2 - Many-Electron Atoms and Self-consistent Fields

Abstract

This chapter develops the Self-consistent field (SCF) restricted (RHF) and unrestricted (RHF) Hartree-Fock (HF) theories for many-electron atoms. It starts with the development of antisymmetrized wavefunctions of polyelectronic atoms, and their representation as Slater determinants constructed from spin orbitals so as to be in agreement with Pauli's antisymmetry principle. The inclusion of electron repulsion in potential energy terms in many-electron systems such as polyelectronic atoms and molecules complicates the solution of Schrodinger equation. This needed the development of the self-consistent field (SCF) theory based on the central field approximation. Hartree theory using spatial orbitals and the HF theory using spin orbitals have therefore been developed in the chapter for many-electron atoms. Interpretation has been provided to the eigenvalues and eigenvectors of the corresponding operators. Electronic configurations and electronic states of systems having even and odd number of electrons and those resulting from excitation of more than one electron have been described. The restricted and unrestricted wavefunctions for the closed shell and open shell configurations have been developed in terms of Slater determinants.