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This paper reviews basic results from a theory of the classical probabilitiesin state-averaged complete active space self-consistent field wave functions.It is proposed that a canonical (Boltzmann) weighting scheme makes theself-consistency condition invariant with respect to configurationaltransformations that act locally on the support of the equilibrated SA-CASSCFensemble. This is illustrated with a complete active space valence-bond (CASVB)analysis of low-energy electronic states in a monomethine cyanine dye.

Canonical-ensemble SA-CASSCF strategy for problems with more diabatic than adiabatic states: Charge-bond resonance in monomethine cyanines