Multiple complete active space self-consistent field solutions

It is proved that the CASSCF equations for the ground state of weakly interacting systems admit many non-equivalent solutions for a given type of active space. For instance, in the case of N weakly interacting hydrogen molecules, there are at least N different minima in the case of a CAS(2/2), involving one bonding and one antibonding orbital on the same molecule. A similar result still holds for many systems for which the interaction is far from small. As an example, the case of the ethylene molecule is discussed, where three CAS(2/2) and six CAS(4/ 4) non-equivalent minima are present. The use of localized orbitals permits one to choose the particular solution one wants to converge to. The implications of these results on CASSCF calculations are significant, since by choosing different minima one can focus the CASSCF description on a given characteristic (e.g., the spatial position) of the active orbitals. In this way, a significant reduction of the active-space size is possible, a fact particularly important in the case of large systems.