Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques

TLDR

The study implements a multi‑reference double‑excitation CI (MRD‑CI) method and compares its results with related computational techniques. The method selects configurations based on their energy‑lowering effect and applies a perturbation‑theory‑based energy extrapolation to approximate the full MRD‑CI eigenvalues. The approach can evaluate 2000–4000 symmetry‑adapted functions per second, enabling extrapolation to CI spaces of hundreds of thousands of species; increasing reference configurations approaches the full‑CI limit, and tests on molecules show MRD‑CI captures about 95 % of valence‑shell correlation with few references.

Abstract

Implementation of a multi-reference double-excitation CI (MRD-CI) method is discussed and its results are compared with those of related techniques. This approach employs a configuration selection procedure to order the various generated species according to their energy-lowering capability and then uses an energy extrapolation procedure based on perturbation theory to obtain suitably accurate estimates of the eigenvalues of the entire MRD-CI space. By employing this selection procedure it is possible to test from 2000 to 4000 symmetry-adapted functions (SAF's) per second of CPU time on an IBM 370–168 system, thereby allowing one to apply the energy extrapolation quite conveniently to CI spaces consisting of several hundred thousand species. By systematically increasing the number of reference configurations in the MRD-CI it is clear that the limit of a full CI can be approached and as a result such a computational procedure appears to be generally valid for any type of electronic state and for any nuclear geometry as well as being quite practical. Applications to a number of molecular systems are considered and comparison is made with the results of other theoretical techniques presently available, from which studies it is concluded that the MRD-CI can account for roughly 95 per cent of the total valence-shell correlation attainable with a given AO basis while still employing a relatively small number of reference configurations to generate the associated CI space.