SIMPLEST RULES TO PREDICT THE RELATIVE ORDER OF GAS-CHROMATOGRAPHIC ELUTION OF ISOMERIC ORGANIC COMPOUNDS, BASED ON MOLECULAR DYNAMICS MODELING

Igor G. Zenkevich

Chemical Research Institute of St. Petersburg State University,
Universitetsky pr., 2, St. Petersburg 198504, Russia
gc_lab@nonel.chem.lgu.spb.su, igor@IZ6246.spb.edu

Numerous anomalies of boiling points and GC retention regularities of isomeric organic compounds (illustrated by examples) lead us to the following conclusion:

There is the simple linear dependence between GC retention parameters (e.g. retention indices, RI) and total innermolecular vibration and rotational energies (E).

No ways to determine E-values experimentally are known, but HyperChem software can be used for their theoretical estimation by molecular dynamics modeling.

The RI values are proportional to the molar free energies of “sorbat-stationary phase” or “sorbat-sorbent” interaction (DGm0), which consist of Van der Waals (dispersion, DGVdW0) and polar (orientation and induction, DGpolar0) addends. So far as DGVdW0»const for isomeric organic compounds without active hydrogen atoms and DGpolar0»const < DGVdW0 for combinations of low polar sorbates and low polar stationary phases or sorbents, the differences between boiling points or RIs of isomers can be explained only by differences in their innermolecular energies:

DGm0 = DGVdW0 + DGpolar0 - E

Hence the dependencies (1) or (2) can de used both for precalculation of GC retention indices, and for prediction of relative order of elution of isomeric compounds:

RI » a E + b, (a < 0), |r| » 0.7 – 0.9 “absolute” form
(1)
DRI = a DE + b, (a < 0), |r|  0.9 “differential” form
(2)

It is important that chemical domains of determination are principally different for these two equations: the groups of isomers with the same molecular formula (eq. 1) and the multitudes of compounds which can be derived from corresponding precursors by the same transformations of structures in real or hypothetical organic reactions (eq. 2).

Next step of simplification of the concept under consideration is to restrict the innermolecular energies only by vibration component (U), which exceeds rotational one in many times. It can be estimated by simple relationship

(3)
where M – molecular weight of compound, mi and (M – mi) – the masses of fragments at the every bond of the molecule, ki – the coefficient being proportional to the forth constant of the bonds. The U-values are equal to the E-values both in absolute form (1), and differential form (2).

It is noteworthy that mathematical form of eq. 3 is quite similar to the numerous known molecular topological indices, for instance, Wiener indices (1947) W = S Dij/2, where Dij are the interatomic distances in the molecule. Good correlations of various molecular connectivity indices with innermolecular energies (E,U) can be interpreted as an attribution of new physico-chemical sense of them as the variables which are proportional to the molecular dynamics parameters.

So far as the coefficients “a” in eqs. (1) and (2) are negative, the order of GC elution of isomeric organic compounds corresponds to the decreasing order of their E or U values. For example, the monoacetylation of octaethoxy-1,3,5-trisiloxane gives two isomeric products with RI 1951 ± 2 and 1964 ± 2 (capillary column with standard non-polar phase OV-101). First of them has the structure (EtO)3Si-O-Si(OEt)(OAc)-O-Si(OEt)3 which characterizes by E = 127.2 ± 2.0 kcal/mol, that is more than E = 123.7 ± 1.6 kcal/mol for second isomer (EtO)3Si-O-Si(OEt)2-O-Si(OEt)2(OAc).