First-order nonadiabatic couplings in extended systems by time-dependent density functional theory

We propose an ab initio formulation that enables a rigorous calculation of the first-order nonadiabatic couplings (NAC) between electronic states based on time-dependent density functional theory in conjunction with planewave bases, projector augmented-wave pseudopotentials, and hybrid exchange-correlation functionals. The linear and quadratic time-dependent response theory is used to derive analytic expressions for the NAC matrix elements. In contrast to the previous formulation in atomic basis sets, the present formulation eliminates explicit references to Kohn-Sham virtual orbitals. With the introduction of Lagrangian functionals, the present formulation circumvents expensive derivative calculations of Kohn-Sham orbitals with respect to ionic coordinates. As a validation of the formulation, the NAC matrix elements of small molecules LiH and HeH+ are calculated and compared to previous results with the atomic orbital basis. This development paves the way for accurate ab initio nonadiabatic molecular dynamics in extended systems. Published by AIP Publishing.