Configuration weights in coupled-cluster theory

TL;DR

This paper introduces a new way to quantify the importance of Slater determinants in coupled-cluster wave functions, enabling detailed analysis and revealing insights into the method's basis and subsystem properties.

Contribution

It defines the weight of determinants in coupled-cluster theory and demonstrates its application across various formulations, improving wave-function analysis and addressing basis insensitivity issues.

Findings

Coupled-cluster weights agree with full configuration interaction for single-reference systems.

Weights reveal basis insensitivity of truncated coupled-cluster energies.

Extended and quadratic coupled-cluster theories improve weight behavior in noninteracting systems.

Abstract

We introduce a simple definition of the weight of any given Slater determinant in the coupled-cluster state, namely as the expectation value of the projection operator onto that determinant. The definition can be applied to any coupled-cluster formulation, including conventional coupled-cluster theory, perturbative coupled-cluster models, nonorthogonal orbital-optimized coupled-cluster theory, and extended coupled-cluster theory, allowing for wave-function analyses on par with configuration-interaction-based wave functions. Numerical experiments show that for single-reference systems the coupled-cluster weights are in excellent agreement with those obtained from the full configuration-interaction wave function. Moreover, the well-known insensitivity of the total energy obtained from truncated coupled-cluster models to the choice of orbital basis is clearly exposed by weights computed in the $\hat{T}_1$-transformed determinant basis. We demonstrate that the inseparability of the conventional linear parameterization of the bra (left state) for systems composed of noninteracting subsystems may lead to ill-behaved (negative or greater than unity) weights, an issue that can only be fully remedied by switching to extended coupled-cluster theory. The latter is corroborated by results obtained with quadratic coupled-cluster theory, which is shown numerically to yield a significant improvement.