Appendix A: Derivation of Hartree–Fock Theory

Abstract

The purpose of this appendix is to give the reader a ®rm understanding of the require-ments for the description of many-electron wave functions, the standard procedures used to obtain energies and wave functions, and the role of one-electron wave functions (orbitals) in the scheme of things. It should be read in parallel with Chapter 2. It provides in as simple a way as possible the theory behind the most straightforward applications of prevailing nonempirical quantum chemistry computer codes such as the GAUSSIAN package of quantum chemistry codes [315]. A brief description of procedures for sys-tematic improvement of the theoretical description and an introduction to the alternative density functional methods are also provided. At the same time, the simpli®cations which can be made to derivethempirical or semiempirical MO'' methods are placed in proper perspective. More complete descriptions of the theoretical methods used by computational chemists may be found in references 55 and 316. is the only known quantity (by virtue of a postulate of quantum mechanics) in equation (A.1). It consists of a set of instructions involving arithmetical operations (addition, subtraction, multiplication, and division) as well as di¨erentiations, which must be carried out on the wave function, and we will derive an 218