Can single-reference coupled cluster theory describe static correlation?

TL;DR

This paper introduces CCD0, a generalized coupled cluster method that effectively describes static correlation while maintaining the structure and invariances of traditional coupled cluster theory.

Contribution

The authors develop CCD0, a new singlet-paired coupled cluster model that bridges CCSD and pCCD, improving the description of static correlation with stability and symmetry.

Findings

CCD0 retains coupled cluster invariances and structure.

CCD0 accurately models static correlation.

CCD0 is more stable than traditional methods.

Abstract

While restricted single-reference coupled cluster theory truncated to singles and doubles (CCSD) provides very accurate results for weakly correlated systems, it usually fails in the presence of static or strong correlation. This failure is generally attributed to the qualitative breakdown of the reference, and can accordingly be corrected by using a multi-determinant reference, including higher-body cluster operators in the ansatz, or allowing symmetry breaking in the reference. None of these solutions are ideal; multi-reference coupled cluster is not black box, including higher-body cluster operators is computationally demanding, and allowing symmetry breaking leads to the loss of good quantum numbers. It has long been recognized that quasidegeneracies can instead be treated by modifying the coupled cluster ansatz. The recently introduced pair coupled cluster doubles (pCCD) approach is one such example which avoids catastrophic failures and accurately models strong correlations in a symmetry-adapted framework. Here we generalize pCCD to a singlet-paired coupled cluster model (CCD0) intermediate between coupled cluster doubles and pCCD, yielding a method that possesses the invariances of the former and much of the stability of the latter. Moreover, CCD0 retains the full structure of coupled cluster theory, including a fermionic wave function, antisymmetric cluster amplitudes, and well-defined response equations and density matrices.