Ground States of Few Electron Atoms in a Strong Magnetic Field Using Diffusion Monte Carlo Method

S.B. Doma¹ , N.A. El-Nohy² , M.A. Salem³

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.1 , pp.1-7, Feb-2020

CrossRef-DOI:   https://doi.org/10.26438/ijsrpas/v8i1.17

Online published on Feb 28, 2020

Copyright © S.B. Doma, N.A. El-Nohy, M.A. Salem . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

390 Views    291 Downloads    85 Downloads

Abstract :
We applied the diffusion quantum Monte Carlo method to investigate the effect of a strong magnetic field on the few-electron atoms. Gaussian type orbital basis sets are used in the computations developed by using Post-Hartree-Fock methods. We calculated the ground state energy eigenvalues of the helium, lithium, beryllium, and boron atoms. The advantages of adding the electrons correlations to the wave function in the technique of diffusion Monte Carlo method enabled us to solve the Schrödinger equation for these atoms in the external magnetic field for different strengths. The method showed good agreements with the previous results.

Key-Words / Index Term :
Diffusion Monte Carlo method, Few electron atoms, Strong magnetic field

References :
[1] L. K. Wagner, “First-Principles Quantum Monte Carlo,” in Encyclopedia of Nanotechnology, Springer, Dordrecht, pp. 1217 - 1223, 2016.
[2] Xiaojun Zhou and Fan Wang, “Singlet–triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater-Jastrow trial wavefunction with a minimum number of determinants,” Phys. Chem. Chem. Phys., Vol. 21, Issue. 36, pp. 20422–20431, 2019.
[3] Zakarya Zarezadeh and Giovanni Costantini, “Particle diffusion Monte Carlo (PDMC), Monte Carlo Methods Appl., Vol. 25, Issue. 2, pp. 120–130, 2019.
[4] J. B. Anderson, “A random-walk simulation of the Schrödinger equation: H3+,” J. Chem. Phys., Vol. 63, Issue. 4, pp. 1499–1503, 1975.
[5] J. E. Lynn, I. Tews, S. Gandolfi and A. Lovato, “Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances,” Annu. Rev. Nucl. Part. Sci., Vol. 69, Issue. 1, pp. 279–305, 2019.
[6] W. A. Lester, L. Mitas, and B. Hammond, “Quantum Monte Carlo for atoms, molecules and solids,” Chem. Phys. Lett., Vol. 478, Issue. 1–3, pp. 1–10, 2009.
[7] J. Kolorenč and L. Mitas, “Applications of quantum Monte Carlo methods in condensed systems,” Reports Prog. Phys., Vol. 74, Issue. 2, pp. 026502-1 – 026502-28, 2011.
[8] T. Pang, “Diffusion Monte Carlo: A powerful tool for studying quantum many-body systems,” Am. J. Phys., Vol. 82, Issue. 10, pp. 980–988, 2014.
[9] W. M. C. Foulkes et al., “Quantum Monte Carlo Simulations of Real Solids,” in High-Performance Computing, Springer, Boston, pp. 165-174 , 1999.
[10] W. Becken, P. Schmelcher, and F. K. Diakonos, “Helium atom in a strong magnetic field,” J. Phys. B At. Mol. Opt. Phys., Vol. 32, Issue. 6, pp. 1557–1584, 1999.
[11] M. V. Ivanov and P. Schmelcher, “Ground state of the lithium atom in strong magnetic fields,” Phys. Rev. A, Vol. 57, Issue. 5, pp. 3793–3800, 1998.
[12] O. A. Al-Hujaj and P. Schmelcher, “Lithium in strong magnetic fields,” Phys. Rev. A, Vol. 70, Issue. 3, pp. 033411-1 – 033411-12, 2004.
[13] M. V. Ivanov and P. Schmelcher, “The beryllium atom and beryllium positive ion in strong magnetic fields,” Eur. Phys. J. D, Vol. 17, Issue. 3, pp. 279–288, 2001.
[14] O. A. Al-Hujaj and P. Schmelcher, “Beryllium in strong magnetic fields,” Phys. Rev. A, Vol. 70, Issue. 2, pp. 023411-1 – 023411-11, 2004.
[15] M. V. Ivanov and P. Schmelcher, “The boron atom and boron positive ion in strong magnetic fields,” J. Phys. B At. Mol. Opt. Phys., Vol. 34, Issue. 10, pp. 2031–2044, 2001.
[16] Y. P. Kravchenko and M. A. Liberman, “Application of gaussian-type basis sets to Ab initio calculations in strong magnetic fields,” Int. J. Quantum Chem., Vol. 64, Issue. 5, pp. 513–522, 1997.
[17] M. D. Jones, G. Ortiz, and D. M. Ceperley, “Hartree-Fock studies of atoms in strong magnetic fields,” Phys. Rev. A - At. Mol. Opt. Phys., Vol. 54, Issue. 1, pp. 219–231, 1996.
[18] 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, Issue. 24, pp. 244108 -1 – 244108 -11, 2017.
[19] 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, Issue. 10, pp. 1–5, 2018.
[20] 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, Vol. 126, Issue. 3, pp. 700–704, 2014.
[21] 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., Vol. 92, Issue. 3, pp. 279–288, 2018.
[22] 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., Vol. 124, Issue. 1, pp. 1–9, 2017.
[23] T. Pang, “Diffusion Monte Carlo,” in An Introduction to Quantum Monte Carlo Methods, Morgan & Claypool Publishers, USA, pp. 4-1 – 4-14, 2016.
[24] 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, Issue. 6, pp. 1087–1092, 1953.
[25] Andrea Zen, Jan Gerit Brandenburg, Angelos Michaelides and Dario Alfè, “A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias,” J. Chem. Phys., Vol. 151, Issue. 13, pp. 134105-1 – 134105-15, 2019.
[26] M. Troyer and U. J. Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett., Vol. 94, Issue. 17, pp. 170201-1 – 170201-4, 2005.
[27] B. P. Prascher, D. E. Woon, K. A. Peterson, T. H. Dunning, and A. K. Wilson, “Gaussian basis sets for use in correlated molecular calculations. VII. Valence, core-valence, and scalar relativistic basis sets for Li, Be, Na, and Mg,” Theor. Chem. Acc., Vol. 128, Issue. 1, pp. 69–82, 2011.
[28] D. E. Woon and T. H. Dunning, “Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties,” J. Chem. Phys., Vol. 100, Issue. 4, pp. 2975–2988, 1994.
[29] T. H. Dunning, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen,” J. Chem. Phys., Vol. 90, Issue. 2, pp. 1007–1023, 1989.
[30] G. Dhingra, “Static Pair Correlation Functions and Static Structure Factors of Unidirectional Quantum Systems,” Int. J. Sci. Res. Phys. Appl. Sci., Vol. 7, Issue. 3, pp. 1 – 5, 2019.
[31] 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., Vol. 128, Issue. 15, pp. 154107-1 – 154107-7,2008.
[32] 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, Vol. 80, Issue. 5, pp. 053425-1 – 053425-5, 2009.
[33] 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., Vol. 77, Issue. 4, pp. 043414-1 – 043414-7, 2008.
[34] Z. C. Yan and G. W. F. Drake, “Eigenvalues and expectation values for the 1s22s 2S, 1s22p 2P, and 1s23d 2D states of lithium,” Phys. Rev. A, Vol. 52, Issue. 5, pp. 3711–3717, 1995.
[35] A. Kotchoubey and L. H. Thomas, “Numerical Calculation of the Energy and Wavefunction of the Ground State of Beryllium,” J. Chem. Phys., Vol. 45, Issue. 9, pp. 3342–3349, 1966.
[36] S. J. Chakravorty, S. R. Gwaltney, E. R. Davidson, F. A. Parpia and C. Froesse Fisher, “Ground-state correlation energies for atomic ions with 3 to 18 electrons,” Phys. Rev. A, Vol. 47, Issue. 5, pp. 3649–3670, 1993.