Resolving a puzzling anomaly in the spin-coupled generalized valence bond description of benzene

In an earlier study of benzene, Small and Head-Gordon found that the spin-coupled generalized valence bond (SCGVB) wave function for the π system predicted a distorted (non-D_6h ) geometry, one with alternating CC bond lengths. However, the variations in the energy were very small and the predictions were made using a very small basis set (STO-3G). We re-examined this prediction using a much larger basis set (aug-cc-pVTZ) to determine the dependence of the energy of benzene on the distortion angle, Δθ_CXC (Δθ_CXC = 0° corresponds to the D_6h structure). We also found a distorted geometry with the optimum Δθ_CXC being 0.31° with an energy 0.040 kcal mol^-1 lower than that for the D_6h structure. In the optimum geometry, adjacent CC bond lengths are 1.3861 Å and 1.4004 Å. Analysis of the SCGVB wave function led us to conclude that the cause of the unusual non-D_6h geometry predicted by the SCGVB calculations seems to be a result of the interaction between the Kekulé and Dewar components of the full SCGVB wave function. The addition of doubly ionic configurations to the SCGVB wave function leads to the prediction of a D_6h geometry for benzene and a dependence on Δθ_CXC essentially the same as that predicted by the complete active space self-consistent field wave function.