Nonadiabatic coupling terms for the GVVPT2 variant of multireference perturbation theory

Abstract A Lagrangian based approach was used to obtain analytic formulas for nonadiabatic coupling terms within a multireference perturbation theory description of molecular electronic structure. Specifically, formulas were developed for the second-order generalized Van Vleck perturbation theory (GVVPT2) description of electron correlation. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. Since GVVPT2 wave functions are not strictly orthogonal, the definition of nonadiabatic coupling terms is untrivial and a perturbation-order consistent definition is suggested herein from which working equations are developed.