Isaiah Shavitt

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].

Several aspects of the matrix diagonalization method used for CI calculations in the COLUMBUS Program System are discussed, including a linear basis‐contraction algorithm and the use of a nonorthogonal expansion basis. Both of these features significantly reduce the I/O requirements during the iterations. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1121–1125, 2002

The convergence properties of several iterative methods for the optimization of orbitals and configuration mixing coefficients in multiconfigurational electronic wave functions are compared. All of the iterative methods considered here are derived from corresponding approximate energy expressions. These energy expressions are discussed within the context of their suitability for the calculation of noninfinitesimal wave function corrections. A method based on the partitioned orbital Hessian matrix and which uses an approximate super‐CI secular equation for the wave function corrections is shown to posses second‐order convergence and to have the largest radius of convergence of the methods analyzed in detail in this work for several molecular examples. Particular attention is given to convergence properties for excited states, where the differences between these methods are most significant.