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

Holas and March (1995) established a force-balance equation from the many-e lectron Schrodinger equation. Here, we propose this as a basis for the cons truction of a (usually approximate) differential equation for the ground-st ate electron density. By way of example we present the simple case of two-e lectron systems with different external potentials bur with weak electron-e lectron Coulomb repulsion lambda e(2)/r(12). In this case first-order Rayle igh-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 corre sponding 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 Hook ean atom is treated: For this case one can also transcend the first-order R S perturbation theory and get exact results for discrete choices of force c onstants (external potential). (C) 2000 John Wiley & Sons, Inc.