Degenerate coupled-cluster theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster (CC) theory is a powerful quantum chemistry method for calculating electronic structure.
• Existing methods face challenges with degenerate references, strong correlation, and convergence.
• Accurate computation of energies and wave functions is crucial for understanding chemical systems.

Purpose of the Study:

• Introduce a size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz.
• Develop a new multireference coupled-cluster theory for general model spaces (quasidegenerate coupled-cluster, QCC).
• Provide a unified framework for computing energies and wave functions from diverse references.

Main Methods:

• Developed a size-extensive, converging, black-box, ab initio ΔCC ansatz.
• Introduced quasidegenerate coupled-cluster (QCC) theory for strong correlation.
• Implemented determinant-based, general-order algorithms for ΔCC and QCC theories.
• Computer-synthesized algebraic, optimal-scaling algorithms for ΔCCS and ΔCCSD.

Main Results:

• ΔCC theory reduces to single-reference CC for nondegenerate cases and extends degenerate Møller-Plesset perturbation (ΔMP) theory.
• ΔCC functions as a coupled-cluster Green's function for ionized/electron-attached states, converging to full-configuration-interaction limits.
• QCC theory is exactly converging for strong correlation.
• Performance order: QCC ≈ ΔCC > EOM-CC > CI (same order) or QCC ≈ ΔCC > ΔMP > MBGF (same cost scaling).

Conclusions:

• The new ΔCC and QCC theories provide robust and accurate methods for electronic structure calculations.
• These methods offer advantages in convergence and applicability to diverse electronic states compared to existing theories.
• The developed algorithms enable efficient computation, with optimized scaling for practical applications.