Applications of Mathematics, Vol. 62, No. 6, pp. 679-698, 2017


Low-rank tensor representation of Slater-type and Hydrogen-like orbitals

Martin Mrovec

Received June 30, 2017.   First published December 5, 2017.

Abstract:  The paper focuses on a low-rank tensor structured representation of Slater-type and Hydrogen-like orbital basis functions that can be used in electronic structure calculations. Standard packages use the Gaussian-type basis functions which allow us to analytically evaluate the necessary integrals. Slater-type and Hydrogen-like orbital functions are physically more appropriate, but they are not analytically integrable. A numerical integration is too expensive when using the standard discretization techniques due the dimensionality of the problem. However, it can be effectively performed using the tensor representation of basis functions. Furthermore, this approach can take advantage of parallel computing.
Keywords:  Slater-type orbital; Hydrogen-like orbital; Gaussian-type orbital; electronic structure; tensor numerical methods; sinc approximation
Classification MSC:  15A69, 30E20, 33B15, 33C45, 33C55, 33F05, 41A05, 44A10, 65Z05, 81Q05
DOI:  10.21136/AM.2017.0177-17


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Affiliations:   Martin Mrovec, Department of Applied Mathematics & IT4Innovations - National Supercomputing Center, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic, e-mail: martin.mrovec@vsb.cz


 
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