-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 -diagnostic. We provide a derivation of the -diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the -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], [Cu(NH)], and [Cu(HO)]. Throughout the numerical investigations, the -diagnostic is compared to other SRCC diagnostic procedures, that is, the , , max , and diagnostics as well as different indices of multideterminantal and multireference character in coupled-cluster theory. Our numerical investigations show that the -diagnostic outperforms the , , max and 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 -diagnostic for geometry optimizations using SRCC reveal that the -diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the -diagnostic for electronic correlation simulations show that the -diagnostic correctly predicts strong multireference regimes. The -diagnostic, moreover, correctly detects the successful SRCC computations for [CuCl], [Cu(NH)], and [Cu(HO)], which have been known to be misdiagnosed by and diagnostics in the past. This shows that the -diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.