Exact non-adiabatic part of the Kohn-Sham potential and its fluidic approximation

We present a simple geometrical “fluidic” approximation to the non-adiabatic part of the Kohn-Sham potential, $v_{\mathrm{K}\mathrm{S}}$, of time-dependent density functional theory. This part of $v_{\mathrm{K}\mathrm{S}}$ is often crucial, but most practical functional approximations utilize an adiabatic approach based on ground-state DFT. For a variety of prototype systems, we calculate the exact time-dependent electron density, and find that the fluidic approximation corrects a large part of the error arising from the “exact adiabatic” approach, even when the system is evolving far from adiabatically.