Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms

Salah Badawi Doma; Nazih Abdelhamid Elnohy; Mahmoud Ahmed Salem

doi:doi:10.11648/j.ijhep.20190602.13

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Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem

Published in International Journal of High Energy Physics (Volume 6, Issue 2)

Received: 7 November 2019 Accepted: 28 November 2019 Published: 24 December 2019

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Abstract

The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li⁺, and Be²⁺ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.

Published in	International Journal of High Energy Physics (Volume 6, Issue 2)
DOI	10.11648/j.ijhep.20190602.13
Page(s)	42-53
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Variational Monte Carlo Method, Correlation Functions, Helium Like Ions, Helium Excited States, Confined Helium, Strong Magnetic Field

References

[1]	J. E. Lynn, I. Tews, S. Gandolfi, and A. Lovato, “Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances,” Annu. Rev. Nucl. Part. Sci., 2019.
[2]	N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys., vol. 21, no. 6, pp. 1087–1092, 1953.
[3]	U. Kleinekathöfer, S. H. Patil, K. T. Tang, and J. P. Toennies, “Boundary-condition-determined wave function for the ground state of helium and isoelectronic ions,” Phys. Rev. A - At. Mol. Opt. Phys., 1996.
[4]	H. Nakashima and H. Nakatsuji, “Solving the electron-nuclear Schrödinger equation of helium atom and its isoelectronic ions with the free iterative-complement-interaction method,” J. Chem. Phys., 2008.
[5]	C. Le Sech, “Accurate analytic wavefunctions for two-electron atoms,” J. Phys. B At. Mol. Opt. Phys., 1997.
[6]	D. Bressanini and G. Morosi, “A compact boundary-condition- determined wavefunction for two-electron atomic systems,” J. Phys. B At. Mol. Opt. Phys., 2008.
[7]	R. S. Chauhan and M. K. Harbola, “Improved le Sech wavefunctions for two-electron atomic systems,” Chem. Phys. Lett., 2015.
[8]	A. J. Thakkar and T. Koga, “Variational calculations for helium-like ions using generalized Kinoshita-type expansions,” Theor. Chem. Acc., 2003.
[9]	R. Habrovský, “An explicitly correlated helium wave function in hyperspherical coordinates,” Chem. Phys. Lett., 2018.
[10]	E. G. Drukarev, M. Y. Amusia, E. Z. Liverts, R. Krivec, and V. B. Mandelzweig, “Wavefunctions of helium-like systems in limiting regions,” J. Exp. Theor. Phys., 2006.
[11]	A. W. King, A. L. Baskerville, and H. Cox, “Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 2018.
[12]	H. E. Montgomery, J. Katriel, and K. D. Sen, “Asymptotic behavior of two-electron expectation values in two-electron excited states,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 383, no. 36, p. 126007, 2019.
[13]	J. Li, N. D. Drummond, P. Schuck, and V. Olevano, “Comparing many-body approaches against the helium atom exact solution,” SciPost Phys., vol. 6, no. 4, pp. 1–37, 2019.
[14]	M. Mostafanejad, “Structure of free complement wavefunction for the ground and the first excited state of helium atom,” J. Theor. Comput. Chem., vol. 16, no. 6, pp. 1–14, 2017.
[15]	A. Flores-Riveros and A. Rodríguez-Contreras, “Compression effects in helium-like atoms (Z = 1,..., 5) constrained by hard spherical walls,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 372, no. 40, pp. 6175–6182, 2008.
[16]	X. Wen-Fang, “A Study of Confined Helium Atom,” Commun. Theor. Phys., 2007.
[17]	C. Laughlin and S. I. Chu, “A highly accurate study of a helium atom under pressure,” J. Phys. A Math. Theor., 2009.
[18]	H. E. Montgomery, N. Aquino, and A. Flores-Riveros, “The ground state energy of a helium atom under strong confinement,” Phys. Lett. Sect. A Gen. At. Solid State Phys., 2010.
[19]	M. Rodriguez-Bautista, C. Díaz-García, A. M. Navarrete-López, R. Vargas, and J. Garza, “Roothaan’s approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior,” J. Chem. Phys., vol. 143, no. 3, 2015.
[20]	M. Rodriguez-Bautista, R. Vargas, N. Aquino, and J. Garza, “Electron-density delocalization in many-electron atoms confined by penetrable walls: A Hartree–Fock study,” Int. J. Quantum Chem., vol. 118, no. 13, pp. 1–11, 2018.
[21]	T. D. Young, R. Vargas, and J. Garza, “A Hartree-Fock study of the confined helium atom: Local and global basis set approaches,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 380, no. 5–6, pp. 712–717, 2016.
[22]	E. Ley Koo, “Recent Progress in Confined Atoms and Molecules: Superintegrability and Symmetry Breakings,” Rev. Mex. Física, vol. 64, no. 4, p. 326, 2018.
[23]	J. Katriel, H. E. Montgomery, A. Sarsa, and E. Buendía, “Hund’s rule in open-shell states of two-electron systems: From free through confined and screened atoms, to quantum dots,” Nanosyst. Physics, Chem. Math., vol. 10, no. 1, pp. 31–41, 2019.
[24]	Á. Luzón, E. Buendía, and F. J. Gálvez, “One and two body densities for excited states of the helium confined atom,” Int. J. Quantum Chem., no. August, pp. 1–12, 2019.
[25]	R. Vargas, “Shannon Entropy for the Hydrogen Atom Confined by Four Different Potentials,” pp. 208–218, 2019.
[26]	X. Wang, J. Zhao, and H. Qiao, “Helium atom in strong magnetic fields: An application of the configuration-interaction method with Hylleraas-Gaussian basis,” Phys. Rev. A - At. Mol. Opt. Phys., 2009.
[27]	S. Boblest, C. Schimeczek, and G. Wunner, “Ground states of helium to neon and their ions in strong magnetic fields,” Phys. Rev. A - At. Mol. Opt. Phys., 2014.
[28]	W. Zhu and S. B. Trickey, “Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields,” J. Chem. Phys., vol. 147, no. 24, 2017.
[29]	A. Zafar, E. Martin, and S. Shannon, “High resolution magnetic field measurements in hydrogen and helium plasmas using active laser spectroscopy,” Rev. Sci. Instrum., vol. 89, no. 10, pp. 1–5, 2018.
[30]	S. B. Doma, M. O. Shaker, A. M. Farag, and F. N. El-Gammal, “Ground states of helium atom and hydrogen negative ion in the presence of magnetic field using variational Monte Carlo technique,” Acta Phys. Pol. A, 2014.
[31]	S. B. Doma and F. N. El-Gammal, “Application of variational Monte Carlo method to the confined helium atom,” J. Theor. Appl. Phys., 2012.
[32]	S. Doma, M. Shaker, A. Farag, and F. El-Gammal, “Excited states of helium atom in a strong magnetic field using variational Monte Carlo technique,” Indian J. Phys., 2018.
[33]	S. B. Doma, M. O. Shaker, A. M. Farag, and F. N. El-Gammal, “Variational Monte Carlo calculations of lithium atom in strong magnetic field,” J. Exp. Theor. Phys., 2017.
[34]	S. B. Doma and F. N. El-Gammal, “Atomic properties of the two-electron system using variational Monte Carlo technique,” Acta Phys. Pol. A, 2012.
[35]	T. M. Whitehead, M. H. Michael, and G. J. Conduit, “Jastrow correlation factor for periodic systems,” Phys. Rev. B, 2016.
[36]	J. O. Hirschfelder, “Removal of electron-electron poles from many-electron hamiltonians,” J. Chem. Phys., 1963.
[37]	A. Banerjee, C. Kamal, and A. Chowdhury, “Calculation of ground- and excited-state energies of confined helium atom,” Phys. Lett. Sect. A Gen. At. Solid State Phys., 2006.
[38]	J. L. Marin and S. A. Cruz, “Enclosed quantum systems: Use of the direct variational method,” J. Phys. B At. Mol. Opt. Phys., 1991.
[39]	E. V. Ludeña and M. Gregori, “Configuration interaction calculations for two-electron atoms in a spherical box,” J. Chem. Phys., 1979.
[40]	X. Wang and H. Qiao, “Configuration-interaction method with Hylleraas-Gaussian-type basis functions in cylindrical coordinates: Helium atom in a strong magnetic field,” Phys. Rev. A - At. Mol. Opt. Phys., 2008.

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APA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. (2019). Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. International Journal of High Energy Physics, 6(2), 42-53. https://doi.org/10.11648/j.ijhep.20190602.13

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ACS Style

Salah Badawi Doma; Nazih Abdelhamid Elnohy; Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int. J. High Energy Phys. 2019, 6(2), 42-53. doi: 10.11648/j.ijhep.20190602.13

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AMA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int J High Energy Phys. 2019;6(2):42-53. doi: 10.11648/j.ijhep.20190602.13

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@article{10.11648/j.ijhep.20190602.13,
  author = {Salah Badawi Doma and Nazih Abdelhamid Elnohy and Mahmoud Ahmed Salem},
  title = {Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms},
  journal = {International Journal of High Energy Physics},
  volume = {6},
  number = {2},
  pages = {42-53},
  doi = {10.11648/j.ijhep.20190602.13},
  url = {https://doi.org/10.11648/j.ijhep.20190602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20190602.13},
  abstract = {The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.},
 year = {2019}
}

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TY  - JOUR
T1  - Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms
AU  - Salah Badawi Doma
AU  - Nazih Abdelhamid Elnohy
AU  - Mahmoud Ahmed Salem
Y1  - 2019/12/24
PY  - 2019
N1  - https://doi.org/10.11648/j.ijhep.20190602.13
DO  - 10.11648/j.ijhep.20190602.13
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 42
EP  - 53
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20190602.13
AB  - The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.
VL  - 6
IS  - 2
ER  -

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Author Information

Salah Badawi Doma

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Nazih Abdelhamid Elnohy

Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt
Mahmoud Ahmed Salem

Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt

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APA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. (2019). Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. International Journal of High Energy Physics, 6(2), 42-53. https://doi.org/10.11648/j.ijhep.20190602.13

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ACS Style

Salah Badawi Doma; Nazih Abdelhamid Elnohy; Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int. J. High Energy Phys. 2019, 6(2), 42-53. doi: 10.11648/j.ijhep.20190602.13

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AMA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int J High Energy Phys. 2019;6(2):42-53. doi: 10.11648/j.ijhep.20190602.13

Copy | Download

@article{10.11648/j.ijhep.20190602.13,
  author = {Salah Badawi Doma and Nazih Abdelhamid Elnohy and Mahmoud Ahmed Salem},
  title = {Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms},
  journal = {International Journal of High Energy Physics},
  volume = {6},
  number = {2},
  pages = {42-53},
  doi = {10.11648/j.ijhep.20190602.13},
  url = {https://doi.org/10.11648/j.ijhep.20190602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20190602.13},
  abstract = {The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms
AU  - Salah Badawi Doma
AU  - Nazih Abdelhamid Elnohy
AU  - Mahmoud Ahmed Salem
Y1  - 2019/12/24
PY  - 2019
N1  - https://doi.org/10.11648/j.ijhep.20190602.13
DO  - 10.11648/j.ijhep.20190602.13
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 42
EP  - 53
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20190602.13
AB  - The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.
VL  - 6
IS  - 2
ER  -

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