New procedure to evaluate aromaticity at the density functional theory, Hartree-Fock, and post-self-consistent field levels

Abstract

The spatial exchange interaction, arising from the exchange-type two-electron integrals (i(p)j(q)/i'(p)j'(q)) between two different groups P and Q, is another driving force for the delocalization of π-electrons besides orbital charge-transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange-type two-electron integrals, ensuring that the corresponding π-electrons are completely localized within their respective groups and the π-orbitals are fully localized. The extra stabilization energy (ESE) of benzene is -36.3 kcal/mol (B3LYP/6-31G*), and the level of density functional theory, Hartree-Fock, and post-self-consistent field (Møller-Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled-cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block-localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the CC single bond lengths in the ground state with its π-localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π-delocalization on single bonds is so small as to be negligible.