A new mixed self-consistent field procedure

† Dedicated to Sourav Pal on the occasion of his 60th birthday.

Abstract

A new approach for the calculation of three-centre electronic repulsion integrals (ERIs) is developed, implemented and benchmarked in the framework of auxiliary density functional theory (ADFT). The so-called mixed self-consistent field (mixed SCF) divides the computationally costly ERIs in two sets: far-field and near-field. Far-field ERIs are calculated using the newly developed double asymptotic expansion as in the direct SCF scheme. Near-field ERIs are calculated only once prior to the SCF procedure and stored in memory, as in the conventional SCF scheme. Hence the name, mixed SCF. The implementation is particularly powerful when used in parallel architectures, since all RAM available are used for near-field ERI storage. In addition, the efficient distribution algorithm performs minimal intercommunication operations between processors, avoiding a potential bottleneck. One-, two- and three-dimensional systems are used for benchmarking, showing substantial time reduction in the ERI calculation for all of them. A Born–Oppenheimer molecular dynamics calculation for the Na⁺₅₅ cluster is also shown in order to demonstrate the speed-up for small systems achievable with the mixed SCF.

Keywords:

• asymptotic expansion
• density functional theory
• electronic repulsion integrals
• parallel calculations
• self-consistent field

Acknowledgements

This work was supported by the CONACYT project CB-179409. High-performance computing resources have been provided by Compute Canada/Westgrid and CINVESTAV.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

† Dedicated to Sourav Pal on the occasion of his 60th birthday.