Accurate Computation of Nonadiabatic Coupling with Projector Augmented-Wave Pseudopotentials

Synergy of nonadiabatic molecular dynamics with real-time time-dependent density functional theory has led to significant progress in modeling excited-state dynamics in nanoscale and condensed matter systems over the past decade. Nonadiabatic coupling (NAC) is the central quantity in such simulations, and its accurate and efficient evaluation is an enduring challenge in time-dependent Kohn-Sham theory, particularly in conjunction with planewave basis sets and projector augmented-wave (PAW) pseudopotentials because of the complexity of the PAW "all-electron"wave function. We report a method for rigorous evaluation of the NAC with PAW wave functions and demonstrate an efficient approximation to the rigorous NAC that gives comparable accuracy. As a validation, we intensely examine the NAC matrix elements calculated using both pseudo- and all-electron wave functions under the PAW formalism in six representative systems. The approximate NAC obtained with pseudowave functions is close to the exact all-electron NAC, with the largest deviations observed when subshell d-electrons are involved in the transitions. The developed approach provides a rigorous and convenient methodology for the numerical computation of NAC in the Kohn-Sham theory framework.