Multiconfiguration self-consistent field theory of localized orbitals: The secular problem

In MC SCF theory both the orbitals and the wavefunction expansion coefficients are optimized by minimizing the energy of the system with respect to arbitrary variations of the orbitals and the wavefunction expansion coefficients. This procedure leads to separate equations for the optimal orbitals and to the secular equation for the expansion coefficients which must be solved self-consistently. In a previous paper we discussed the properties of several different choices of localization potential which may be used in the orbital equation. In this paper we derive an alternative native secular equation by making use of the transformation properties of the localized orbitals. This secular equation is considerably simpler than the conventional secular equation and leads to a simplified scheme for the self-consistent solution of the orbital and secular equations.