A posteriori corrections to the configuration interaction method: a single-reference and multi-reference study

Abstract

The single-reference (SR) configuration interaction (CI) method is nowadays rather rarely used in quantum-chemical calculations. The reason is that the method is not competitive with the coupled-cluster (CC) approach that uses the same number of parameters but is size-extensive and more accurate. The accuracy of the CI method can be increased by applying size-extensivity a posteriori corrections but even that does not make the SR-CI method much more attractive. The CI scheme has, however, one important advantage over the CC one. Due to its formal simplicity, the SR-CI approach can be easily generalised to the multi-reference (MR) case while such a generalisation for the CC method turned out nontrivial. Two basic MR-CC formulations are formally complicated, numerically demanding, vulnerable to intruder states, and sensitive to the problem of multiple solutions. Contrary to that the MR-type CI schemes are among very few methods that are used in routine calculations for systems requiring a MR description. The problem of improving the MR-type CI results by applying an a-posteriori correction is in this context very appealing. In the paper, we discuss different types of corrections trying to show that the one based on the SR cluster expansion is both well theoretically justified and reliable in numerical applications. That is illustrated on model CI calculations of SR and MR type.

Keywords:

• electron correlation
• ab initio methods
• configuration interaction method
• coupled cluster method
• Davidson type correction

Acknowledgements

This work has been financially supported by the Scientific and Technological Research Council of Turkey-TÜBITAK, Grant no.: TUBITAK-BIDEB-2219 International Postdoctoral Research Fellowship Programme (2012-1). Also a partial support by the Polish National Science Center under Grant no. DEC-2013/11/B/ST4/00771 is gratefully acknowledged.

This paper is dedicated to Professor Sourav Pal on the occasion of his 60th birthday in appreciation of his outstanding contribution to the field of theoretical and computational quantum chemistry.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The Scientific and Technological Research Council of Turkey-TÜBITAK: International Postdoctoral Research Fellowship Programme (2012-1) [grantnumber TUBITAK-BIDEB-2219]; The Polish National Science Center [grant number DEC-2013/11/B/ST4/00771].