MCSCF

MCSCF, or multiconfigurational self-consistent field, is a family of electronic structure methods designed to treat static correlation by allowing the wavefunction to be a linear combination of multiple electron configurations within a chosen active space. Unlike single-reference methods, MCSCF accounts for near-degeneracies and bond-breaking situations by explicitly including several important configurations in the reference wavefunction. In practice, MCSCF optimizes both the molecular orbitals and the coefficients of configurations in a self-consistent loop.

The key idea is the active space, a selected set of active electrons and active orbitals that are allowed to occupy different configurations. The wavefunction is expanded within this space, and the configuration coefficients are determined by a configuration interaction within the active space. In state-averaged MCSCF (SA-MCSCF or SA-CASSCF), the optimization targets a weighted average of several electronic states to obtain balanced orbitals for ground and excited states. Inactive core orbitals are typically kept doubly occupied and frozen, while virtual orbitals are unoccupied or treated in a restricted manner. The optimization alternates between updating configuration coefficients and refining orbitals until convergence.

Because MCSCF by itself neglects much of the dynamic electron correlation, it is commonly augmented by post-MCSCF methods such as perturbation theory (e.g., CASPT2, NEVPT2) or multireference configuration interaction (MRCI) to recover additional correlation energy. MCSCF is widely used for problems involving bond dissociation, excited states, diradicals, and transition-metal complexes. A central practical challenge is selecting an appropriate active space and configurations, since the accuracy and cost grow with the size of the active space; generalized active space (GAS) schemes are sometimes employed to mitigate this.