Geometric interpretation for coupled-cluster theory. A comparison of accuracy with the corresponding configuration interaction model

Although coupled-cluster theory is well-known for its accuracy, the geometry associated with the manifold of wave functions reached by the coupled-cluster Ansatz has not been deeply explored. In this article, we look for an interpretation for the high accuracy of coupled-cluster theory based on how the manifold of coupled-cluster wave functions is embedded within the space of n-electron wave functions. We define the coupled-cluster and configuration interaction manifolds and measure the distances from the full-configuration interaction (FCI) wave function to these manifolds. We clearly observe that the FCI wave function is closer to the coupled-cluster manifold that is curved than to the configuration interaction manifold that is flat for the selected systems studied in this work. Furthermore, the decomposition of the distances among these manifolds and wave functions into excitation ranks gives insights into the failure of the coupled-cluster approach for multireference systems. The present results show a new interpretation for the quality of the coupled-cluster method, as contrasted to the truncated configuration interaction approach, besides the well-established argument based on size extensivity. Furthermore, we show how a geometric description of wave function methods can be used in electronic structure theory.

Automated summary

This article explores the accuracy of coupled-cluster theory by examining the geometry of the coupled-cluster wave function manifold within the space of n-electron wave functions. The findings suggest that the coupled-cluster manifold, which is curved, is closer to the full-configuration interaction (FCI) wave function than the flat configuration interaction manifold. The study also provides insights into the failure of the coupled-cluster approach for multireference systems.