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The formalism for multi-state multireference configuration-based Rayleigh-SchrÃƒÂ¶dinger perturbation theory and procedures for its implementation for the second-order and third-order energy within a multireference configuration interaction computer program are reviewed. This formalism is designed for calculations on electronic states that involve strong mixing between different zero-order contributions, such as avoided crossings or mixed valence-Rydberg states. Such mixed states typically display very large differences in reference-configuration mixing coefficients between the reference MCSCF wave function and an accurate correlated wave function, differences that cannot be reflected in state-specific (diagonalize-then-perturb) multireference perturbation theory through third order. A procedure described in detail applies quasidegenerate perturbation theory based on a model space of a few state-averaged MCSCF functions for the states expected to participate strongly in the mixing, and can be characterized as a Ã¢Â€Âœdiagonalize-then-perturb-thendiagonalizeÃ¢Â€Â approach. It is similar in various respects to several published methods, including an implementation by Finley, Malmqvist, Roos, and Serrano-AndrÃƒÂ©s [Chem. Phys. Lett. 1998, 288, 299Ã¢Â€Â“306]

Multi-state Multireference Rayleigh–Schrödinger Perturbation Theory for Mixed Electronic States: Second and Third Order