Influence of the noninteracting density response function on the exchange-only kernel in time-dependent density-functional theory

A formally exact expression for the interaction density response function χ(r,r',ω) exists in terms of (i) its noninteracting counterpart χ0(r,r',ω) and (ii) an exchange (x)-correlation (c) kernel fxc(r,r',ω). In the absence of a first-principles theory for the ω dependence of fxc, the adiabatic approximation is most frequently made in this term, to construct a workable time-dependent density-functional theory. In the present study, a proposal is put forward to avoid the adiabatic approximation by working in the exchange-only limit in which fxc is set equal to fx(r,r',ω). We then refer to a result for the exchange energy given by Pines and Nozieres to motivate the assumption that fx=fx[Im χ0(r,r',ω)]. The essential proposal here is therefore that the integral equation to be solved for the interacting density response function χ is in the exchange-only case characterized entirely by the noninteracting response function χ0