Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Calculating molecular orbital electron repulsion integrals (MO-ERIs) from atomic orbital ERIs (AO-ERIs) is computationally intensive.
• This integral transformation is a significant bottleneck in second-order electron propagator calculations, especially for single-orbital studies.

Purpose of the Study:

• To develop and implement efficient algorithms for computing MO-ERIs.
• To address the computational bottlenecks in second-order electron propagator methods.

Main Methods:

• Combined asymmetric density fitting with modified Cholesky decomposition for efficient MO-ERI generation.
• Utilized partial contractions of three-center AO-ERIs, storing contractions in RAM instead of full AO-ERIs.
• Developed two implementations: an in-core version and a semidirect version to handle memory limitations.

Main Results:

• The proposed methods are fast and numerically stable.
• Modified Cholesky factorization effectively controlled ill-conditioning issues in density fitting.
• The in-core implementation is competitive for medium to large basis sets; the semidirect version shows memory independence.

Conclusions:

• The developed algorithms provide an efficient and stable approach for MO-ERI computation.
• These methods significantly improve the performance of second-order electron propagator calculations.
• The approach is applicable to relatively large molecular systems.