Determining the Basis of Homodesmotic Reactions of Cyclic Organic Compounds by Means of Graph Theory

Abstract

Comparative calculations based on the use of a homodesmotic reaction (HDR)—an isodesmic process with the additional requirement for group balance—is used to analyze the thermochemical characteristics of cyclic organic compounds exemplified by bicyclo[2.1.0]pentene-2. To avoid confusion in selecting HDRs, an algorithm is developed for determining the HDR basis, i.e., the set of all possible independent homodesmotic reactions. The algorithm for constructing the set of HDRs is based on an analysis and transformations of the bond graph of groups for the investigated chemical compound. The use of graph theory allows us to automate the procedure for deriving the basis of homodesmotic reactions, and to obtain a visual geometric interpretation of the basis, which is important for subsequent physicochemical analysis. The energetics of bicyclo[2.1.0]pentene-2 is investigated using the proposed approach, and the independent basis of HDRs is found to include 19 formal transformations. Standard enthalpies for the test compound and the participants of homodesmotic reactions are calculated using the G3 composite approach. Thermochemical analysis of the obtained data allows us to determine the standard enthalpy of formation of the bicycle (Δ_fH° = 336.4 kJ/mol) and value Δ_fH° of a number of cyclic and acyclic alkenes and alkadienes that are products of theoretical decomposition of the test compound. The proposed method is shown to be extremely effective in analyzing the effects of nonbonded interactions in the structure of organic molecules. The ring strain energy of the bicycle is calculated or the test compound: E_S = 295.2± 2.2 kJ/mol.