Force-Balance and Differential Equation for the Ground-State Electron Density in Atoms and Molecules

C. Amovilli, N. H. March, T. Gál, Á Nagy

Research output: Contribution to journalArticle

3 Citations (Scopus)


Holas and March (1995) established a force-balance equation from the many-electron Schrödinger equation. Here, we propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example we present the simple case of two-electron systems with different external potentials but with weak electron-electron Coulomb repulsion λe2/r12. In this case first-order Rayleigh-Schrödinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix γ(r,r′) in terms of its diagonal density ρ(r) and the density corresponding to λ = 0. This result allows the force-balance equation to be written as a third-order linear, differential homogeneous equation for the ground-state electron density ρ(r). The example of the two-electron Hookean atom is treated: For this case one can also transcend the first-order RS perturbation theory and get exact results for discrete choices of force constants (external potential).

Original languageEnglish
Pages (from-to)716-720
Number of pages5
JournalInternational Journal of Quantum Chemistry
Issue number4
Publication statusPublished - Apr 15 2000


  • Ground-state electron density
  • Rayleigh-Schrödinger perturbation theory
  • Virial theorem

ASJC Scopus subject areas

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

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