Configuration Weights in Coupled-Cluster Theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster (CC) theory is a powerful quantum chemistry method for electronic structure calculations.
• Analyzing the weight of Slater determinants within CC wave functions is crucial for understanding electron correlation.
• Existing methods for determinant weighting in CC theory have limitations, especially for complex systems.

Purpose of the Study:

• To introduce a universally applicable definition for the weight of Slater determinants in coupled-cluster states.
• To enable wave function analysis in various coupled-cluster formulations comparable to configuration-interaction methods.
• To investigate the behavior and implications of these weights, particularly concerning orbital basis sets and subsystem interactions.

Main Methods:

• Definition of determinant weight as the expectation value of a projection operator.
• Application across diverse CC formalisms: conventional, perturbative, nonorthogonal orbital-optimized, and extended CC.
• Numerical experiments on single-reference systems and systems with noninteracting subsystems.
• Comparison with full configuration-interaction (FCI) wave functions and analysis in different determinant bases.

Main Results:

• The proposed CC weights show excellent agreement with FCI weights for single-reference systems.
• Orbital basis set insensitivity of truncated CC energies is reflected in the computed determinant weights.
• Conventional CC parametrization can lead to unphysical weights for noninteracting subsystems.
• Extended CC theory and quadratic CC theory demonstrate significant improvements in handling such systems.

Conclusions:

• The introduced definition provides a robust tool for wave function analysis in a wide range of CC theories.
• Extended CC theory is essential for accurately describing systems with noninteracting subsystems and avoiding ill-behaved weights.
• Quadratic CC theory offers a promising avenue for improved accuracy and reliability in determinant weighting and wave function analysis.