Tensor Approximation of Slater-Type Orbital Basis Functions
This paper deals with a tensor representation of the Slater-type orbital basis functions. Localized basis systems are primarily used in electronic structure calculations. A choice of the system is usually limited to Gaussian-type orbitals due to the impossibility of the analytical evaluation of nece...
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| Format: | Article |
| Language: | English |
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VSB-Technical University of Ostrava
2017-01-01
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| Series: | Advances in Electrical and Electronic Engineering |
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| Online Access: | http://advances.utc.sk/index.php/AEEE/article/view/2235 |
| _version_ | 1827947554400108544 |
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| author | Martin Mrovec |
| author_facet | Martin Mrovec |
| author_sort | Martin Mrovec |
| collection | DOAJ |
| description | This paper deals with a tensor representation of the Slater-type orbital basis functions. Localized basis systems are primarily used in electronic structure calculations. A choice of the system is usually limited to Gaussian-type orbitals due to the impossibility of the analytical evaluation of necessary integrals using other basis types. Unfortunately, it is not possible to use direct discretization techniques due to the dimensionality of the problem so the numerical integration is problematic. Tensor Numerical Methods overcome this problem by using special data representations, which are discussed. Finally, it is demonstrated how to use these methods to construct a tensor approximation of Slater-type orbital basis functions including an error estimate and its numerical verification. |
| first_indexed | 2024-04-09T12:40:36Z |
| format | Article |
| id | doaj.art-4784412dd30f47f7baa515b00b498a0f |
| institution | Directory Open Access Journal |
| issn | 1336-1376 1804-3119 |
| language | English |
| last_indexed | 2024-04-09T12:40:36Z |
| publishDate | 2017-01-01 |
| publisher | VSB-Technical University of Ostrava |
| record_format | Article |
| series | Advances in Electrical and Electronic Engineering |
| spelling | doaj.art-4784412dd30f47f7baa515b00b498a0f2023-05-14T20:50:11ZengVSB-Technical University of OstravaAdvances in Electrical and Electronic Engineering1336-13761804-31192017-01-0115231432110.15598/aeee.v15i2.2235901Tensor Approximation of Slater-Type Orbital Basis FunctionsMartin Mrovec0Department of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava 708 33, Czech Republic & IT4Innovations National Supercomputing Center, VSB-Technical University of Ostrava, Studentska 6231/1B, Ostrava 708 33, Czech RepublicThis paper deals with a tensor representation of the Slater-type orbital basis functions. Localized basis systems are primarily used in electronic structure calculations. A choice of the system is usually limited to Gaussian-type orbitals due to the impossibility of the analytical evaluation of necessary integrals using other basis types. Unfortunately, it is not possible to use direct discretization techniques due to the dimensionality of the problem so the numerical integration is problematic. Tensor Numerical Methods overcome this problem by using special data representations, which are discussed. Finally, it is demonstrated how to use these methods to construct a tensor approximation of Slater-type orbital basis functions including an error estimate and its numerical verification.http://advances.utc.sk/index.php/AEEE/article/view/2235electronic structuregaussian-type orbitalsinc approximationslater-type orbitaltensor numerical methods. |
| spellingShingle | Martin Mrovec Tensor Approximation of Slater-Type Orbital Basis Functions Advances in Electrical and Electronic Engineering electronic structure gaussian-type orbital sinc approximation slater-type orbital tensor numerical methods. |
| title | Tensor Approximation of Slater-Type Orbital Basis Functions |
| title_full | Tensor Approximation of Slater-Type Orbital Basis Functions |
| title_fullStr | Tensor Approximation of Slater-Type Orbital Basis Functions |
| title_full_unstemmed | Tensor Approximation of Slater-Type Orbital Basis Functions |
| title_short | Tensor Approximation of Slater-Type Orbital Basis Functions |
| title_sort | tensor approximation of slater type orbital basis functions |
| topic | electronic structure gaussian-type orbital sinc approximation slater-type orbital tensor numerical methods. |
| url | http://advances.utc.sk/index.php/AEEE/article/view/2235 |
| work_keys_str_mv | AT martinmrovec tensorapproximationofslatertypeorbitalbasisfunctions |