Diagrammatic Simplification of Linearized Coupled Cluster Theory.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Linearized Coupled Cluster Doubles (LinCCD) struggles with static correlation in small-gap systems, often yielding near-singular energies.
• This divergence has been incorrectly attributed to missing quadratic T̂₂² terms, while the actual cause lies elsewhere.

Purpose of the Study:

• To identify the true cause of divergence in LinCCD methods for statically correlated systems.
• To propose a new, robust, and size-consistent theoretical approach for accurate quantum chemical calculations.

Main Methods:

• Analysis of exchange contributions in ring and crossed-ring contractions within LinCCD.
• Development of Linearized Ladder CCD (LinLCCD) by retaining only linear ladder diagrams.
• Implementation of a hole-hole approximation to achieve O(n⁴_occ n²_vir) scaling.

Main Results:

• Exchange contributions, not small denominators, cause LinCCD divergence.
• LinLCCD is shown to be robust in the presence of static correlation.
• LinLCCD and its approximation accurately capture energy differences, outperforming full CCD and CCSD for noncovalent interactions.

Conclusions:

• LinCCD and Configuration Interaction Doubles (CID) can be simplified to achieve size-consistency.
• LinLCCD provides a stable and accurate method for systems with static correlation.
• Further adaptations of LinLCCD can incorporate dynamical correlation for enhanced accuracy.