Abstract
It is well known that single-reference coupled cluster theory truncated to low orders of excitations gives the right answer for the right reason when systems are dominated by dynamical or weak correlation. Static or strong correlation is more problematic, causing often catastrophic breakdown of restricted coupled cluster. This failure can be remedied, e.g., by allowing symmetry breaking in the reference or taking a multi-reference approach, but poses an interesting theoretical problem, especially since many groups have found that simplifying the T2 operator or the doubles amplitude equations gives better results. In singlet-paired coupled cluster, eliminating the triplet-pairing channel recovers reasonable qualitative behavior for strong correlation at the cost of a decreased description of dynamical correlation in weakly correlated situations. This behavior seems to hold for both closed- and open-shell systems. In this work, we explore the coupling of the singlet- and triplet-pairing channels of T2 and attempt to recouple them in order to recover dynamical correlation without reintroducing catastrophic failure due to strong correlation. In the weakly correlated regime, these pairing channels are only weakly coupled, and a simple recoupling gives good results. However, as strong correlation dominates, the coupling strength between the singlet- and triplet-pairing channels increases, making it difficult to perturbatively recouple the singlet- and triplet-pairing channels in this regime.
Highlights
The electronic structure of weakly correlated systems is accurately described by the coupled cluster (CC) family of methods.1–4 Coupled cluster with single, double and perturbative triple excitations, CCSD(T), gives quantitative results for weakly correlated systems, and is routinely applied to a wide range of quantum chemical problems
The breakdown of standard coupled cluster is apparent, with CCSD turning over at around 3.6 bohrs. Both FPiCCSD and FSigCCSD recover correlation at equilibrium, giving values comparable to those given by unrestricted CCSD(T)
We asked whether a first-order recoupling of the singletand triplet-pairing channels of T2 might recover dynamical correlation without breaking down due to strong correlation
Summary
The electronic structure of weakly correlated systems is accurately described by the coupled cluster (CC) family of methods. Coupled cluster with single, double and perturbative triple excitations, CCSD(T), gives quantitative results for weakly correlated systems, and is routinely applied to a wide range of quantum chemical problems. Single-reference coupled cluster often breaks down catastrophically in the presence of strong correlation, e.g., near degeneracies in bond-breaking processes, a failure typically associated with the qualitatively incorrect nature of the mean-field reference. An archetype of this failure is in the CCSD description of the dissociation of N2 in the STO-3G basis, shown, where the potential energy surface unphysically turns over around 3.2 bohrs and predicts N2 to have a very low binding energy. This failure persists even in larger bases. Despite the inadequacy of the restricted HartreeFock (RHF) reference at dissociation, recent work has shown that simplifying CC by eliminating or decoupling channels of the T2 operator enables restricted single-reference CC to recover qualitatively correct behavior in describing strongly correlated systems. failures of CC to describe strong correlation can be attributed in part to instabilities in the truncated CC ansatz itself.
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