Nonadiabatic couplings from the Kohn-Sham derivative matrix: Formulation by time-dependent density-functional theory and evaluation in the pseudopotential framework

Abstract

We study the time-dependent density-functional theory formulation of nonadiabatic couplings (NAC's) to settle problems regarding practical calculations. NAC's have so far been rigorously formulated on the basis of the density response scheme and expressed using the nuclear derivative of the Hamiltonian, $\ensuremath{\partial}H/\ensuremath{\partial}R$, whereby causing the pseudopotential problem. When rewritten using the nuclear derivative operator, $\ensuremath{\partial}/\ensuremath{\partial}R$, or the $d$ operator, the formula is found free of the problem and thus provides a working numerical scheme. The $d$-operator-based formulation also allows us to lay a foundation on the empirical Slater transition-state method and to show an improved way of using the auxiliary excited-state wave-function ansatz, both of which have been utilized in previous works. Evaluation of NAC near either the Jahn-Teller or the Renner-Teller intersection in various molecular systems shows that the values of NAC are much improved over previous calculations when the $d$-operator formula is implemented in the pseudopotential framework.