An efficient algorithm for Cholesky decomposition of electron repulsion integrals

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Approximating electron repulsion integrals is crucial for reducing computational cost in electronic structure calculations.
• Inner projection methods are established techniques for integral approximation.
• Efficient algorithms are needed for large-scale quantum chemistry simulations.

Purpose of the Study:

• To present a novel two-step Cholesky decomposition algorithm for approximating electron repulsion integrals.
• To improve screening efficiency and reduce memory usage and computational cost.
• To extend the applicability of inner projection methods to larger systems and multilevel approaches.

Main Methods:

• A two-step Cholesky decomposition algorithm determining only the Cholesky basis pivots.
• Construction of Cholesky vectors using the inner projection formulation.
• A partitioned decomposition approach using a reduced Cholesky basis from diagonal blocks.

Main Results:

• The algorithm significantly reduces memory usage and computational cost through improved screening.
• The partitioned decomposition extends the methodology's application range, suitable for multilevel methods.
• The approach was successfully applied to systems with up to 80,000 atomic orbitals.
• Accuracy was demonstrated for a formaldehyde-water system with a new Cholesky-based CCSD implementation.

Conclusions:

• The developed two-step Cholesky decomposition offers a computationally efficient and memory-saving approach for integral approximation.
• The partitioned decomposition enhances the versatility of inner projection methods for large-scale electronic structure calculations.
• This method provides accurate integral approximations, validated by its application in a Cholesky-based CCSD implementation.