Atomic additivity of the correlation energy in molecules—an ab initio MP4 and G3 study

Abstract

It is shown that the closed shell valence electron molecular correlation energy of organic molecules in their ground states is a homogeneous multilinear function of the numbers of neutral atoms in their canonical hybridization state. The additivity is a robust feature, which holds for MP2(fc), MP3(fc) and MP4(fc) model calculations. The latter results obtained on a test set of 91 widely different organic molecules, exhibiting a whole gamut of electronic structure patterns, are excellent as evidenced by the absolute average deviation from the additivity values (AAD) of only 1.4 kcal mol−1 and R 2 = 0.999 93. The maximum absolute deviation (MAD) is 5.3 kcal mol−1. The additivity formula for the total molecular electron correlation retrieved from G3 calculations also has an excellent performance (AAD = 1.2 kcal mol−1, R 2 = 0.999 98 and MAD = 7.2 kcal mol−1). If it is taken into account that the additivity formulae require only back of the envelope calculations, these results are remarkable indeed, in particular since the G3 correlation energies span a very large range from 180.7 (methane) to 1642.8 (hexafluorocyclopropane) kcal mol−1. Comparison of the exact electron correlation energies in free atoms with the corresponding average correlation energies in molecules reveals that a substantial increase in the latter provides an important contribution in overcoming a very strong Coulomb repulsion between the nuclei. It is shown that the additivity formulae are useful in detecting some special molecular features such as strong resonance and anti-aromaticity.