A Unified Framework for the Polarizable Embedding and Continuum Methods Within Multiconfigurational Self-consistent Field Theory

This review provides, within the framework of multiconfigurational self-consistent field (MCSCF) theory, a unified description of three polarizable environment models: the discrete polarizable embedding model and the two continuum approaches, the spherical cavity and the polarizable continuum model. In particular, we derive, using a common effective one-electron operator formulation, the working equations for optimizing an MCSCF state, embedded in a polarizable environment. The unified view is further extended to general order response theory, using a nonequilibrium formulation of the environmental response. The explicit expressions needed for evaluation of linear response properties are given, and these form the basis for discussing the differences between the polarizable models and more approximate ones. The generality of both the environment formulation and the wave function parameterization leaves the expressions provided here applicable to any embedding model compatible with the general effective one-electron operator (Eq. 4.40), simultaneously covering an SCF, a Cl, or an MCSCF description of the embedded molecule.