Multi-Configuration Self-Consistent-Field Theory

A general formalism is presented to solve in a practical way the equations resulting from applying the variation principle to a mixture of configurations, constructed from a common orthonormal set of orbitals. The optimization of the configuration mixing coefficients leads to the usual eigenvalue problem and secular equation; the optimization of the orbitals leads to Self-Consistent-Field equations which strongly resemble the Hartree-Fock equations. Since the mathematical provides for adjusting the orbitals to a more proper electronic environment as represented by a better total wave function, it is expected that short expansions in terms of configurations will yield wave functions of high quality.