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

Martin Mrovec

Applications of Mathematics (2017)

  • Volume: 62, Issue: 6, page 679-698
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Mrovec, Martin. "Low-rank tensor representation of Slater-type and Hydrogen-like orbitals." Applications of Mathematics 62.6 (2017): 679-698. <http://eudml.org/doc/294269>.

@article{Mrovec2017,
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.},
author = {Mrovec, Martin},
journal = {Applications of Mathematics},
keywords = {Slater-type orbital; Hydrogen-like orbital; Gaussian-type orbital; electronic structure; tensor numerical methods; sinc approximation},
language = {eng},
number = {6},
pages = {679-698},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Low-rank tensor representation of Slater-type and Hydrogen-like orbitals},
url = {http://eudml.org/doc/294269},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Mrovec, Martin
TI - Low-rank tensor representation of Slater-type and Hydrogen-like orbitals
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 6
SP - 679
EP - 698
AB - 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.
LA - eng
KW - Slater-type orbital; Hydrogen-like orbital; Gaussian-type orbital; electronic structure; tensor numerical methods; sinc approximation
UR - http://eudml.org/doc/294269
ER -

References

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  1. Abramowitz, M., Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards. A Wiley-Interscience Publication; John Willey, New York (1972). (1972) Zbl0543.33001MR0167642
  2. Chisholm, C. D. H., Group Theoretical Techniques in Quantum Chemistry, Academic Press, New York (1976). (1976) 
  3. Fang, G., 10.1006/jath.1996.0033, J. Approximation Theory 85 (1996), 115-131. (1996) Zbl0845.94003MR1385811DOI10.1006/jath.1996.0033
  4. Hehre, W. J., Stewart, R. F., Pople, J. A., 10.1063/1.1672392, J. Chem. Phys. 51 (1969), 2657-2664. (1969) DOI10.1063/1.1672392
  5. Khoromskaia, V., Khoromskij, B. N., 10.1039/C5CP01215E, Phys. Chem. Chem. Phys. 17 (2015), 31491-31509. (2015) DOI10.1039/C5CP01215E
  6. Khoromskaia, V., Khoromskij, B. N., Schneider, R., 10.1137/120884067, SIAM J. Sci. Comput. 35 (2013), A987--A1010. (2013) Zbl1266.65069MR3040965DOI10.1137/120884067
  7. Khoromskij, B. N., 10.2478/cmam-2006-0010, Comput. Methods Appl. Math. 6 (2006), 194-220. (2006) Zbl1120.65052MR2280939DOI10.2478/cmam-2006-0010
  8. Khoromskij, B. N., 10.1016/j.chemolab.2011.09.001, Chemometrics and Intelligent Laboratory System 110 (2012), 1-19. (2012) DOI10.1016/j.chemolab.2011.09.001
  9. Khoromskij, B. N., Khoromskaia, V., 10.2478/s11533-007-0018-0, Cent. Eur. J. Math. 5 (2007), 523-550. (2007) Zbl1130.65060MR2322828DOI10.2478/s11533-007-0018-0
  10. Khoromskij, B. N., Khoromskaia, V., 10.1137/080730408, SIAM J. Sci. Comput. 31 (2009), 3002-3026. (2009) Zbl1197.65215MR2520309DOI10.1137/080730408
  11. Lang, S., 10.1007/978-1-4757-2698-5, Undergraduate Texts in Mathematics, Springer, New York (1997). (1997) Zbl0962.46001MR1476913DOI10.1007/978-1-4757-2698-5
  12. Mrovec, M., 10.15598/aeee.v15i2.2235, Advances in Electrical and Electronic Engineering. (2017). (2017) DOI10.15598/aeee.v15i2.2235
  13. Saad, Y., Chelikowsky, J. R., Shontz, S. M., 10.1137/060651653, SIAM Rev. 52 (2010), 3-54. (2010) Zbl1185.82004MR2639608DOI10.1137/060651653
  14. Schiff, J. L., 10.1007/978-0-387-22757-3, Undergraduate Texts in Mathematics, Springer, New York (1999). (1999) Zbl0934.44001MR1716143DOI10.1007/978-0-387-22757-3
  15. Stenger, F., 10.1007/978-1-4612-2706-9, Springer Series in Computational Mathematics 20, Springer, New York (1993). (1993) Zbl0803.65141MR1226236DOI10.1007/978-1-4612-2706-9
  16. Stewart, R. F., 10.1063/1.1671406, J. Chem. Phys. 50 (1969), 2485-2495. (1969) DOI10.1063/1.1671406

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