Linear and nonlinear response functions for an exact state and for an MCSCF state

Abstract

We have examined the response of an exact and an MCSCF reference state to a general time-dependent field. The time development of both the exact and the MCSCF reference state have been parametrized in terms of explicit exponential time-dependent transformations. The time development has been determined by requiring the Ehrenfest theorem to be satisfied through each order in the interaction between the molecular system and the field. The response of the exact and the MCSCF reference state has been used to evaluate linear, quadratic, and cubic response functions. It has been shown how a large variety of molecular properties may be expressed in terms of these response functions. It has also been demonstrated that molecular properties containing the electric dipole operator may be expressed in equivalent forms involving the momentum operator both for the exact and the MCSCF state. The MCSCF response functions have been transformed to computationally attractive expressions which do not contain summation indices over intermediate states and which allow direct techniques to be straightforwardly applied.