Assessing the Reliability of Truncated Coupled Cluster Wave Function: Estimating the Distance from the Exact Solution

A new approach is proposed to assess the reliability
of the truncated
wave function methods by estimating the deviation from the full configuration
interaction (FCI) wave function. While typical multireference diagnostics
compare some derived property of the solution with the ideal picture
of a single determinant, we try to answer a more practical question:
how far is the solution from the exact one. Using the density matrix
renormalization group (DMRG) method to provide an approximate FCI
solution for the self-consistently determined relevant active space,
we compare the low-level CI expansions and one-body reduced density
matrixes to determine the distance of the two solutions (d̃Φ, d̃γ).
We demonstrate the applicability of the approach for the CCSD method
by benchmarking on the W4–17 data set, as well as on transition-metal-containing
species. We also show that the presented moderate-cost, purely wave
function-based metric is truly unique in the sense that it does not
correlate with any popular multireference measures. We also explored
the usage of CCSD natural orbitals (d̃γ,NO) and its effect on the active space size and the
metric. The proposed diagnostic can also be applied to other wave
function approximations, and it has the potential to provide a quality
measure for post-Hartree–Fock procedures in general.