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 behavior, 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 ${\text{H}}_6$ and ${\text{H}}_{10}$ rings using basis sets of the triple- and double-$\zeta$ quality and the ${\text{H}}_{50}$ linear chain treated with a minimum basis, for which the conventional CCSD and CCSDT methods fail.

56 pages, 7 tables, 4 figures

References in corpus (15)

• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group
• Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
• Quasiparticle Coupled Cluster Theory for Pairing Interactions
• A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states
• Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo
• Variational coupled cluster for ground and excited states
• The Adaptive Shift Method in Full Configuration Interaction Quantum Monte Carlo: Development and Applications
• Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
• Is Externally Corrected Coupled Cluster Always Better than the Underlying Truncated Configuration Interaction?
• On the distinguishable cluster approximation for triple excitations
• Coupled Cluster Externally Corrected by Adaptive Configuration Interaction
• Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations