multireference

Multireference refers to a class of theoretical and computational approaches that employ more than one reference configuration or state to describe a system, typically where a single-reference description is insufficient. In quantum chemistry, multireference methods are used to treat electronic structures with near‑degenerate or strongly correlated orbitals, such as bond dissociation, transition metal complexes, excited states, and diradicals. The multireference wavefunction is constructed from a set of configuration state functions (CSFs) or determinants that span an active space, capturing static correlation, while dynamic correlation is added by perturbative or coupled‑cluster corrections.

Common multireference techniques include the Complete Active Space Self‑Consistent Field (CASSCF) method, which optimizes orbitals and CI coefficients within a chosen active space, and the Multireference Configuration Interaction (MRCI) and Multireference Perturbation Theory (e.g., CASPT2, NEVPT2) that provide post‑CASSCF correlation. Multireference coupled‑cluster (MR‑CC) methods extend coupled‑cluster theory to multireference contexts, albeit with higher computational cost.

The selection of an appropriate active space is a critical step, influencing accuracy and tractability. Automated active‑space selection algorithms and density‑matrix renormalization group (DMRG) approaches have expanded the applicability of multireference calculations to larger systems. Despite advances, challenges remain in balancing computational expense, size‑consistency, and the description of both static and dynamic correlation.

Beyond chemistry, the term multireference can appear in statistics and information retrieval, indicating the use of multiple reference points or models for validation, calibration, or comparison. In all contexts, the underlying idea is to improve fidelity by incorporating several foundational descriptions rather than relying on a single, potentially inadequate, reference.