Abstract
The aim of the paper is to compare the convergence of chosen numerical methods, namely the Direct Inversion of the Iterative Subspace and the Inexact Restoration Method, for solving the nonlinear eigenvalue problem occurring in the electronic structure calculations. We have selected the Hartree-Fock approximation where the behavior of the energy functional is known. The numerical experiments are performed on the modeling of the potential curve of the Hydrogen fluoride molecule. The results will be used as a clue for the development of optimization methods in the area of the Density Functional Theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
\(a_0\) is Bohr radius (\(1 \ a_0 = 5.2917721067\times 10^{-11}\) m). As an energy unit we use the Hartree energy (\(1 \ E_h = 4.359744650\times 10^{-18}\) J). These units are commonly used in the quantum chemistry.
References
Pan, Y., Lin, Y.: Influence of re concentration on the mechanical properties of tungsten borides from first-principles calculations. JOM 69(10), 2009–2013 (2017). https://doi.org/10.1007/s11837-017-2483-7. ISSN 1047-4838
Saad, Y., Chelikowsky, J.R., Shontz, S.M.: Numerical methods for electronic structure calculations of materials. SIAM Rev. (2010). https://doi.org/10.1137/060651653. ISSN 0036-1445, Zbl 1185.82004
Khoromskaia, V., Khoromskij, B.N., Schneider, R.: Tensor-structured factorized calculation of two-electron integrals in a general basis. SIAM J. Sci. Comput. 35(2), A987–A1010 (2013). https://doi.org/10.1137/120884067. ISSN 1064-8275, Zbl 1266.65069
Mrovec, M.: Tensor approximation of slater-type orbital basis functions. Adv. Electr. Electron. Eng. 15(2) (2017). https://doi.org/10.15598/aeee.v15i2.2235, http://advances.utc.sk/index.php/AEEE/article/view/2235. ISSN 1804-3119
Mrovec, M.: Low-rank tensor representation of Slater-type and Hydrogen-like orbitals. Appl. Math. 62(6), 679–698 (2017). https://doi.org/10.21136/AM.2017.0177-17, http://articles.math.cas.cz/10.21136/AM.2017.0177-17
Pulay, P.: Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73(2), 393–398 (1980)
Hu, W., Lin, L., Yang, C.: Projected commutator DIIS method for accelerating hybrid functional electronic structure calculations. J. Chem. Theory Comput. 13(11), 5458–5467 (2017). https://doi.org/10.1021/acs.jctc.7b00892. ISSN 1549-9618
Pratapa, P.P., Suryanarayana, P.: Restarted Pulay mixing for efficient and robust acceleration of fixed-point iterations. Chem. Phys. Lett. 635, 69–74 (2015). https://doi.org/10.1016/j.cplett.2015.06.029. ISSN 00092614
Kudin, K.N., Scuseria, G.E., Cances, E.: A black-box self-consistent field convergence algorithm: one step closer. J. Chem. Phys. 116(19), 8255 (2002). https://doi.org/10.1063/1.1470195. ISSN 00219606
Francisco, J.B., Martínez, J.M., Martínez, L.: Globally convergent trust-region methods for self-consistent field electronic structure calculations. J. Chem. Phys. 121(22), 10863 (2004). https://doi.org/10.1063/1.1814935. ISSN 00219606
Martínez, J.M., Martínez, L., Pisnitchenko, F.: Inexact restoration method for minimization problems arising in electronic structure calculations. Comput. Optim. Appl. 50(3), 555–590 (2011)
Dai, X., Liu, Z., Zhang, L., Zhou, A.: A conjugate gradient method for electronic structure calculations. SIAM J. Sci. Comput. 39(6), A2702–A2740 (2017). https://doi.org/10.1137/16M1072929. ISSN 1064-8275
Hehre, W.J., Ditchfield, R., Pople, J.A.: Self-consistent molecular orbital methods. XII. Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Physi. 56(5), 2257–2261 (1972). https://doi.org/10.1063/1.1677527. ISSN 0021-9606
Dill, J.D., Pople, J.A.: Self-consistent molecular orbital methods. XV. Extended Gaussian-type basis sets for lithium, beryllium, and boron. J. Chem. Phys. 62(7), 2921–2923 (1975). https://doi.org/10.1063/1.430801. ISSN 0021-9606
Acknowledgements
This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPS II) project IT4Innovations excellence in science - LQ1602, by Grant of SGS No. SP2018/165 and SP2018/178, VŠB - Technical University of Ostrava, Czech Republic. An important support has been provided by project OPEN-10-35 within the Open Access Call announced by IT4Innovations which enabled us to use the supercomputing services.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Mrovec, M. (2020). Convergence Study of Different Approaches of Solving the Hartree-Fock Equation on the Potential Curve of the Hydrogen Fluoride. In: Zelinka, I., Brandstetter, P., Trong Dao, T., Hoang Duy, V., Kim, S. (eds) AETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2018. Lecture Notes in Electrical Engineering, vol 554. Springer, Cham. https://doi.org/10.1007/978-3-030-14907-9_45
Download citation
DOI: https://doi.org/10.1007/978-3-030-14907-9_45
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-14906-2
Online ISBN: 978-3-030-14907-9
eBook Packages: EngineeringEngineering (R0)