Externally and internally corrected coupled cluster approaches: an overview

Abstract

The single-reference (SR) coupled-cluster (CC) approaches proved to be remarkably efficient in handling the dynamic correlation and continue to be widely exploited in quantum chemical computations of the molecular electronic structure. Yet, in the presence of quasi-degeneracy, e.g., when handling molecules away from their equilibrium geometry or when dealing with strongly correlated systems, a proper account of a non-dynamic correlation becomes essential and calls, in general, for a multi-reference (MR) type methodology. However, in view of the ambiguity, complexity, and computational demands of such MR approaches it is tempting to design SR CC type methods that are capable of accommodating both kinds of correlation effects. One avenue how to achieve this goal is to employ the complementarity of perturbative (i.e., CC) and variational (i.e., UHF, VB, CI, CAS SCF, etc.) type approaches and exploit the latter to remedy the CC methods—primarily CCSD or CCSD(T)—for the lack of the static or non-dynamic correlation effects. This leads to the so-called externally corrected (ec) ecCCSD or ecCCSD(T) approaches, which amend the standard CCSD or CCSD(T) methods by accounting for higher-than-pair clusters, extracted from various external sources. The same goal that leads simultaneously to more efficient SR CC algorithms may also be achieved by an effective implicit account of higher-order clusters via the so-called internally corrected methods (e.g., ACP-D45, ACCD, ACPQ, etc). While both types of these approaches were formulated and exploited long time ago, they recently enjoyed a certain renaissance. The objective of this work is to review, classify, and interrelate these efforts and highlight the advances made in this direction.