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 [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 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 multideterminantal 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 [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 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.