Approximately extensive modifications of the multireference configuration interaction method: A theoretical and practical analysis

Abstract

The extensivity error of configuration interaction (CI) is well understood and unlinked diagram corrections must be applied to get reliable results. Besides the well known a posteriori Davidson-type corrections, several methods attempt to modify the CI equations a priori to obtain nearly extensive results, while retaining the convenience of working in a configuration space. Such unlinked diagram corrections are particularly important for multireference cases for which coupled-cluster (CC) calculations, which require a many-body, integral-based calculation, are more difficult. Several such multireference methods have been presented recently, ranging from the multireference linearized coupled cluster method (MR-LCCM), averaged coupled pair functional (MR-ACPF), through various quasidegenerate variational perturbation theory (QD-VPT), MR-coupled electron pair method (MR-CEPA) to size-consistent, self-consistent, selected CI [(SC)2SCI]. We analyze all of these methods theoretically and numerically, paying particular attention to the new multireference averaged quadratic CC method (MR-AQCC), and demonstrate its comparative quality of performance even when using small references spaces. We consider several demanding molecular examples that benefit from a multireference description, like bond stretching in H2O; N2 and C2; the insertion of Be into H2; and the singlet–triplet splitting in CH2. We also investigate the extensivity error.