Exploring Ground and Excited States Via Single Reference Coupled-Cluster Theory and Algebraic Geometry

Area of Science:

• Computational quantum chemistry
• Algebraic geometry
• Theoretical chemistry

Background:

• Coupled cluster (CC) equations are fundamental in computational quantum chemistry.
• Understanding the root structure of CC equations is crucial for accurate chemical predictions.
• Previous studies have not fully explored the complete solution set of CC equations.

Purpose of the Study:

• To investigate the intricate root structures of coupled cluster (CCD and CCSD) equations.
• To compare computed CC roots against theoretical upper bounds for accuracy and efficiency.
• To assess the capability of single-reference CC methods in approximating excited state energies.

Main Methods:

• Utilized algebraic geometry techniques, including monodromy and parametric homotopy continuation.
• Calculated the full solution set of CC equations.
• Focused on dissociation processes of four-electron systems: (H2)2, H4, and lithium hydride.

Main Results:

• Computed CC roots were compared against established theoretical upper bounds.
• Multiple CC roots were found to accurately describe excited state energies.
• For systems like lithium hydride, CC methods approximated both excited state energies and the states themselves with high accuracy.

Conclusions:

• The study provides significant insights into the root structure of CC equations.
• CC methods demonstrate a strong capability in describing excited states accurately.
• This work enhances the understanding and application of CC theory in computational chemistry.