Solution to the π-Distortivity Problem.

Abstract

Traditionally, the delocalized π system of benzene is believed to be responsible for its perfectly symmetric D6h geometry. However, it has also been suggested that the π system prefers a distorted D3h geometry. Arguments for this have been based on clever use of VB methods as well as through shifts in the frequency of the distortive b2u mode. Evidence has been provided through different ways of partitioning the total electronic energy between the σ and the π systems. These methods are plagued by the fact that there is no unique way to partition the energy, leading to questions regarding the validity of the conclusions. Here we note that even though energy cannot be partitioned exactly, force acting on a nucleus depends only on the single particle density and can hence be partitioned exactly. Using good-quality wave functions that are numerically found to obey the Hellmann-Feynman theorem to good accuracy, we calculate the σ and π components of the force and provide conclusive evidence of π-distortivity at the HF level. Our approach provides an unambiguous way to approach the problem with wave functions that account for electron correlation. Our calculations suggest that the conclusion is valid at the MP2 level, too.