A rigorous description of TDKS theory from first principles can be found in the work of Gross et al. and a simplified tutorial, with a discussion of contemporary problems, can be found in Ref. 23. The adiabatic approximation (i.e., locality in time) is assumed throughout this work, so that the time dependence of the exchange-correlation functional is carried strictly by the time-evolving density, ρ(r, t); ground-state functionals are therefore used without alteration. The timedependent electron density is expressed in terms of timedependent Kohn-Sham molecular orbitals (MOs),