Abstract
The paper focuses on a low-rank tensor structured representation of Slatertype 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.
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This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science—LQ1602”, by Grants of SGS Nos. SP2017/122 and SP2017/168, VŠB—Technical University of Ostrava, Czech Republic.
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Mrovec, M. Low-rank tensor representation of Slater-type and Hydrogen-like orbitals. Appl Math 62, 679–698 (2017). https://doi.org/10.21136/AM.2017.0177-17
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DOI: https://doi.org/10.21136/AM.2017.0177-17
Keywords
- Slater-type orbital
- Hydrogen-like orbital
- Gaussian-type orbital
- electronic structure
- tensor numerical methods
- sinc approximation