Dirac-Hartree-Fock Electronic Energy in Basis Set Representation

Dirac-Hartree-Fock Electronic Energy in Basis Set Representation 

In the preceding chapter on isolated, spherically symmetric atoms, we chose to derive Cl and SCF equations from the most general expression of the total electronic energy in which the total state is expanded in a CSF many-particle basis set. Here, we could proceed in the same way but start instead with the simple Dirac-Hartree-Fock theory for the sake of convenience. Its extension we discuss later in this chapter. 

The starting point for our discussion is the Dirac-Hartree-Fock energy expression in Eq. (8.121) which we may write as 

This expression is formally the same for its nonrelativistic one-component Hartree-Fock relative. 

The one-electron integrals over the predefined basis functions need to be calculated and can be arranged in the form of an m-dimensional matrix h = hpix, with its elements defined by 

---