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