Addressing strong correlation by approximate coupled-pair methods with active-space and full treatments of three-body clusters

Abstract

When the number of strongly correlated electrons becomes larger, the single-reference coupled-cluster (CC) CCSD, CCSDT, etc. hierarchy displays an erratic behaviour, while traditional multi-reference approaches may no longer be applicable due to enormous dimensionalities of the underlying model spaces. These difficulties can be alleviated by the approximate coupled-pair (ACP) theories, in which selected $(T_2{)}^2$ diagrams in the CCSD amplitude equations are removed, but there is no generally accepted and robust way of incorporating connected triply excited ($T_3$) clusters within the ACP framework. It is also not clear if the specific combinations of $(T_2{)}^2$ diagrams that work well for strongly correlated minimum-basis-set model systems are optimum when larger basis sets are employed. This study explores these topics by considering a few novel ACP schemes with the active-space and full treatments of $T_3$ correlations and schemes that scale selected $(T_2{)}^2$ diagrams by factors depending on the numbers of occupied and unoccupied orbitals. The performance of the proposed ACP approaches is illustrated by examining the symmetric dissociations of the ${\mathrm{H}}_6$ and ${\mathrm{H}}_{10}$ rings using basis sets of the triple- and double-ζ quality and the ${\mathrm{H}}_{50}$ linear chain treated with a minimum basis, for which the conventional CCSD and CCSDT methods fail.

GRAPHICAL ABSTRACT

Keywords:

• Strongly correlated electrons
• coupled-cluster theory
• approximate coupled-pair methods
• three-body clusters
• hydrogen clusters

Acknowledgments

We dedicate this article to the memory of the late Professor Lutosław Wolniewicz, whose pioneering work on high-precision molecular quantum mechanics inspired our interest in becoming quantum chemists. One of us (P.P.) would like to thank Professors Stanisław Dembiński, Jacek Karwowski, and Józef Szudy for inviting him to contribute an article to the Special Issue of Molecular Physics commemorating Professor Lutosław Wolniewicz.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy (Grant No. DE-FG02-01ER15228).