Self-consistent field orbital approximation method Generating

Hartree and Fock (Fock 1930 Hartree 1928) formalism uses the single SD form of the total wave function, which is solved under self-consistent field (SCF) approximation. This involves an iterative process in which the orbitals are improved cycle to cycle until the electronic energy reaches a constant minimum and the orbitals no longer change. Upon convergence of the SCF method, the minimum-energy MOs produce an electric field that generates the same orbitals and hence the self-consistency. 

The self-consistent field (SCF) orbital approximation method developed by Hartree is especially well suited for applications in chemistry. Hartree s method generates a set of approximate one-electron orbitals, associated energy levels, s , reminiscent of those for the H atom. The subscript a represents the appropriate set of quantum numbers (see later in this chapter for a definition). The electronic structure of an atom with atomic number Z is then built up by placing Z electrons into these orbitals in accordance with certain rules (see later in this chapter for descriptions of these rules). 

A conceptually straightforward improvement on the CI approximation is to reoptimize the molecular orbitals for a truncated CI expansion. This approach is called multi-configuration self-consistent field method (MCSCF) and its most prominent variant is the complete active space SCF method (CASSCF) [64]. In the first generation of MCSCF methods [65, 66], the CI coefficients C/ in Eq. 

It is clear that this approximation, like the much cruder one described earlier, factorizes the original problem into n independent one-planet problems. Moreover, if we know the field V, we can solve these problems to find the n planetary orbits i/f,(r). However, v must depend on the V, (r) and it appears that we have created a chicken-and-egg paradox Fortunately, this difficulty can be resolved simply by stipulating that the field generated from the orbits must also generate those orbits. This requirement defines a self-consistent field method. 

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