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

TL;DR

This paper introduces a new wavefunction-based metric to estimate the deviation of truncated coupled cluster solutions from the exact FCI wavefunction, providing a practical reliability assessment tool.

Contribution

It proposes a novel, cost-effective diagnostic for quantifying the distance from the exact wavefunction, applicable to various wavefunction methods including CCSD.

Findings

The metric effectively distinguishes solutions far from the FCI wavefunction.

It is independent of common multireference diagnostics.

Application to CCSD shows reliable assessment on benchmark datasets.

Abstract

A new approach is proposed to assess the reliability of the truncated wavefunction methods by estimating the deviation from the full configuration interaction (FCI) wavefunction. 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 ($\tilde{d}_\Phi$, $\tilde{d}_\gamma$). We demonstrate the applicability of the approach for the CCSD method by benchmarking on the W4-17 dataset, as well as on transition metal-containing species. We also show that the presented moderate-cost, purely wavefunction-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 ($\tilde{d}_{\gamma,\mathrm{NO}}$) and its effect on the active space size and the metric. The proposed diagnostic can also be applied to other wavefunction approximations, and it has the potential to provide a quality measure for post-Hartree-Fock procedures in general.