Going beyond the adiabatic approximation in TDDFT
Neepa T. Maitra
Hunter College of the City University of New York
Time-Dependent Density Functional Theory (TDDFT) has achieved an unprecedented balance between accuracy and efficiency for the calculation of excitation spectra and response. Users generally know when to apply caution for classes of excitations for which the usual adiabatic functional approximations fail. The situation is quite different for non-perturbative electron dynamics, where sometimes TDDFT has been very useful in interpreting and analyzing results of electron dynamics in strong fields, while other times, it fails completely to even qualitatively capture the correct dynamics. We describe some of our recent studies investigating why. We then present a new class of non-adiabatic approximations in time-dependent density functional theory derived from an exact expression for the time dependent exchange-correlation potential. The approximations reproduce dynamical step and peak features in the exact potential that are missing in adiabatic approximations. Central to this approach is an approximation for the onebody reduced density-matrix as a functional of the Kohn-Sham density matrix, and we demonstrate three such examples. We will also discuss the challenges related to this approach.