Multiconfiguration

Multiconfiguration refers to the representation of an electronic wavefunction as a linear combination of multiple electron configurations, rather than a single Slater determinant as in Hartree-Fock theory. Each configuration, typically expressed as a Slater determinant or a configuration state function, contributes with a coefficient optimized to minimize the energy. This approach addresses static electron correlation and near-degeneracy that cannot be captured by a single determinant.

In practice, multiconfiguration methods define an active space of orbitals and electrons. Configurations are generated by distributing the active electrons among the active orbitals, allowing different occupation patterns. The resulting multiconfiguration wavefunction can be optimized by methods that treat both the orbitals and the configuration weights simultaneously. The most widely used framework is multiconfigurational self-consistent field (MCSCF), with a common specialization called complete active space self-consistent field (CASSCF), denoted CAS(n,m) for n electrons in m active orbitals.

Beyond the active-space wavefunction, dynamic correlation is typically addressed by additional techniques such as multireference configuration interaction (MRCI) or perturbation theories like CASPT2 and NEVPT2. These approaches combine a robust description of static correlation with corrections for dynamic correlation.

Applications of multiconfiguration methods include systems with strong electronic near-degeneracy, such as transition metal complexes, bond dissociation processes, and excited-state or photochemical phenomena. Limitations arise from rapid combinatorial growth of configurations, necessitating careful selection of the active space and substantial computational resources. Consequently, multiconfiguration methods are often used when single-reference approaches are inadequate.