Nonadiabatic Ehrenfest molecular dynamics within the projector   augmented-wave method
  We have derived equations for nonadiabatic Ehrenfest molecular dynamics which conserve the total energy in the case of time-dependent discretization for electrons. A discretization is time-dependent in all cases where it or part of it depends on the positions of the nuclei, for example, in atomic orbital basis sets, and in the projector augmented-wave (PAW) method, where the augmentation functions depend on the nuclear positions. We have derived, implemented, and analyzed the energy conserving equations and their most common approximations for a 1D test system where we can achieve numerical results converged to a high accuracy. Based on the observations in 1D, we implement and analyze the Ehrenfest molecular dynamics in 3D using the PAW method and the time-dependent density functional formalism. We demonstrate the applicability of our method by carrying out calculations for small and medium sized molecules in both the adiabatic and the nonadiabatic regime. 
Ari Ojanper\"a, Ville Havu, Lauri Lehtovaara, and Martti Puska
cond-mat.mtrl-sci