S-Diagnostic-An a Posteriori Error Assessment for Single-Reference Coupled-Cluster Methods

We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S-diagnostic. We provide a derivation of the S-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl4](2-), [Cu(NH3)(4)](2+), and [Cu(H2O)(4)](2+). Throughout the numerical investigations, the S-diagnostic is compared to other SRCC diagnostic procedures, that is, the T-1, D-1, max T-2, and D-2 diagnostics as well as different indices of multi-determinantal and multireference character in coupled-cluster theory. Our numerical investigations show that the S-diagnostic outperforms the T-1, D-1, max T-2 and D-2 diagnostics and is comparable to the indices of multideterminantal and multireference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S-diagnostic for geometry optimizations using SRCC reveal that the S-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S-diagnostic for electronic correlation simulations show that the S-diagnostic correctly predicts strong multireference regimes. The S-diagnostic, moreover, correctly detects the successful SRCC computations for [CuCl4](2-), [Cu(NH3)(4)](2+), and [Cu(H2O)(4)](2+), which have been known to be misdiagnosed by T-1 and D-1 diagnostics in the past. This shows that the S-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.