A new functional with homogeneous coordinate scaling in density functional theory: F[ρ, λ]

As previously shown [M. Levy and J. P. Perdew, Phys. Rev. A (in press)], the customary Hohenberg-Kohn density functional, based on the universal functional F[ρ], does not exhibit naively expected scaling properties. Namely, if ρλ = λ³ρ(λr) is the scaled density corresponding to ρ(r), the expected scaling, not satisfied, is T[ρλ ] = λ²T[ρ] and V[ρλ] = λV[ρ], where T and V are the kinetic and potential energy components. By defining a new functional of ρ and λ, F[ρ, λ], it is now shown how the naive scaling can be preserved. The definition isF[ρ(r),λ] = 〈λ ^3N/2Φρλ^min(λr 1⋯λrN)|T̂(r1⋯r N) + Vee(r1⋯rN) λ^3N/2Φρλ^min(λ r1⋯λrN)〉,where λ^3N/2 Ωρλ^min(λr 1⋯λrN) is that antisymmetric function Ω which yields ρλ(r) = λ³ρ(λr) and simultaneously minimizes 〈Ω|T̂(r1⋯r N) + λVee(r1⋯r N)|Ω〉. The corresponding variational principle is E G.S.^v = Infλ,ρ(r) {∫drv(r)ρλ(r) + λ²T[ρ(r)] + λV ee[ρ(r)]}, where EG.S.^v is the ground-state energy for potential v(r). One is thus allowed to lower the energy and satisfy the virial theorem by optimum scaling just as if the naive scaling relations were correct for F[ρ]. © 1985 American Institute of Physics.

Duke Scholars

Author Weitao Yang Chemistry