Minimizing the time-dependent density functional error in Ehrenfest dynamics

Simulating electron-ion dynamics using time-dependent density functional theory within an Ehrenfest dynamics scheme can be done in two ways that are in principle exact and identical: propagating time-dependent electronic Kohn-Sham equations or propagating electronic coefficients on surfaces obtained from linear-response. We show here that using an approximate functional leads to qualitatively different dynamics in the two approaches. We argue that the latter is more accurate because the functionals are evaluated on domains close to the ground-state where current approximations perform better. We demonstrate this on an exactly-solvable model of charge-transfer, and discuss implications for time-resolved spectroscopy.