The Direct-Product Decomposition Approach for Symmetry Exploitation in Many-Body Methods in Case of Non-Abelian Point...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster (CC) calculations are vital for accurate molecular electronic structure.
• Symmetry adaptation in CC calculations can significantly reduce computational cost.
• Existing methods primarily focus on Abelian point groups, limiting applications.

Purpose of the Study:

• To extend the direct-product decomposition scheme for symmetry treatment in CC calculations to non-Abelian point groups.
• To develop a strategy for efficiently handling integrals and amplitudes using both reduced and nonreduced representations.
• To demonstrate the computational savings achievable by exploiting non-Abelian symmetry in CC methods.

Main Methods:

• Developed a direct-product decomposition scheme applicable to non-Abelian point groups.
• Introduced a hybrid strategy using both reduced and nonreduced representations for integrals and amplitudes.
• Implemented and tested the CC singles and doubles (CCSD) method with non-Abelian symmetry.

Main Results:

• Achieved a block structure for two-electron integrals and CC amplitudes by resolving reducible products into irreducible representations.
• Demonstrated significant computational savings (over 20% compared to no symmetry, ~5% compared to C_s symmetry) in CCSD calculations for NH₃ and PH₃.
• Confirmed the feasibility and efficiency of the proposed strategy for exploiting non-Abelian symmetry.

Conclusions:

• The direct-product decomposition scheme can be effectively extended to non-Abelian point groups for CC calculations.
• The hybrid representation strategy efficiently manages computational steps, leading to substantial cost reductions.
• Exploiting non-Abelian symmetry is crucial for enabling accurate CC computations on large, highly symmetric molecules.