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Virial fragments and the Hohenberg–Kohn functional
Author(s) -
Ludeña Eduardo V.,
Mujica Vladimiro
Publication year - 1982
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560210518
Subject(s) - virial theorem , virial coefficient , energy functional , context (archaeology) , density functional theory , virial expansion , variation (astronomy) , kohn–sham equations , physics , statistical physics , thermodynamics , quantum mechanics , galaxy , paleontology , biology , astrophysics
Starting from the Hohenberg‐Kohn functional we show that when the energy density is given as a function of ρ and ∇ ρ , i.e., ξ = ξ(ρ, ∇ ρ ), the condition ∇ ρ · n = 0 (which was found by Bader et al. to define virial fragments), appears as a natural boundary condition for the variation of this functional. We also show that when the energy density includes second order derivatives (∇ 2 ρ ) this condition is necessary but not sufficient to guarantee the vanishing of the variation. The implications of these results are discussed in the context of a density functional theory for virial fragments.