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- W2018541907 abstract "The Hohenberg-Kohn theorem is extended to the case that the external potential is nonlocal. It is shown that, in this more general case, a nondegenerate ground-state wave function is a universal functional of the one-particle density kernel $ensuremath{mu}(x,{x}^{ensuremath{'}})$, but probably not of the particle density $n(stackrel{ensuremath{rightarrow}}{mathrm{r}})=ensuremath{Sigma}{s}^{}ensuremath{mu}(stackrel{ensuremath{rightarrow}}{mathrm{r}}s,stackrel{ensuremath{rightarrow}}{mathrm{r}}s)$. The variational equations for the local and nonlocal cases are compared. The former must be replaced by a variational equation for an equivalent system of noninteracting particles, following a prescription of Kohn and Sham, in order to obtain a Schrodinger-like form, and contains only local potentials. The latter may be obtained directly in Schrodinger-like form, but the exchange-correlation potential is nonlocal. If the nonlocal pseudo-Hamiltonian exists [i.e., if the functional derivative $frac{ensuremath{delta}E}{ensuremath{delta}ensuremath{mu}(x,{x}^{ensuremath{'}})}$ exists for a nondegenerate ground-state density kernel], then the eigenfunctions of the pseudo-Hamiltonian are natural spin orbitals, and all partially occupied orbitals ($0<〈{ensuremath{varphi}}_{i}|ensuremath{mu}|{ensuremath{varphi}}_{i}〉<1$) belong to the same degenerate eigenvalue of the pseudo-Hamiltonian. Finally, it is shown, as a corollary of Coleman's theorem for $N$-representable density kernels, that any finite non-negative differentiable function is an $N$-representable particle density." @default.
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- W2018541907 date "1975-09-15" @default.
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- W2018541907 title "Hohenberg-Kohn theorem for nonlocal external potentials" @default.
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- W2018541907 doi "https://doi.org/10.1103/physrevb.12.2111" @default.
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