Application of Gas Chromatographic Retention Indices to GC and GC–MS Identification with Variable Limits for Deviations Between Their Experimental and Reference Values

1. Introduction

At present, gas chromatography–mass spectrometry (GC-MS) appeared to be the most effective and widely applicable hyphenated technique for analysis of organic com pounds in complex mixtures. This is due to the availability not only of modern equip ment, but also of detailed and well-systemized informational support. It includes data bases of standard mass spectra (electron ionization, 70 eV) and gas chromatographic retention indices (RI [1]) on standard nonpolar (polydimethylsiloxanes) and polar (polyethylene glycols) stationary phases. The example of combination of these parame ters is NIST mass spectral database [2], which has been supplemented with RIs since 2005. The last version of this database (2023) contains mass spectra of 347,000 compounds and RIs of 153,000 compounds.

The database application efficiency is determined not by the number of objects included, but by the algorithms for comparing experimental and reference (library) data, both mass spectra and RIs. Many of previously proposed mass spectrometric algorithms (some of them were considered in the monograph [3]) are currently of only historical interest because the most widely used is the algorithm proposed by employees of the Finnigan Co. in 1978 [4] and its subsequent modifications. Its essence is as follows: Each mass spectrum under comparison can be represented as a vector in an N-dimensional space, where N is the number of signals (in other words, the maximal m/z value). The numerical expression of mutual correspondence of these vectors (other terms are Similarity, Match Factor (MF), etc.) is the square of cosine of the angle (Θ) between them, 0 ≤ cos²Θ ≤ 1. For greater clarity, the normalization condition often transforms into 0 ≤ MF ≤ 100, or 0 ≤ MF ≤ 1000 (the maximal MF value corresponds to the maximal similarity of mass spectra, and the minimal MF value, to their complete dissimilarity). The normalization 0 ≤ MF ≤ 100 is sometimes called a percentage match, which is incorrect.

In contrast to multidimensional mass spectra, GC retention indices are unidimen sional analytical parameters (one number). It would seem that assessing the degree of coincidence of unidimensional values should be much simpler compared to multidimensional values. However, this is not the case, and this problem remains unsolved to date. The experimental RI values cannot exactly match with reference data, because the former values are influenced by experimental errors, and the latter values, by interlaboratory irreproducibility. The reason of restricted interlaboratory reproducibility of RIs is their dependence on the conditions of GC analyses, primarily on temperature, even at fixing the stationary phase. In turn, the temperature depends on the geometry of the chromatographic column and the amount of the stationary phase in it. In addition, the RI values depend on the ratio of peak areas of the analytes and reference compounds [5]. Hence, if we postulate any RI values as the reference information, RI_ref, and compare the experimental RI_exp values with them, the differences ΔRI between them turn out to be inconstant. Theoretically, we can imagine the existence of limiting values for these differences, ΔRI_lim. Combining all these premises, we can formulate the simplest condition of GC identification using retention indices:

ΔRI = |RI_exp–RI_ref| ≤ ΔRI_lim

(1)

If ΔRI > ΔRI_lim, the identification must be considered impossible even at the “ideal” mutual correspondence of the mass spectra.

The values ΔRI_lim depend not only on the nature of the stationary phase and specific conditions of the analysis, but also on the chemical nature of analytes and the features of the database used. In accordance with the long-established practice, the correctness of GC identification is most often illustrated by direct comparison (for visual perception) of the experimental and reference values; see, e.g., publications [6,7,8,9,10,11,12,13,14,15], but the number of examples can be increased many times.

Attempts have been made to create combined criteria for joint mass spectrometric and gas chromatographic identification. For example, Smith with coauthors [16] propo sed the criterion F = U⋅MF as follows:

U = 1, if ΔRI ≤ 5,

(2)

1 – 0.05|ΔRI|, if 5 < |ΔRI| ≤ 20 = ΔRI_lim

(2)

0, if |ΔRI| > 20,

(2)

where MF is the mass-spectrometric match factor and U is the measure of correspon dence of GC RIs. In other words, small differences ΔRI (≤ 5 index units) do not affect the results of mass-spectrometric identification, while large differences (> 20 i.u.) mean elimination of this option from further consideration despite the best correspondence of mass spectra. Such condition (cited in publication [17]) seems to be useful as very preliminary estimates, but it has obvious disadvantages, namely:

• The choice of fixed value ΔRI_lim = 20 i.u. seems to be illogical because the differences between experimental and reference data can take both larger and smaller values depending on the chemical nature of analytes and types of stationary phases under comparison;
• Condition (2) implies the symmetrical distribution of ΔRI, in other words, the equally probable deviations of experimental and reference data both at ΔRI < 0 and ΔRI > 0, but in the general case it is not obvious.

The differences in the real interlaboratory RI distribution can be best illustrated by histograms for 2,6-dimethyloctane (Figure 1a) and 1,2,3,4-tetrahydronaphthalene (tetralin), (Figure 1b). Both histograms are unsymmetrical, which means the theoretical incorrectness of conventional statistical data processing. Moreover, the histogram for tetralin allows us to identify the two-modality RI distribution, which is quite common, but the explanations for this can be quite complex [17]. However, because other algorithms of data processing are too complicated, we have to calculate arithmetic averages together with their standard deviations, which gives 933 ± 3 for 2,6-dimethyloctane (a) and 1152 ± 15 for tetralin (b). The first compound illustrates the good interlaboratory RI reproducibility, but the second case is more typical of numerous organic compounds.

Such spread of RI values depends on the chemical nature of analytes and determines the difficulties and uncertainties of their application [18,19]. It explains the use of arith metic averages in combination with the corresponding evaluations of permissible deviati ons. The author’s preferences are commonly accepted standard deviations, <RI> ±s_RI [20]. According to the relationships of statistical processing, the intervals <RI> ± s_RI include about 68% of values of the initial data set; the intervals <RI> ± 2s_RI, about 95%; and the intervals <RI> ± 3s_RI, about 99.7%. In addition, the reference data presented without deviations are known, e.g., reference data for constituents of essential oils [21]. In the NIST database [2] and in some secondary data summaries based on [2] (see, e.g., [22]), the RI spread historically is customarily characterized by MAD values (medians of absolute deviations). This means that the intervals <X> ± MAD contain only 50% of values of the initial data set. Furthermore, the number of single RI measurements (measured in one laboratory) in the last versions of the NIST database increased noticeably; such data have no measures of possible deviations at all.

The mentioned features of interlaboratory distributions of RI values explain the difficulties of selecting the criteria for comparing their experimental and reference values. Nevertheless, there is an actual need for creating the corresponding algorithm. The algorithm must have the following properties:

- it should not include any limiting values of possible deviations between experimental and reference RI values;

- it should be applicable to asymmetrically distributed reference RI values;

- it should be applicable to both statistically processed reference data and the results of single measurements;

- it should be applicable to comparing the RI values determined using columns with semi-standard stationary phases (terminology used in database [2]) with reference data for standard nonpolar stationary phases and vice versa;

- it should be applicable to RI values measured for both capillary and packed chroma tographic columns at various temperatures without any artificial restrictions.

This paper discusses the possibilities of creating an algorithm that meets all the above-listed conditions.

2. Results and Discussion

It is appropriate to start the discussion of an algorithm that meets a priori require ments listed above not with a theoretical consideration, but with a specific example. At the same time, this example illustrates the symbolism used.

2.1. Optimization of Comparing the Experimental and Reference Values of GC Reten tion Indices

To start the discussion, let us select the example of GC retention indices of 20 compounds of the same chemical class (alkylarenes) listed in Table 1, but measured under very specific conditions, namely, packed column with semi-standard phase Apiezon L (15% on Celite C-22) at 100°C [23]. According to contemporary concepts, such conditions are completely outdated because too high content of the stationary phase leads to too high temperature of chromatographic separation.

As a result of using such obsolete analytical conditions and semi-standard phase, all the experimental RIs exceed contemporary reference RI values [2] by approximately 30 i.u. (differences vary from 12 to 48 i.u.). The values of Δ_ref-exp = RI_ref – RI_exp for all the compounds are presented in Table 1. The comparison of these values requires taking into account not only their random variations, but also systematic differences caused by nonequivalence of determination conditions. This means that we must take into account the possible dependence of amendments Δ_ref-exp = RI_ref – RI_exp on the values of RI_exp themselves:

Δ_ref-exp = (RI_ref – RI_exp) = aRI_exp + b

(3)

The plot of the dependence (3) (swarm of dots) is shown in Figure 2(a).

Thus, we come to the following conclusions. Firstly, the Δ_ref-exp values show significant scatter. Hence, secondly, there are no reasons to approximate these data by polynomials of higher orders. Thirdly, the standard deviation of coefficient “a” of dependence (3) exceeds in absolute value the value of the coefficient itself, which means weak dependence of amendments Δ_ref-exp on RI_exp values. Finally, the determination of the parameters of equation (3) (even at the small value of coefficient “a”) allows us to con vert the experimental data published in [23] to the corrected RI_corr values specially for comparing with information from the contemporary database [2]:

RI_corr = RI_exp + Δ_ref-exp

(4)

All the RI_corr values are listed in Table 1 also. As we can see, the average absolute values of differences Δ_corr-ref (9 ± 6) appeared to be three times smaller than the average absolute value of differences Δ_ref-exp (29 ± 10). In should be noted that the average corrected values ± standard deviations considered taking the signs of the initial data into account differ from zero statistically insignificantly (0 ± 11). Their distribution can be additionally illustrated by the corresponding histogram (Figure 3). It is slightly asymmetric, but this is typical of GC retention indices of many organic compounds:

However, the correction of the experimental RI values for providing the possibility of their optimal comparison with the available reference data is only the “half” of the problem. The second part is the evaluation of the permissible deviations of RI_corr values from RI_ref for accepting or rejecting the gas chromatographic identification. In the least-squares method, the formula exists for so-called “corridor of errors” for evaluating the possible deviations of points from the regression equation y = ax + b [24]:

$$\mathit{S}\left(\mathit{x}\right) = {\mathit{s}}_{\mathit{y}}\sqrt{{\displaystyle \frac{\left(1-\mathit{R}\uparrow 2\right)}{\mathit{N}-2}}\left[1+{\displaystyle \frac{\left(\mathit{a}-<\mathit{x}>\right)\uparrow 2}{\mathit{s}\mathit{x}\uparrow 2}}\right]}$$

(5)

where s_x² = (<x²>$-$<x>²/N)/N, s_y² = (<y²>$-$<y>²/N)/N, R = (<xy>$-$<x><y>/N)/(Ns_xs_y)

However, this relationship seems too complicated for routine calculations; simpler evaluations are preferable. If the dependence ΔRI_corr = f(RI_exp) is expressed rather weakly (like it is in the example considered), we can accept ΔRI_corr ≈ const. The first recommen dation implies using the evaluations of the standard deviations of ΔRI_corr, namely, s_ΔRIcorr. Most of ΔRI_corr values do not exceed ΔRI_corr + s_ΔRIcorr, while the values exceeding ΔRI_corr + 2s_ΔRIcorr can be excluded from consideration. The second way to evaluate the possible deviations is based on such parameter as “sum of residuals”, S₀. For numerous examples (including those considered above), the following inequality is correct:

ΔRI_corr + s_ΔRI < S₀ < ΔRI_corr + 2s_ΔRI

(6)

This means that the RI_corr data for GC identification should be chosen within intervals RI_ref ± 2S₀:

RI_ref – 2S₀ < RI_corr < RI_ref + 2S₀

(7)

The Δ_corr-ref values in Table 1 indicate that only one of 20 compounds (1,2,3-tri me thyl benzene) does not meet this criterion. It is a statistically acceptable result (95% of correct answers).

However, the illustration of data processing mentioned above looks like an artificial example because it implies recalculating RI values of all analytes without exception (at the hypothetical condition that we know all of them a priori). In real analyses of complex mixtures, we do not know all analytes before analysis (to identify them is the final aim), but usually we can identify only several constituents using their specific mass spectro metric signs or preliminary chemical information. Hence, the application of the algorithm considered to real multicomponent mixtures requires modification.

2.2. Application of the Algorithm of Comparing the Experimental and Reference GC Retention Indices to Multicomponent Mixtures

This is one of the most common analytical tasks. Most often, complex multicomponent mixtures under analysis contain some simple constituents that can be unambiguously identified without special proces sing of GC data. These components are, for example, impurities in commonly used solvents and reagents, plasticizers (like, e.g., phthalates), and so on. Hence, we can select just these compounds for comparing their RI_exp and RI_ref values. The number of such “reference points” may not be so large, but it is important that they should be evenly distributed in different parts of chromatograms (at the beginning, in the middle, and in the final part). Of course, if the samples under analysis contain small number of constitu ents (e.g., 1–2), the preliminary analysis of artificial mixtures of similar composition becomes necessary.

Continuing the consideration of the above-mentioned example (Table 1, Figure 2 and Figure 3), we can select from 20 alkylarenes only five, namely, benzene, toluene (the first segment of the chromatogram), 1,3,5-trimethylbenzene (middle position), butylbenzene, and 1,2,4,5-tetramethylbenzene (the last part). All the selected compounds are marked in Table 1 in bold. After that, we should repeat the same mathematical operations as were done for the complete data set (equations (3), (4), (6), and (7)) for this reduced data set. Obviously, we obtain different values of the coefficients of the linear regression equation (3) than for the full data set (see footnotes to Table 1).

The plot of the dependence (3) for the reduced data set is shown in Figure 2(b). It illus trates slight variations of the angular coefficient “a” in equation (3); the dependence becomes slightly ascending instead of slightly descending. The values of ΔRI_corr* = (RI_corr – RI_ref) together with Δ_corr-ref* are marked with asterisks in Table 1 for comparison with the initial values of ΔRI_corr = (RI_corr – RI_ref) and Δ_corr-ref. However, the average value of Δ_corr-ref* (8 ± 6) appeared to be very close to Δ_corr-ref (9 ± 6). The same is true for the sum of residuals (S₀): 10.8 and 8.4, respectively. This means that RI_corr* does not correspond to RI_ref ± 2S₀ intervals for only one compound of 20 (namely, for tert-butylbenzene), which is statistically acceptable (95% of correct results).

The above reasoning can be illustrated by considering the RI values for 32 essential oil constituents, published by Engewald and co-authors [25] for a column with a standard nonpolar polydimethylsiloxane stationary phase, DB-1. The results of this data proces sing in comparison with the reference RI values from database [2] for identical phases are presented in Table 2. The reduced data set includes six compounds easily identifiable by mass spectra, namely, α-pinene, limonene, linalool, camphor, neral, and geranial (marked in bold). Similarly to Table 1, the parameters of all equations (RI_ref – RI_exp) = aRI_exp + b for both complete and reduced data sets are indicated in the footnotes to Table 2. The average value of the difference RI_ref – RI_exp for the complete data set is 13 i.u., and for the corrected reduced data set it is twice less, 6 i.u.

The single compound with RI_corr values that do not meet condition (7) for both complete and reduced data sets is isosafrole, 5-(1-propenyl)-1,3-benzodioxole. This is most probably due to the unreliable reference RI value for this compound in database [2]. Indeed, the RI value for isosafrole in [25] is 1357, while the reference value is 1327 ± 31 [2]. Such a large standard deviation is explained by uniting the RI values for so-called α- and β-isosafroles (cis and trans isomers) together. The RI value for the most often determined β-isosafrole (trans-isomer) is 1358 ± 6 (value from author’s RI collection). Keeping this fact in mind, we obtain for this compound Δ_corr-ref* = –1 instead of +30. After this correction, the RI value for isosafrole (the last eluted compound) can be inclu ded into reduced data set. It is an additional illustration of the efficiency of the suggested approach.

The same example of 32 essential oil components can be considered using another database of reference information for semi-standard stationary phases [21]. Data proces sing in this case is illustrated by Table 3 similar to Table 2. The parameters of the equations (RI_ref – RI_exp) = aRI_exp + b are presented in the footnotes.

The statistical characteristics of the data sets in Table 2 and Table 3 are close to each other. For the second of them, the average value of the difference Δ_ref-exp for the complete initial data set is 8 i.u., the average value of Δ_corr-ref for the corrected values is 5± 4 i.u., and for the reduced data set it is 6 ± 4 i.u. However, this example illustrates the possibility of identifying compounds characterized by RIs on standard nonpolar phases using reference data for semi-standard phases. The algorithms of data processing are the same in both cases.

Among 32 compounds in Table 3, only one, myrcene, does not meet criterion (7). The values of RI_corr and RI_corr* for myrcene differ from reference RIs [21] by more than 2S₀; the cause of this difference remains unclear.

Similarly to Figure 3 (above), it seems reasonable to characterize the distributions of Δ_ref-exp and Δ_corr-ref for the reduced data set by the corresponding histograms. Figure 4(a) illustrates the spread of the initial differences (RI_ref – RI_exp); it is rather asymmetric, and most of the values are located within the range from –15 to +15 i.u. The distribution of the (RI_corr – RI_ref) values (b) corresponds to the data of Table 3 for comparing the RI data measured on standard nonpolar phases with the reference data for semi-standard phases and, moreover, calculated for the reduced data set. It is only slightly narrower (from –10 to +15 i.u.), but it becomes much more symmetric.

Hence, the algorithm proposed minimizes the shift of the differences of the initial experimental and reference RI values relative to zero and makes the distribution of these values narrower and more symmetric.

An important illustration of this algorithm is the situation when the reference RI values are determined under the conditions close to those of the experimental determina tion of RI values. It arises when the types of stationary phases are the same and the temperature conditions are close. In these cases, both coefficients “a” and “b” of equation (3) are obviously close to zero. To confirm this, let us consider the last Table 5, which illustrates the results of experimental testing of the algorithm using as an example a simple (only 10 constituents whose content exceeds 0.1% of the total peak area) sample of Lavandula angustifolia essential oil. Both experimental and reference data relate to the same semi-standard nonpolar stationary phases: HP-5 (experimental) and DB-5 (refe rence [21]). Therefore, the coefficients of the equation (RI_ref – RI_exp) = aRI_exp + b (3) appear to be minimal among all examples considered above: a = 0.008, b = –8.5; the difference Δ_corr-ref = RI_corr – RI_ref is only 2 ±1, and the sum of residuals is S₀ = 5.

The list of compounds in Table 4 includes two minor sesquiterpenes С₁₅Н₂₄ with the retention indices of 1365 and 1384, remaining unidentified. The application of the algorithm considered gives corrected values of their retention indices, namely, 1361 and 1380. Hence, in the reference set of data [21] we should find sesquiterpenes with RIs within the intervals 1356–1366 and 1375–1385. Screening in the first of them leads to the rather “exotic” silfiperfol-4,7(14)-diene with RI 1358. However, an analog of this compound previously was identified in some species of Lavandula genus [26], and RI of silfiperfol-4,7(14)-diene determined in [27] (1367) is also close to RI_corr in Table 5. However, the identification of this compound should be considered as tentative.

For the next sesquiterpene with RI within the interval 1375–1385, according to data bases [2] and [21], there are several possible candidates:

RI	Compound	Number of RI values for stan dard/semi-standard phases in [2]
1376 [2]	α-Copaene	377/698
1377 [21]	Silfiperfol-6-ene	None
1379 [21]	β-Patchoulene	10/23
1380 [21]	Daucene	16/14
1381 [21]	β-Panansinene	1/5

Let us additionally take into account the number of averaged RI values available for every compound in database [2] for standard/semi-standard nonpolar phases. It allows using such auxiliary (probability) criterion as the number of previous mentions of a par ticular compound [28]. Four compounds with the suitable RI from [21] appear to be little mentioned compared to α-copaene with RI 1376 [2] (377/698). However, this identifi cation should also be considered as tentative.

3. Materials and Methods

The principal feature of this work is the possibility of using practically unlimited number of examples taken from the literature. However, for special consideration we selected the RI values of alkylarenes on Apiezon L phase [23] (can be classified as semi-standard),data for essential oil constituents on standard DB-1 nonpolar phase [25], and experimental data for essential oil of Lavandula angustifolia L. on semi-standard HP-5phase. The reference RI data for the standard and semi-standard nonpolar phases were taken from the NIST17 database [2].

The sample of Lavandula angustifolia essential oil (Technical Specification 20.53.10-006-74840603-2018, Mirrolla Lab., Leningrad district, n_D²⁰ 1.4568) was purchased in a regular pharmacy. Isobutyl alcohol was of chemically pure grade (GOST (State Standard) 6016-77, Angarsk Chemical Reagent Plant, Russia); the internal references (n-tridecane and n-tetradecane) and other reference n-alkanes С₇–С₁₈ were of chemically pure grade for chromatography (Reakhim, Moscow, Russia).

Gas chromatographic analysis of Lavandula angustifolia essential oil was carried out using its 10% solution in isobutyl alcohol with a Khromatek-Kristall 5000.2 gas chromatograph (Yoshkar-Ola, Russia) equipped with a flame ionization detector and a WCOT capillary column (length 10 m, internal diameter 0.53 mm, semi-standard HP-5 stationary phase, film thickness 2.65 μm). The analysis was performed with programmed heating from 90 to 240°С, ramp 6 deg min^–1. The carrier gas was nitrogen, flow rate 3.8 mL min^–1, linear velocity 34 cm s^–1, split ratio 1 : 3. The injector and detector temperature was 200°С. A 10 μL microsyringe volume was used for injecting 1.0 μL samples. The solution of n-alkanes C₇–C₁₈ for determining the retention indices was injected separately.

Before GC–MS analysis, the previous sample of Lavandula angustifolia essential oil was diluted 100-fold with the same solvent. The analysis was performed with a Shimadzu QO 2010 SE gas chromatograph–mass spectrometer equipped with an Optima 5 MS GC column, length 30 m, internal diameter 0.32 mm, and film thickness 0.25 μm, with programmed heating in the range 90–270°С, ramp 6 deg min^–1. The carrier gas was helium, flow rate 1.82 mL min^–1, linear velocity 53.3 cm s^–1, split ratio 1 : 10. The injector temperature was 200°С, and the interface and ion source temperature was 250°С. The ionization energy was 70 eV, the mass range was 40–500 Da,and the chromatogram recording start delay time was 2.0 min.

Processing and presentation of the results. Excel (Microsoft Office 2010) and Origin (versions 4.1 and 8.1) software was used for the statistical data processing and construction of the histograms. The QBasic program was used for calculating the linear-logarithmic RIs [1].

4. Conclusion

The suggested algorithm for comparing the experimental and reference GC retention indices as an important element of chromatographic and GC–MS identification of organic compounds is aimed at eliminating a significant element of uncertainty inherent in many contemporary recommendations: the use of fixed limiting differences between the experimental and reference GC retention indices, ΔRI = (RI_ref – RI_exp) ≤ RI_lim.The new algorithm is the most effective for complex multicomponent mixtures in which reliably identified components with known reference RI values can be revealed. It includes calculating the coefficients of regression equations ΔRI = (RI_ref – RI_exp) = aRI_exp + b, followed by using these relations for recalculating of all other RI values into corrected data RI_corr = RI_exp + ΔRI. This algorithm allows interpreting retention indices measured on standard nonpolar polydimethylsiloxane stationary phases using reference data for semi-standard nonpolar phases like polydimethylsiloxanes containing 5% phenyl groups and vice versa. It is applicable both to statistical processing of reference data (presented in the format “average arithmetic value ± permissible deviation”) and to the results of single determinations. Furthermore, it allows using different RI databases and, if neces sary, comparing different databases with each other and even recalculating the reference data from one database (e.g., semi-standard) into another one (standard).