Separated-Electron-Pair Model: Application to the π-Electronic Structure of the Ground State of Benzene

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Abstract
The separated‐electron‐pair (geminal) model appears to be a reasonable way to extend the single‐particle picture while maintaining most of the simplicity of that picture. There seems to be no doubt about the utility of the model as applied to ``localized'' systems such as H2O, NH3, CH4, etc., although quantitative information is still needed. The question of how the model will do when applied to a ``delocalized'' system is studied in the present paper by applying the model to a π‐electron system—the ground state of benzene. The symmetry of the system allows one to set up without difficulty two different separated‐pair wavefunctions. Both of these functions are shown to satisfy the variational equations for an extremal, although the calculated energies are quite different. One function is constructed from geminals which are symmetry adapted; and the complete wavefunction is totally symmetric as it should be. The other separated‐pair function is constructed from geminals which are equivalent to one another under threefold rotations; the natural orbitals of the geminals are localized. It happens that there are an infinite number of sets of such localized orbitals; all give identical results. As expected the localized geminal function is energetically superior to the symmetry geminal function. When ``resonance'' is accounted for, about 64% of the correlation energy (by comparison with full configuration interaction) is obtained.