Nonadiabatic couplings from time-dependent density functional theory: Formulation by the Kohn-Sham derivative matrix within density functional perturbation theory

Abstract

We present an improved method for accurately calculating nonadiabatic couplings (NACs) between the ground and excited states of electronic systems, using time-dependent density functional theory (TDDFT) within the plane-wave pseudopotential framework. Based on our previous work that the TDDFT formulation of NACs by the Kohn-Sham derivative matrix elements can avoid the accuracy problem caused by the nonlocal pseudopotentials, we extend the evaluation of these matrix elements to the analytical scheme, achieved by density functional perturbation theory (DFPT). As DFPT has been a standard implementation in many ab initio codes, our scheme requires little effort in the coding. Extensive calculations of NACs near various Jahn-Teller or Renner-Teller intersections show the good accuracy of our results. A comparison of our present and previous work has also clarified an important fact in the TDDFT computation of NACs, regarding the evaluation of the nuclear derivative of the many-body Hamiltonian after mapping to the Kohn-Sham system.