The Spin-Projected Extended Hartree-Fock Method

Abstract

This chapter focuses on the spin-projected extended Hartree–Fock (HF) method. The HF method, in its most usual form, applies the restriction for the one-electron functions that (for closed-shell systems) two electrons with opposite spins are put on the same spatial orbital. Almost all the methods used in quantum chemistry are based on the well-known variation theorem. Choosing the type of the trial wave function used in the variation procedure, one must take into account a great number of different factors—for example, the given class of the wave functions must be adequate to describe the most important physical features of the system, contain as many free variational parameters as feasible from the computational point of view, etc. The one-particle approximations-the Hartree–Fock method and its generalizations-are of upmost importance in this respect. This is one of the reasons why just the HF or selfconsistent field (SCF) method is the basic one in quantum chemistry. Many-electron wave function is approximated as a single Slater determinant—such as, an antisymmetrized product of functions each of which depends on coordinates of only one electron. These one-electron functions (orbitals) are then optimized in a variational way. In addition, a number of actual calculations are also done by using the “extended Hartree–Fock” (EHF) method and the related approaches; these clarified the possibilities and limitations of the method.