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

Abstract

Holas and March (1995) established a force-balance equation from the many-electron Schroedinger equation. Here, the authors propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example they present the simple case of two-electron systems with different external potentials but with weak electron-electron Coulomb repulsion {lambda}e{sup 2}/r{sub 12}. In this case first-order Rayleigh-Schroedinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix {gamma}(r,r{prime}) in terms of its diagonal density {rho}(r) and the density corresponding to {lambda} = 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 {rho}(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).