Missing-orbital analysis of molecular hyperpolarizability β calculated by a simplified sum-over-states method: “multi-state” model for β zxx

Abstract

Missing-orbital analysis is applied to the diagonal and off-diagonal components of the first-order hyperpolarizability tensor β evaluated by a simplified sum-over-states method. Various molecules assumed to have C 2v symmetry are examined: benzene, pyridine-oxide and polyynes substituted with amino and either cyano or nitro groups. The missing-orbital analysis shows that the diagonal component β zzz ( z-axis in the donor-to-acceptor direction) for most of the molecules is essentially dominated by only one strongly charge-transfer excited configuration, and is describable by the conventional two-state model. For the off-diagonal component β zxx , it is revealed that the excitations from a 2 and b 2 orbitals cooperatively make an important contribution. This indicates that, even for the molecules whose β zzz is described well by the two-state model, β zxx is necessarily modeled by a “multi-state” model consisting of the ground state and at least two excited configurations belonging to two different symmetries.