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

摘要

Holas and March (1995) established a force-balance equation from the many-electron Schrodinger 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 bur with weak electron-electron Coulomb repulsion lambda e(2)/r(12). In this case first-order Rayleigh-Schrodinger (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') 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). (C) 2000 John Wiley & Sons, Inc. [References: 17]