Energy additivity in branched and cyclic hydrocarbons

Abstract

This paper considers the degree to which branched hydrocarbons obey a group additivity scheme for energy and population, extending the study of the known experimental and theoretical transferability of the methyl and methylene groups of the linear hydrocarbons. The chemical groups are defined and their properties are determined using the quantum theory of atoms in molecules (QTAIM). The calculations are carried out with a large basis set at the restricted Hartree–Fock and MP2(full) levels of theory. The deviations from additivity, noted for small ring hydrocarbons leading to the definition of strain energy, are also investigated, showing that the QTAIM energies recover the experimental values. The particular delocalization of the electron density over the surface of the cyclopropane ring, responsible for its “homoaromatic” properties, is discussed in some detail. The calculations reported here satisfy the virial theorem as required for the atomic definition of energy. The problems associated with the use of DFT theory arising from its failure to satisfy the virial theorem are discussed with reference to the study of group transferability.