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 chi(r,r('),omega) exists in terms of (i) its noninteracting counterpart chi(0)(r,r('),omega) and (ii) an exchange (x)-correlation (c) kernel f(xc)(r,r('),omega). In the absence of a first-principles theory for the omega dependence of f(xc), 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 f(xc) is set equal to f(x)(r,r('),omega). We then refer to a result for the exchange energy given by Pines and Nozieres to motivate the assumption that f(x)=f(x)[Im chi(0)(r,r('),omega)]. The essential proposal here is therefore that the integral equation to be solved for the interacting density response function chi is in the exchange-only case characterized entirely by the noninteracting response function chi(0).