Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate computation of exact exchange is crucial for Hartree-Fock (HF) and hybrid density functional theory (DFT) models.
• Traditional methods for calculating exact exchange contributions are computationally expensive, limiting their application to large systems.

Purpose of the Study:

• To present an efficient algorithm for computing exact exchange contributions in HF and hybrid DFT.
• To leverage the fast multipole method (FMM) for enhanced computational efficiency.

Main Methods:

• The algorithm utilizes the fast multipole method (FMM) with hierarchical boxes.
• It exploits the constraint that at least one index of the exchange matrix must be an occupied orbital for efficient FMM application.
• The method was benchmarked on various molecular systems, including alkane chains, graphene, water clusters, and the Crambin protein.

Main Results:

• The developed FMM-based algorithm demonstrates significant efficiency in computing exact exchange.
• For the Crambin protein, the far-field exchange evaluation cost was approximately 3% of a self-consistent field iteration using multipoles up to rank 2.
• Benchmarks on diverse systems confirm the algorithm's scalability and applicability.

Conclusions:

• The FMM-based approach provides an efficient solution for calculating exact exchange in electronic structure calculations.
• This method enables accurate HF and hybrid DFT calculations for larger and more complex molecular systems.
• The reduced computational cost opens new possibilities for high-accuracy theoretical studies in chemistry and materials science.