Virial fragments and the Hohenberg–Kohn functional

Eduardo V. Ludeña, Vladimiro Mujica

Research output: Contribution to journalArticlepeer-review


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 (∇2ρ) 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.

Original languageEnglish (US)
Pages (from-to)927-935
Number of pages9
JournalInternational Journal of Quantum Chemistry
Issue number5
StatePublished - May 1982
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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