On the Characterization of Molecular Stereostructure:  1. Cis−Trans Isomerism

Abstract

The definition of the graph isomorphism has been generalized for a more precise description of molecular structure. The adjacency matrix and different topological indices were modified with the help of the complex numbers. Some of the compounds were characterized. The obtained indices were substantiated to be more isomer sensitive than the 2D ones. The quantitative structure−property relationship was ascertained in an alkene series (r > 0.99).

Cis−Trans Isomerization of Organic Molecules and Biomolecules: Implications and Applications

“…Organic molecules as well as metal complexes may exist as several geometric isomers which display distinct physical properties and chemical reactivities. A molecule containing two atoms (in general, two carbons) attached together by a double bond with substituents W−Z may be found as two isomeric forms as long as W ≠ X and Y ≠ Z (Figure ).…”

Novel ZE-Isomerism Descriptors Derived from Molecular Topology and Their Application to QSAR Analysis

“…In fact, it is only an artifact. In both data sets considered in ref , for each isomer containing cis- and trans- bonds, there is a corresponding dual isomer in which all trans-bonds are substituted for cis-bonds, and all cis-bonds are substituted for trans-bonds. It can be said that these data sets are “symmetrical” (or invariant) relative to the substitution of all cis-bonds with trans-bonds and simultaneously all trans-bonds with cis-bonds (i.e.…”

“…2D descriptors, which are currently used in the majority of QSAR applications, database mining, and design of combinatorial libraries do not take π-diastereomerism into account. An attempt to introduce cis−trans isomerism descriptors was undertaken by G. Lekishvili followed by further developments . The indices introduced in ref were based on a generalized definition of the graph isomorphism, which was used in modification of the adjacency matrix: the author used imaginary number i (square root of −1) or − i instead of zero for the adjacency matrix elements corresponding to two atoms separated by three bonds (where the central bond is a double bond).…”

“…An attempt to introduce cis−trans isomerism descriptors was undertaken by G. Lekishvili followed by further developments . The indices introduced in ref were based on a generalized definition of the graph isomorphism, which was used in modification of the adjacency matrix: the author used imaginary number i (square root of −1) or − i instead of zero for the adjacency matrix elements corresponding to two atoms separated by three bonds (where the central bond is a double bond). The signs of these entries depended on whether these atoms were on the same or on different sides of the middle bond.…”

“…Since complex numbers cannot be used as descriptors directly, the author used the descriptors in the following general form, − mB | B |, where m and n are parameters that could be varied to obtain better models. As an application example, the author showed that for these indices there is an excellent correlation between the modified Randić index and the standard entropies of formation of alkenes …”