Miscellaneous Selection Schemes

The CI space selection schemes provided so far cover the majority of CI methods one commonly finds in the literature, but these schemes are not the only ones possible. For example, Greener[9] has suggested a radical CI selection scheme in which CSFs are chosen based on a random Monte Carlo algorithm. Rather than persue a random scheme, many methods employ some kind of extra calculation to determine the importance of individual CSFs or determinants to the exact wave function. For example, Bunker and Peyerimhoff[10] have suggested that one should include configurations in an MRCI based on their energetic contribution to a small CI including only the references and the CSFs formed from that configuration. This method is extremely tedious as it requires one to perform a number of smaller CI calculations; thus, Gershgorn and Shavitt[11] go one step farther and propose a method, the so-called B_k method, which is able to evaluate the importance of all configurations simultaneosly. A third method of this type one is likely to encounter is the CISPI method of Malrieu and coworkers[12,13] in which determinants are chosen based on perturbation theory estimates of their coefficients in the first-order wave function. In conclusion, while this section provides a few additional techniques, the number of schemes can be as diverse as the number of scientists working in the field, and one must be careful to understand exactly what methods are being used in a given article and work to reproduce the results, if necessary.