Abstract
The formalism for multi-state multireference configuration-based Rayleigh-Schrödinger 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 “diagonalize-then-perturb-thendiagonalize” approach. It is similar in various respects to several published methods, including an implementation by Finley, Malmqvist, Roos, and Serrano-Andrés [Chem. Phys. Lett. 1998, 288, 299–306].
Highlights
The term “mixed electronic states” refers to states in which electronic structures of different types, such as valence and Rydberg, or covalent and ionic, contribute strongly to the wave function
The crossing point between the potential energy curves of the covalent and ionic configuration in alkali halides can vary by several Bohr between an MCSCF and a multireference CI calculation [1]
Mixed electronic states are characterized by large changes in the relative contributions of the reference configurations in a well-correlated final wave function compared to the zero-order MCSCF function
Summary
The term “mixed electronic states” refers to states in which electronic structures of different types, such as valence and Rydberg, or covalent and ionic, contribute strongly to the wave function. The reference function and deal with the mixed-states problem It begins with a state-averaged MCSCF [12,13] calculation to provide a small number of model-state zero-order functions, and applies quasidegenerate perturbation theory to obtain an effective Hamiltonian in that small model space, followed by diagonalization of the effective Hamiltonian to obtain properly-mixed wave functions and energies. The model states used to construct the effective Hamiltonian are a small subset of the eigenstates of the state-averaged MCSCF Hamiltonian, and if they can be chosen to be well-separated in energy from any other zero-order states the intruder-state problem can be reduced This approach has been proposed and implemented, in one form or another, by a number of researchers, including Malrieu and co-workers [14], Sheppard et al [15], Lisini and Decleva [16], Nakano [17], and Roos and co-workers [18].
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