Efficient calculation of molecular integrals over London atomic orbitals

Irons, Tom J.P.; Zemen, Jan; Teale, Andrew M.

Abstract

The use of London atomic orbitals (LAOs) in a non-perturbative manner enables the determination of gauge-origin invariant energies and properties for molecular species in arbitrarily strong magnetic fields. Central to the efficient implementation of such calculations for molecular systems is the evaluation of molecular integrals, particularly the electron repulsion integrals (ERIs). We present an implementation of several different algorithms for the evaluation of ERIs over Gaussian-type LAOs at arbitrary magnetic field strengths. The efficiency of generalized McMurchie-Davidson (MD), Head-Gordon-Pople (HGP) and Rys quadrature schemes is compared. For the Rys quadrature implementation, we avoid the use of high precision arithmetic and interpolation schemes in the computation of the quadrature roots and weights, enabling the application of this algorithm seamlessly to a wide range of magnetic fields. The efficiency of each generalised algorithm is compared by numerical application, classifying the ERIs according to their total angular momenta and evaluating their performance for primitive and contracted basis sets. In common with zero-field integral evaluation, no single algorithm is optimal for all angular momenta thus a simple mixed scheme is put forward, which selects the most efficient approach to calculate the ERIs for each shell quartet. The mixed approach is significantly more efficient than the exclusive use of any individual algorithm.

Citation

Irons, T. J., Zemen, J., & Teale, A. M. (in press). Efficient calculation of molecular integrals over London atomic orbitals. Journal of Chemical Theory and Computation, https://doi.org/10.1021/acs.jctc.7b00540

• Journal Article Type: Article
• Acceptance Date: Jul 10, 2017
• Online Publication Date: Jul 10, 2017
• Deposit Date: Aug 4, 2017
• Publicly Available Date: Aug 4, 2017
• Journal: Journal of Chemical Theory and Computation
• Print ISSN: 1549-9618
• Electronic ISSN: 1549-9626
• Publisher: American Chemical Society
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1021/acs.jctc.7b00540
• Public URL: https://nottingham-repository.worktribe.com/output/872208
• Publisher URL: http://pubs.acs.org/doi/full/10.1021/acs.jctc.7b00540
• Contract Date: Aug 4, 2017