Efficient calculation of molecular integrals over London atomic orbitals
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 eva...
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| Format: | Article |
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American Chemical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/44646/ |
| _version_ | 1848796964675649536 |
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| author | Irons, Tom J.P. Zemen, Jan Teale, Andrew M. |
| author_facet | Irons, Tom J.P. Zemen, Jan Teale, Andrew M. |
| author_sort | Irons, Tom J.P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:56:21Z |
| format | Article |
| id | nottingham-44646 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:56:21Z |
| publishDate | 2017 |
| publisher | American Chemical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-446462020-05-04T18:55:03Z https://eprints.nottingham.ac.uk/44646/ Efficient calculation of molecular integrals over London atomic orbitals Irons, Tom J.P. Zemen, Jan Teale, Andrew M. 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. American Chemical Society 2017-07-10 Article PeerReviewed Irons, Tom J.P., Zemen, Jan and Teale, Andrew M. (2017) Efficient calculation of molecular integrals over London atomic orbitals. Journal of Chemical Theory and Computation . ISSN 1549-9626 http://pubs.acs.org/doi/full/10.1021/acs.jctc.7b00540 doi:10.1021/acs.jctc.7b00540 doi:10.1021/acs.jctc.7b00540 |
| spellingShingle | Irons, Tom J.P. Zemen, Jan Teale, Andrew M. Efficient calculation of molecular integrals over London atomic orbitals |
| title | Efficient calculation of molecular integrals over London atomic orbitals |
| title_full | Efficient calculation of molecular integrals over London atomic orbitals |
| title_fullStr | Efficient calculation of molecular integrals over London atomic orbitals |
| title_full_unstemmed | Efficient calculation of molecular integrals over London atomic orbitals |
| title_short | Efficient calculation of molecular integrals over London atomic orbitals |
| title_sort | efficient calculation of molecular integrals over london atomic orbitals |
| url | https://eprints.nottingham.ac.uk/44646/ https://eprints.nottingham.ac.uk/44646/ https://eprints.nottingham.ac.uk/44646/ |