DIFFERENCES BETWEEN THE EXACT SUM-OVER-STATES AND THE CANONICAL APPROXIMATION FOR THE CALCULATION OF STATIC AND DYNAMIC HYPERPOLARIZABILITIES

When molecules are subjected to static or dynamic uniform electric fie lds the effects are conveniently described in terms of dipole polariza bilities and hyperpolatizabilities The fields act on both the electron ic and vibrational motions simultaneously and, through perturbation th eory, this leads to the exact sum-over-states (SOS) formulas for the ( hyper) polarizabilities expressed in terms of vibronic stares. As an a pproximation, the fields can be considered to act on the electronic mo tions first and subsequently, through the distorted electronic ground state potential surface, on the vibrational motions. This commonly use d canonical or clamped nucleus approximation, leads to (hyper) polariz ability expressions that are different from the SOS ones. In this pape r we develop a compact first-order treatment of the differences and ca rry out a preliminary examination of the numerical repercussions. Our calculations also bear on a proposed theoretical relationship between The vibrational and electronic first hyperpolarizabilities in push-pul l conjugated systems. (C) 1997 American Institute of Physics.