Multireference Coupled-Cluster Methods: Recent Developments

Abstract

Abstract:The objective of this paper is to provide an overview of various multi-reference (MR) coupled-cluster (CC) approaches, particularly those relating to our own research. Although MR CC methods have been around for almost three decades and much work has been expended on their development and implementation, no general purpose codes are presently available. In view of the complexity, inherent difficulties, and computational demands of both genuine valence and state universal (VU and SU) MR CC methods, attention has been directed towards the state selective or state specific (SS) approaches that focus on one state at a time. These methods are based on either the genuine MR CC formalism or on a singlereference (SR) CC Ansatz, in which higher-than-pair clusters are accounted for by relying on basic ideas of general MR approaches. This is achieved either internally by relying on CC or MBPT formalism or by exploiting some external source providing approximate values of these clusters and accomplished by either correcting equations yielding the cluster amplitudes or directly by evaluating the corrections to the CCSD energy. Nowadays there exists a whole plethora of such various approaches for handling of quasi-degenerate states with a various degree of MR character and our goal is to outline their basic features and comment on their pro's and con's, their usefulness and weaknesses, as well as point out their mutual relationship.

Multireference coupled-cluster Ansatz

“…This form of H with the operator Q = 1 − P , and employ the sufficiency condition [61,109], we find that…”

Perspectives from Quantum Chemistry for molecules and nanograins with astrophysical Interest

“…As already mentionned, excited states can clearly be obtained in the WF approach, such as for instance in the CAS-PT2 scheme, where the CAS-CI excited roots are treated variationnally within the CAS and further perturbed up to second order Perturbation Theory. There is some active work in the framework of multi-reference Coupled Cluster Theory to address excited states [23][24][25][184][185][186], however such formulation is not yet quite standard. In the context of Coupled Cluster theories, an alternative approach is to use the equation of motion (EOM) and response theory following a CC determination of the ground state [187,188].…”

Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies

“…The diverse manifold of higher-order approximations include, among others, categories of active-space, multi-reference, externally corrected, and adaptive approaches, as well as non-iterative corrections and approaches that combine stochastic techniques (for key reviews and papers see Refs. (7,9,(31)(32)(33)(34)(35)(36)(37)(38)(39) and references therein).…”