Center of mass and relative motion in time dependent density functional theory.

It is shown that the exchange-correlation part of the action functional A xc [ρ(r, t)] in time-dependent density functional theory , where ρ(r, t) is the time-dependent density, is invariant under the transformation to an accelerated frame of reference ρ(r, t) → ρ ′ (r, t) = ρ(r + x(t), t), where x(t) is an arbitrary function of time. This invariance implies that the exchange-correlation potential in the Kohn-Sham equation transforms in the following manner: V xc [ρ ′ ; r, t] = V xc [ρ; r + x(t), t]. Some of the approximate formulas that have been proposed for V xc satisfy this exact transformation property, others do not. Those which transform in the correct manner automatically satisfy the " harmonic potential theorem " , i.e. the separation of the center of mass motion for a system of interacting particles in the presence of a harmonic external potential. A general method to generate functionals which possess the correct symmetry is proposed.