Abstract
In density-functional theory (DFT) of the ground state, a density distribution (r) is called v-representable (VR) if it is the ground-state density in some external potential. [It is known that not all ‘‘reasonable’’ (r) are VR.] In DFT of time-dependent linear response of a nondegenerate ground state, a similar question arises: Is a response density, (r,ω), VR, i.e., is it the response to some perturbing potential (r,ω) [E.K.U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985)]? In the present paper we show that (1) if the frequency ω< (the lowest excitation frequency), the answer is affirmative; and (2) if ω>, the answer is not necessarily affirmative, as demonstrated by counterexamples. [We exhibit ‘‘reasonable’’ functions (r,ω) which, at isolated frequencies, are not VR.] Implications for time-dependent DFT of linear response are discussed.
- Received 5 January 1987
DOI:https://doi.org/10.1103/PhysRevA.35.4796
©1987 American Physical Society