ABSTRACT
This chapter estimates the energy of the many-electron system by considering the interaction of all the electrons with the nucleus and the interaction of all the electrons with nucleus and the interaction of all electrons with each other. It includes the mathematical interpretation of energy of many-electron system, Fock equation, and Hartree equation, applications in two-electron systems – for getting Hartree equation and energy of two-electron system. The Hartree and Hartree–Fock self-consistent field methods have also been included, which is a very important method for dealing with the computational purposes. This chapter deals with excited state of helium mathematically. Here, it has been stated that Fermi hole and Fermi heap are quantum mechanical phenomena. This chapter also discusses clearly lithium in the ground state on the mathematical basis. It deals with atomic magnets and magnetic quantum numbers, the gyromagnetic ratio, Landé splitting factor, Landé ‘g’ factor, Landé interval rule, Zeeman effect, Stark effect, coupling of orbital angular momentum, coupling of spin momenta, coupling of orbital and spin angular momenta, Russell–Saunders coupling scheme or L–S coupling, and jj-coupling scheme. This chapter also comprises multiplicity and atomic states, Hund’s rule, atomic terms and symbols, terms of nonequivalent, terms and symbols, terms of equivalent electrons, Slater rules for estimating the screening effect, Slater-type orbitals, Gaussian-type orbitals, Gaussian basis set, and Condon–Slater rules for evaluation of matrix elements. It also gives mathematical idea of Koopman’s theorem, Brillouin’s theorem, and mathematical treatment of Roothaan’s equations for solving the H–F equations numerically. This enables one to calculate the density matrix elements. At the end, this chapter contains references, solved problems, and questions on concepts for exercise.
