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

Area of Science:

• Quantum Chemistry
• Computational Chemistry

Background:

• Truncated wave function methods are widely used but their accuracy is difficult to assess.
• Existing diagnostics often compare derived properties rather than the wave function itself.

Purpose of the Study:

• To develop a novel method for evaluating the reliability of truncated wave function approximations.
• To quantify the deviation of approximate solutions from the exact full configuration interaction (FCI) wave function.

Main Methods:

• Utilized the density matrix renormalization group (DMRG) to obtain an approximate FCI solution.
• Introduced new metrics (d̃Φ, d̃γ) based on comparing low-level CI expansions and one-body reduced density matrices.
• Benchmarked the approach using the CCSD method on the W4-17 dataset and transition-metal compounds.

Main Results:

• Demonstrated the applicability of the new diagnostic for the CCSD method.
• Showcased that the proposed metric is cost-effective, wave function-based, and independent of existing multireference measures.
• Explored the impact of CCSD natural orbitals on the metric and active space size.

Conclusions:

• The developed metric provides a unique and practical way to assess the quality of wave function approximations.
• This diagnostic tool has broad applicability to various post-Hartree-Fock methods.
• It offers a potential quality measure for computational chemistry calculations.