Comparison of ab initio Effective Valence Shell Hamiltonian with Semiempirical Theories of Valence: Pairing Theorem

The pairing properties of electronic structure are investigated from ab initioists' point of view. Numerical results of exact ab initio effective valence shell Hamiltonian are compared with simple semiempirical Hamiltonian calculations. In the oxygen atom case it was found that effective three-electron interaction terms break the similarity between electron-states and hole-states. With the trans-butadiene as an example the pairing theorem was studied. Even for alternant hydrocarbons, the deviation from the pairing was found to be enormous. The pairing theorem, which is usually stated for semiempirical Hamiltonians, is not valid when the exact effective Hamiltonian is considered. The present study indicates that comparisons between the pairing theorem of semiempirical methods and ab initio effective Hamiltonian give important information on the accuracy of semiempirical methods.