Analytic derivative methods for evaluating nonadiabatic coupling matrix elements within the SC-QDPT method

The recently developed self-consistent variant of quasidegenerate perturbation theory (the SC-QDPT method) is shown to allow one to use analytic derivative methods for evaluating both first derivative nonadiabatic couplings and first derivatives of the adiabatic state energies with respect to nuclear perturbations. The expressions obtained for the couplings prove to deviate from the analogous expressions for CI wavefunctions by an additional term arising for inaccuracies in describing the primary–external interactions by perturbation theory. It is shown, however, that this `error-termʹ may be expected to be small in practice and it may be evaluated using reference space wavefunctions (e.g., MCSCF).