Self-consistent field method minimization procedure

The Hartree-Fock or self-consistent field (SCF) method is a procedure for optimizing the orbital functions in the Slater determinant (9.1), so as to minimize the energy (9.4). SCF computations have been carried out for all the atoms of the periodic table, with predictions of total energies and ionization energies generally accurate in the 1-2% range. Fig. 9.2 shows the electronic radial distribution function in the argon atom, obtained from a Hartree-Fock computation. The shell structure of the electron cloud is readily apparent. 

In complete active space self-consistent field (CASSCF) calculations with long configuration expansions the most expensive part is often the optimization of the Cl coefficients. It is, therefore, particularly important to minimize the number of Cl iterations. In conventional direct second-order MCSCF procedures , the Cl coefficients are updated together with the orbital parameters in each micro-iteration. Since the optimization requires typically 100-150 micro-iterations, such calculations with many configurations can be rather expensive. A possible remedy to this problem is to decouple the orbital and Cl optimizations , but this causes the loss of quadratic convergence. The following method allows one to update the Cl coefficients much fewer times than the orbital parameters. This saves considerable time without loss of the quadratic convergence behaviour. 

A more balanced description thus requires multiconfiguration self-consistent field (MCSCF)-based methods, where the orbitals are optimized for each particular state or optimized for a suitable average of the desired states (state-averaged MCSCF). In semiempirical methods, however, an MCSCF procedure is normally not required due to the limited flexibility of the minimal valence atomic orbital basis commonly used in these methods. Instead, a multireference Cl method including a limited number of suitably chosen configurations will be appropriate. 

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