The $S$-diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods

Understand

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 $T_1$, $D_1$, and $D_2$ diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory.