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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Coupled-cluster (CC) theory is a highly accurate quantum chemical method.
• The geometric interpretation of CC wave functions remains underexplored.
• Understanding wave function manifolds is crucial for assessing method accuracy.

Purpose of the Study:

• To interpret the high accuracy of coupled-cluster theory through a geometric lens.
• To compare the embedding of CC and configuration interaction (CI) wave functions.
• To provide insights into the limitations of CC methods for multireference systems.

Main Methods:

• Defining coupled-cluster and configuration interaction manifolds.
• Calculating distances between full-configuration interaction (FCI) wave functions and these manifolds.
• Decomposing distances by excitation rank.

Main Results:

• The FCI wave function is geometrically closer to the curved CC manifold than the flat CI manifold.
• Distance decomposition reveals insights into CC failures for multireference systems.
• A geometric perspective offers a new interpretation of CC method quality.

Conclusions:

• Geometric analysis provides a novel understanding of coupled-cluster accuracy beyond size extensivity.
• The curvature of the CC manifold is key to its high accuracy.
• Geometric descriptions offer a powerful tool for electronic structure theory development.