Speeding up density fitting Hartree–Fock calculations with multipole approximations

Abstract

The multipole approximation is utilised for reducing the computational expenses of the exchange contribution in density fitting Hartree–Fock (DF-HF) calculations. Strategies for approximating the relevant three-centre Coulomb integrals with the multipole expansion are discussed. Based on the factorised form of the integrals, an algorithm is proposed for the evaluation of the exchange term for both conventional and local DF-HF methods. The accuracy of the resulting energies, the numerical stability of the algorithm, and the speedups achieved are benchmarked with respect to the order of the multipole expansion for various molecular systems. Our results suggest that computation times for a conventional DF-HF calculation can be reduced roughly by a factor of 1.5 for molecules of a couple of hundreds of atoms without any loss of accuracy, while the speedups are somewhat more moderate if local density fitting approximations are also deployed.

GRAPHICAL ABSTRACT

Keywords:

• Density fitting
• Hartree–Fock
• exchange
• multipole approximation

Acknowledgments

This paper is dedicated to Professor Jürgen Gauss on the happy occasion of his 60th birthday. MK wishes to express his gratitude to Jürgen for the fruitful scientific collaborations, continuous support, and friendship.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are grateful for the financial support from the National Research, Development, and Innovation Office (NKFIH, Grant No. KKP126451). This work was also supported by the BME-Biotechnology FIKP grant of EMMI (BME FIKP-BIO). The computing time granted on the Hungarian HPC Infrastructure at NIIF Institute, Hungary, is gratefully acknowledged.