Force-balance and differential equation for the ground-state electron density in atoms and molecules

✍ Scribed by C. Amovilli; N. H. March; T. Gál; Á. Nagy

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 165 KB
• Volume: 77
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(2000)77:4<716::aid-qua4>3.0.co;2-c

✦ Synopsis

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 λe 2 /r 12 . 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).