A full-pivoting algorithm for the Cholesky decomposition of two-electron repulsion and spin-orbit coupling integrals

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Cholesky decomposition (CD) efficiently reduces computational cost for electronic repulsion integrals (ERI) in ab initio calculations.
• CD cannot be directly applied to two-electron spin-orbit coupling (2e-SOC) integrals due to their antisymmetric nature.

Purpose of the Study:

• To develop a computational strategy for Cholesky representation of the spatial part of 2e-SOC integrals.
• To propose a new efficient CD algorithm applicable to both ERI and 2e-SOC integrals.

Main Methods:

• A novel Cholesky decomposition algorithm utilizing extensive full-pivoting for univocal Cholesky basis definition.
• Implementation of the strategy within the ab initio program Computational Emulator of Rare Earth Systems (CERES).

Main Results:

• The proposed CD algorithm successfully generates Cholesky representations for the spatial part of 2e-SOC integrals.
• The new algorithm demonstrates improved computational performance for both ERI and 2e-SOC integral evaluations.
• Error analysis shows that 2δ is the upper limit for errors in reconstructed 2e-SOC integrals.

Conclusions:

• The developed computational strategy and CD algorithm offer an efficient approach for evaluating ERI and 2e-SOC integrals in quantum chemistry.
• This method enhances the computational feasibility of ab initio calculations involving spin-orbit coupling effects.
• The implementation in CERES validates the practical applicability and performance benefits of the proposed technique.