr1-xCaxMnO3 is dominated by polarization induced by polaron hopping and exhibits thermally activated relaxation behaviour. The dielectric relaxation behaviour over the investigated temperature range is analysed with the help of small polaron hopping model and as well as variable range hopping model. The estimated polaron parameters also display non-monotonic variation with x and exhibit broad minima between x=0.425-0.45. The observed results suggest that a modulation of checker board type charge ordering pattern in Pr1-xCaxMnO3 is possibly taking place in the Ca-content range of investigation 0.40≤x≤0.50.
ARTICLE | doi:10.20944/preprints201709.0120.v1
Subject: Physical Sciences, Optics Keywords: twisted light; compton scattering; orbital angular momentum
Online: 25 September 2017 (09:00:13 CEST)
The variation of photonic orbital angular momentum at Compton scattering is characterized. We determine scattering matrix of a twisted light based on the fundamental conservation of orbital angular momenta. Numerical values for two different twisted light modes: Laguerre Gaussian and Bessel Gaussian, are generated and illustrated. Our analysis indicate that states of photonic orbital angular momentum are highly changeable at wide angle scattering but more consistent at small angle scattering.
CONCEPT PAPER | doi:10.20944/preprints202210.0337.v1
Subject: Earth Sciences, Atmospheric Science Keywords: Meteorological data; forcing fingerprints; weather forcasting; orbital forcing
Online: 21 October 2022 (11:44:41 CEST)
We identified six natural "control knobs" for global weather and climate, which clearly regulate, increase and decrease global temperatures, thus performing a true temperature "control" on Earth. Identified control knobs act as Earth's orbital forcing. We present a detailed Earth orbital model, from where the analysis proceeds. Based on our orbital model, we compare meteorological data from all over the globe, in order to detect orbital forcing fingerprints. Ninety temperature graphs and bar charts demonstrate the results. Empirical meteorological data covers the Pacific ocean, the Atlantic ocean, Arctic and Antarctic sea ice extent, and presents land based meteorological measurements from all continents for the year 2020, as well as multi-decadal data from global daily temperature datasets. A supplementary file provides another 100 additional graphs of weather data and temperature charts. The global orbital "temperature control" is clearly observable in all graphs and charts. Until today, orbital forcing has not been integrated in weather models and CMIP6 climate models.It is concluded that the proposed new orbital forcing should be part of weather and climate forecasting models.
ARTICLE | doi:10.20944/preprints202201.0095.v2
Subject: Chemistry, General & Theoretical Chemistry Keywords: antioxidant activity; eearomatization; frontier molecular orbital; fukui function f0; DFT
Online: 3 February 2022 (15:19:51 CET)
This study reports a computational investigation on the antioxidant activity of five plant food benzoic acid derivatives, namely gallic acid (GA), para-hydroxybenzoic acid (PHBA), protocatechuic acid (PCA), syringic acid (SA), and vanillic acid (VA). Based on computed thermodynamics parameters, a detailed comparative debate is developed concerning their free radical scavenging activity in the gas phase and polar solutions (in water and methanol solvents). This discussion goes on to elucidate both the most preferred mechanism and the order of antioxidant activity for these molecules in each environment. Paradoxically, calculations using the harmonic oscillator model of aromaticity (HOMA) suggest that H abstraction radicals gain in stability as the central benzene ring loses in structural aromaticity. Finally, spin densities and fukui function f0 seem to be good indicators of the local reactivity of these compounds towards free radicals.
ARTICLE | doi:10.20944/preprints202005.0250.v9
Subject: Physical Sciences, Astronomy & Astrophysics Keywords: Accelerated Expansion; Fast orbital speed of outer stars; Duality; Antimatter.
Online: 29 April 2021 (09:10:40 CEST)
The recent Planck Legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which endorses the positive curvature of the early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wave function of the Universe is utilized to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wave function reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolve in opposite directions as distinct Universe sides. The wave function indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating expansion away from early plasma during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both Universe sides free-fall towards each other under gravitational acceleration. Simulations of the predicted conformal curvature evolution demonstrate the fast orbital speed of outer stars owing to the external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wave function predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that early plasma could have separated and evolved into distinct sides that collectively and geometrically influencing the Universe evolution, physically explanting the effects attributed to dark matter and energy.
ARTICLE | doi:10.20944/preprints202202.0317.v1
Subject: Materials Science, Nanotechnology Keywords: photochromic; diarylethene; bipyridine; high-resolution scanning tunneling microscopy; cooperative switches; molecular orbital; DFT calculations
Online: 24 February 2022 (13:17:29 CET)
Diarylethene is a prototypical molecular switch that can be reversibly photoisomerized between its open and closed forms. Ligands bpy-DAE-bpy, consisting of a phenyl-diarylethene-phenyl (DAE) central core and bipyridine (bpy) terminal substituents, are able to self-organize. They are investigated by scanning tunneling microscopy at the solid-liquid interface. Upon light irradiation, cooperative photochromic switching of the ligands is recognized down to the sub-molecular level. The closed isomers show different electron density of states (DOS) contrasts, attributed to the HOMO or LUMO molecular orbitals observed. More importantly, the LUMO images show remarkable differences between the open and closed isomers, attributed to combined topographic and electronic contrasts mainly on the DAE moieties. The electronic contrasts from multiple HOMO or LUMO distributions, combined with topographic distortion of the open or closed DAE, are interpreted by density functional theory (DFT) calculations.
ARTICLE | doi:10.20944/preprints202202.0006.v1
Subject: Engineering, Electrical & Electronic Engineering Keywords: radio photonics; radio-over-fiber; orbital angular momentum; quadratic-nonlinear structure; difference frequency generation
Online: 1 February 2022 (12:02:54 CET)
The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency.
ARTICLE | doi:10.20944/preprints202102.0014.v1
Subject: Life Sciences, Biochemistry Keywords: canine distemper virus; signaling lymphocytic activation molecule; fragment molecular orbital calculation; molecular dynamics simulation
Online: 1 February 2021 (11:29:27 CET)
Infection of hosts by morbilliviruses is facilitated by the interaction between viral hemagglutinin (H-protein) and the signaling lymphocytic activation molecule (SLAM). Recently, the functional importance of the N-terminal region of human SLAM as a measles virus receptor was demonstrated. However, the functional roles of this region in the infection process by other morbilliviruses and host range determination remain unknown partly because this region is highly flexible, which has hampered accurate structure determination of this region by X-ray crystallography. In this study, we analyzed the interaction between the H-protein from canine distemper virus (CDV-H) and SLAMs by a computational chemistry approach. Molecular dynamics simulations and fragment molecular orbital analysis demonstrated that the unique His28 in the N-terminal region of SLAM from Macaca is a key determinant that enables formation of a stable interaction with CDV-H, providing a basis for CDV infection in Macaca. The computational chemistry approach presented should enable determination of molecular interactions involving regions of proteins that are difficult to predict from crystal structures because of their high flexibility.
ARTICLE | doi:10.20944/preprints202105.0203.v1
Subject: Physical Sciences, Acoustics Keywords: Interaction of gravitational field; Three-body problem; Orbital perturbation theory; Repulsive gravity; Neutralization of gravity
Online: 10 May 2021 (14:49:57 CEST)
Studying the two famous old problems that why the moon can move around the Sun and why the orbit of the Moon around the Earth cannot be broken off by the Sun under the condition that calculating with F=GMm/R^2, the attractive force of the Sun on the Moon is almost 2.2 times that of the Earth. We found that the planet and moon are unified as one single gravitational unit which results in that the Sun cannot have the force of F=GMm/R^2 on the moon. The moon is moved by the gravitational unit orbiting around the Sun. It could indicate that the gravitational field of the moon is limited inside the unit and the gravitational fields of both the planet and moon is unified as one single field interacting with the Sun. The findings are further clarified by reestablishing Newton’s repulsive gravity.
ARTICLE | doi:10.20944/preprints201912.0207.v1
Subject: Engineering, Mechanical Engineering Keywords: press bending; orbital auto welding; steel-tube correction; STKN540B; high-strength steel tube; manufacturing process
Online: 16 December 2019 (06:20:58 CET)
The purpose of this study is to propose a consecutive manufacturing process system to secure the productivity of excellent STKN540B steel tube in the respect of economy and safety as the supporting material for mega structures such as building, bridge and ship. The components of consecutive manufacturing are press-bending, orbital auto welding and steel tube correction. By using STKN540B a high-strength steel material with low yield point that requires a special manufacturing process unlike other steel materials, an actual tube manufacturing is carried out at each stage in this experimental study. With this, the quality of steel tube and the efficiency of the manufacturing process are analyzed to draw out some points to improve in the future.
ARTICLE | doi:10.20944/preprints202107.0512.v1
Subject: Materials Science, Biomaterials Keywords: Quantum Theory of Atoms in Molecules; Viral Theorem; Frontier Orbital Theory; Variational Principle; Transition Metal Structure
Online: 22 July 2021 (11:02:50 CEST)
For the better part of a century researchers across disciplines have sought to explain the crystallography of the elemental transition metals: hexagonal close packed, body centered cubic, and face centered cubic in a form similar to that used to rationalize the structure of organic molecules and inorganic complexes. Pauling himself tried with limited success to address the origins of transition metal stability. These early investigators were handicapped, however, by incomplete knowledge regarding the structure of metallic charge density. Here we exploit modern approaches to charge analysis to first comprehensively describe transition metal charge density. Then, we use topological partitioning and quantum mechanically rigorous treatments of kinetic energy to account for the structure of the density as arising from the interactions between metallic tetrahedra. We argue that the crystallography of the early transition metals results from charge transfer from the so called “octahedral” to “tetrahedral holes” while the face centered cubic structure of the late transition metals is a consequence of antibonding interactions that increase octahedral hole kinetic energy.
ARTICLE | doi:10.20944/preprints202104.0663.v1
Subject: Physical Sciences, Astronomy & Astrophysics Keywords: Solar System, Planetary System, Planet, Satellite, Sun, Earth, Moon, Topology, Circle, Ellipse, Orbit, Trajectory, Orbital Mechanics
Online: 26 April 2021 (12:14:51 CEST)
Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.
COMMUNICATION | doi:10.20944/preprints202108.0504.v1
Subject: Physical Sciences, Atomic & Molecular Physics Keywords: optical pumping; annular permanent magnet; miniature magnet; laser orbital angular mo-mentum; collimated magnetic field; fringe magnetic field
Online: 26 August 2021 (10:03:32 CEST)
Atomic state preparation can benefit from a compact and uniform magnetic field source. Simulations and experimental measurements have been used to design, build, and test such a source as shown by optical pumping of atomic Helium. This source is a 9.5 mm (3/8") OD x 6.7 mm (1/4") ID x 9.5 mm (3/8") long, NdFeB-N42 assembly of 1.6 mm (1/16") thick customized annular magnets. It has octopole decay with a residual dipole far field from imperfect dipole cancelations. It has greater than 50% clear aperture with uniform and collimated magnetic field consistent with the prediction of several models. Octopole roll-off localizes the field minimizing the need for shielding in applications. The device is applied to a high precision 3,4He laser spectroscopy experiment using σ+ or σ- optical pumping currently resulting in a measured 99.3% preparation efficiency and in accordance with a rate-equation model.
ARTICLE | doi:10.20944/preprints202007.0011.v1
Subject: Keywords: quantum mechanics; algebraic geometry; algebraic number theory; commutative algebra; Gr¨onber basis; primary ideal decomposition, eigenvalue problem in quantum mechanics; molecular orbital theory; quantum chemistry; quantum chemistry in algebraic variety; symbolic computation; algebraic molecular orbital theory; Galois theory; class ﬁeld theory
Online: 3 July 2020 (04:54:16 CEST)
Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to ﬁrst-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number ﬁeld, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class ﬁeld theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.
ARTICLE | doi:10.20944/preprints201812.0121.v1
Subject: Physical Sciences, Atomic & Molecular Physics Keywords: one-center method, molecular orbital, higher harmonics, excited state, ionized state, linear molecule, hydrogen fluoride, lithium monofluoride, boron monofluoride
Online: 11 December 2018 (09:37:53 CET)
Modern development of high-intensity and high-resolution X-ray technology allows detailed studies of the multiphoton absorption and scattering of X-ray photons by deep and subvalent shells of molecular systems on a wide energy range. The interpretation of experimental data requires the improvement of computational methods for obtaining excited and ionized electron states of molecular systems with one or several vacancies. The specificity of solving these problems requires the use of molecular orbitals obtained in one-center representation. Slow convergence of one-center expansions is a significant disadvantage of this approach; it affects the accuracy of the calculation of spectroscopic quantities. We offer a method of including higher harmonics in one-center expansion of a molecular orbital with the use of wave functions of electrons of deep shells of a ligand (off-center atom of a molecule). The method allows one to take into account correctly electron density of a linear molecule near the ligand when describing vacancies created in a molecular core leading to radial relaxation of electron density. The analysis of the parameters of one-center expansion of the ligand functions depending on ligand’s charge is performed. The criteria for the inclusion of higher harmonics of one-center decomposition of the ligand functions in the molecular orbital are determined. The efficiency of the method is demonstrated by the example of diatomic molecules HF, LiF, and BF by estimating energy characteristics of their ground and ionized states.
ARTICLE | doi:10.20944/preprints202107.0110.v1
Subject: Medicine & Pharmacology, Allergology Keywords: blow-out; biocompatible materials; computer-aided design; finite element analysis; orbit; implant; orbital fracture; patient-specific modeling; printing; three-dimensional.
Online: 5 July 2021 (15:37:53 CEST)
Pure orbital blowout fractures occur within the confines of the internal orbital wall. Restoration of orbital form and volume is paramount to prevent functional and esthetic impairment. The anatomical peculiarity of the orbit has encouraged surgeons to develop implants with customized features to restore its architecture. This has resulted in worldwide clinical demand for patient-specific implants (PSIs) designed to fit precisely in the patient's unique anatomy. Fused filament fabrication (FFF) three-dimensional (3D) printing technology has enabled the fabrication of implant-grade polymers such as Polyetheretherketone (PEEK), paving the way for a more sophisticated generation of biomaterials. This study evaluates the FFF 3D printed PEEK orbital mesh customized implants with a metric considering the relevant design, biomechanical, and morphological parameters. The performance of the implants is studied as a function of varying thicknesses and porous design constructs through a finite element (FE) based computational model and a decision matrix based statistical approach. The maximum stress values achieved in our results predict the high durability of the implants, and the maximum deformation values were under one-tenth of a millimeter (mm) domain in all the implant profile configurations. The circular patterned implant (0.9 mm) had the best performance score. The study demonstrates that compounding multi-design computational analysis with 3D printing can be beneficial for the optimal restoration of the orbital floor.
ARTICLE | doi:10.20944/preprints201812.0173.v2
Subject: Chemistry, Organic Chemistry Keywords: 2-(Adamantan-1-yl)-2H-isoindole-1-carbonitrile; X-ray diffraction; DFT; molecular orbital calculations; fluorescence; docking; nNOS; fluorescent ligand
Online: 14 December 2018 (11:41:20 CET)
2-(Adamantan-1-yl)-2H-isoindole-1-carbonitrile (1) has been identified as a neurobiological fluorescent ligand that may be used to develop receptor and enzyme binding affinity assays. Compound 1 was synthesised using an optimised microwave irradiation reaction and crystallised from ethanol. Crystallization occurred in the orthorhombic space group P212121 with unit cell parameters: a = 6.4487(12) Å, b = 13.648(3) Å, c = 16.571(3) Å, V = 1458(5) Å3, Z = 4. Density functional theory (DFT) (B3LYP/6-311++G (d,p)) calculations of 1 were carried out. Results showed that the optimised geometry is similar to the crystal structure parameters with a root-mean-squared deviation of 0.143 Å. Frontier molecular orbital energies and net atomic charges are discussed with a focus on potential biological interactions. Docking experiments within the active site of the neuronal nitric oxide synthase (nNOS) protein crystal structure were carried out and analysed. Important binding interactions between the DFT optimised structure and amino acids within the nNOS active site were identified that explain the strong NOS binding affinity reported. Fluorescent properties of 1 were studied using aprotic solvents of different polarities. Compound 1 showed the highest fluorescence intensity in polar solvents with excitation and emission values of 336 nm and 380 nm, respectively.
Subject: Physical Sciences, Mathematical Physics Keywords: quantum mechanics; algebraic geometry; commutative algebra; Grönber basis; primary ideal decomposition; eigenvalue problem in quantum mechanics; molecular orbital theory; quantum chemistry; first principles electronic structure calculation; symbolic computation; symbolic-numeric solving; Hartree-Fock theory; molecular integral; Taylor series; polynomial approximation; algebraic molecular orbital equation
Online: 26 December 2019 (02:17:44 CET)
A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.
ARTICLE | doi:10.20944/preprints202104.0632.v1
Subject: Physical Sciences, Mathematical Physics Keywords: Conic Sections, Topology, Circle, Ellipse, Hyperbola, Parabola, Orbit, Trajectory, Orbital Mechanics, Solar System, Planetary System, Planet, Satellite, Comet, Sun, Earth, Moon
Online: 23 April 2021 (11:36:05 CEST)
Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.
ARTICLE | doi:10.20944/preprints202108.0499.v1
Subject: Chemistry, General & Theoretical Chemistry Keywords: Clusters; planar tetracoordinate carbon (ptC); local and global aromaticity; chemical bonding; orbital localization; electron localization function (ELF); electron delocalization; current density analysis.
Online: 25 August 2021 (16:31:03 CEST)
The minimum energy structures of the Si3C5 and Si4C8 clusters are planar and contain planar tetracoordinate carbons (ptCs). These species have been classified, qualitatively, as global () and local () aromatics according to the adaptive natural density partitioning (AdNDP) method, which is an orbital localization method. This work evaluates these species' aromaticity, focusing on confirming and quantifying their global and local aromatic character. For this purpose, we use an orbital localization method based on the partitioning of the molecular space according to the topology of the electronic localization function (LOC-ELF). In addition, the magnetically induced current density is analyzed. The LOC-ELF-based analysis coincides with the AdNDP study (double aromaticity, global and local). Besides, the current density analysis detects global and local ring currents. The strength of the global and local current circuit is significant, involving 4n+2 - and -electrons, respectively. The latter implicates the Si-ptC-Si fragment, which would be related to the 3c-2e -bond detected by the orbital localization methods in this fragment.
ARTICLE | doi:10.20944/preprints201808.0166.v1
Subject: Chemistry, Physical Chemistry Keywords: Ferrocenium conformers, electron structure of organometallic complexes, excess orbital energy spectrum (EOES), α- and β-electrons of Fc+, energy decomposition analysis (EDA).
Online: 8 August 2018 (11:16:59 CEST)
Ferrocenium (Fc+) inherits a number of molecular/electronic properties from the neutral counterparts’ ferrocene (Fc) including the high symmetry. Both Fc+ and Fc prefer the eclipsed structure (D5h) over the staggered structure (D5d) by an energy of 0.36 kcal·mol-1. The present study using the recently developed excess orbital energy spectrum (EOES) shows that the open shell Fc+ cation exhibits similar conformer dependent configurational changes to the neutral Fc conformer pair. A further energy decomposition analysis (EDA) discloses that the reasons for the preferred structures are different between Fc+ and Fc. The dominant differentiating energy between the Fc+ conformers is the electrostatic energy (EEstat), whereas in neutral Fc, it is the quantum mechanical Pauli repulsive energy (EPauli). Within the D5h conformer of Fc+, the EOES reveals that the -electrons of Fc+ experience more substantial conformer dependent energy changes than the -electrons (assumed the hole is in a β orbital).