A correctly scaling rigorously spin-adapted and spin-complete open-shell CCSD implementation for arbitrary high-spin...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate electronic structure calculations are crucial for understanding molecular properties.
• Coupled Cluster Singles and Doubles (CCSD) is a powerful method but faces challenges with open-shell systems.
• Existing methods may struggle with spin purity and completeness for high-spin states.

Purpose of the Study:

• To develop a novel, correctly scaling coupled cluster singles and doubles (CCSD) implementation for arbitrary high-spin open-shell states.
• To ensure spin completeness and spin adaption (purity) of the coupled cluster wave function.
• To provide an efficient and accurate computational tool for studying open-shell molecular systems.

Main Methods:

• Developed a spin-free cluster operator using Löwdin-type operators.
• Implemented the method using second quantization and factorized tensor contractions.
• Utilized Wick's theorem and Goldstone diagrams for efficient calculation of spin integration prefactors.
• Identified and eliminated redundant diagrams via graph isomorphism.
• Translated non-redundant graphs into factorized tensor contractions.

Main Results:

• The spin-adapted and spin-complete (SASC) CCSD variant shows reasonable convergence for a Baker-Campbell-Hausdorff series truncation of order four.
• SASC-CCSD yields slightly improved correlation energies compared to spin orbital CCSD.
• Demonstrated accuracy with differences up to 1.292 mE_H for quintet CH₂.

Conclusions:

• The novel SASC-CCSD implementation is a significant advancement for high-spin open-shell electronic structure calculations.
• The method ensures spin purity and completeness, leading to more accurate results.
• This approach offers a promising direction for future computational chemistry studies of open-shell systems.