The Central-Field Approximation

Abstract

In the absence of theoretical tools for solving the Schrödinger equation, and with the shortcomings and/or complexities of the approximation methods described in the previous chapter, we will regroup and see if we, with a modified perturbative analysis, can gain more insight into multielectron atomic structure. We have seen that forming a zero-order Hamiltonian with only the electron–nucleus interactions taken into account yields separable zero-order basis functions but at a price. The approximation is crude and for all but the smallest atoms, the variational method becomes forbiddingly complex. In this chapter, we retain the ambition to have separable zero-order functions from a purely radial potential, but we do this without leaving the entire electron–electron interaction as a perturbation. In this central-field approximation, each electron is thought of as moving in a purely central potential and having a wave function akin to hydrogenic orbitals. For a multielectron atom, the zero-order approximation of its state is a product of electron orbitals, whose occupation numbers adhere to the Pauli principle. Such product states are electron configurations and with an understanding of ground state electron configurations, the periodic system of elements can be constructed.