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Multi-electron systems in strong magnetic fields. II: A fixed-phase diffusion quantum Monte Carlo application based on trial functions from a Hartree-Fock-Roothaan method. (English) Zbl 1348.81015

Summary: We present a quantum Monte Carlo application for the computation of energy eigenvalues for atoms and ions in strong magnetic fields. The required guiding wave functions are obtained with the Hartree-Fock-Roothaan code described in the accompanying publication [C. Schimeczek and G. Wunner, “Multi-electron systems in strong magnetic fields. I: The 2D Landau-Hartree-Fock-Roothaan method”, ibid. 185, No. 10, 2655–2662 (2014; doi:10.1016/j.cpc.2014.05.005)]. Our method yields highly accurate results for the binding energies of symmetry subspace ground states and at the same time provides a means for quantifying the quality of the results obtained with the above-mentioned Hartree-Fock-Roothaan method.

MSC:

81-04 Software, source code, etc. for problems pertaining to quantum theory
81V70 Many-body theory; quantum Hall effect
65C05 Monte Carlo methods
85-08 Computational methods for problems pertaining to astronomy and astrophysics
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[1] Schimeczek, C.; Wunner, G., Multi-electron systems in strong magnetic fields I: the 2D Landau-Hartree-Fock-Roothaan method, Comput. Phys. Comm. xxx, xxx (2014)
[2] Becken, W.; Schmelcher, P.; Diakonos, F. K., The helium atom in a strong magnetic field, J. Phys. B, 32, 1557-1584 (1999)
[3] Becken, W.; Schmelcher, P., Non-zero angular momentum states of the helium atom in a strong magnetic field, J. Phys. B, 33, 3, 545 (2000)
[4] Becken, W.; Schmelcher, P., Higher-angular-momentum states of the helium atom in a strong magnetic field, Phys. Rev. A, 63, 053412 (2001)
[5] Al-Hujaj, O.; Schmelcher, P., Lithium in strong magnetic fields, Phys. Rev. A, 70, 3, 033411 (2004)
[6] Al-Hujaj, O.; Schmelcher, P., Beryllium in strong magnetic fields, Phys. Rev. A, 70, 023411, 023411 (2004)
[7] Foulkes, W. M.C.; Mitas, L.; Needs, R. J.; Rajagopal, G., Quantum Monte Carlo simulations of solids, Rev. Modern Phys., 73, 1, 33-83 (2001)
[8] Hammond, B. L.; Lester, W. A.; Reynolds, P. J., Monte Carlo methods in ab initio quantum chemistry, (World Scientific Lecture and Course Notes in Chemistry (1994), World Scientific Publishing Co. Pte. Ltd.: World Scientific Publishing Co. Pte. Ltd. Singapore)
[9] Wagner, L. K., Quantum Monte Carlo for ab initio calculations of energy-relevant materials, Int. J. Quantum Chem., 114, 2, 94-101 (2014)
[10] Schimeczek, C.; Boblest, S.; Meyer, D.; Wunner, G., Atomic ground states in strong magnetic fields: electron configurations and energy levels, Phys. Rev. A, 88, 012509 (2013)
[11] Carlson, J., Green’s function Monte Carlo study of light nuclei, Phys. Rev. C, 36, 5, 2026-2033 (1987)
[12] Ortiz, G.; Jones, M. D.; Ceperley, D. M., Ground state of a hydrogen molecule in superstrong magnetic fields, Phys. Rev. A, 52, R3405-R3408 (1995)
[13] Ortiz, G.; Ceperley, D. M.; Martin, R. M., New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field, Phys. Rev. Lett., 71, 17, 2777-2780 (1993)
[14] Engel, D.; Wunner, G., Hartree-Fock-Roothaan calculations for many-electron atoms and ions in neutron star magnetic fields., Phys. Rev. A., 78, 032515 (2008)
[15] Schimeczek, C.; Engel, D.; Wunner, G., A highly optimized code for calculating atomic data at neutron star magnetic field strengths using a doubly self-consistent Hartree-Fock-Roothaan method, Comp. Phys. Comm., 183, 1502-1510 (2012)
[16] Boblest, S.; Schimeczek, C.; Wunner, G., Ground states of helium to neon and their ions in strong magnetic fields, Phys. Rev. A, 89, 012505 (2014)
[17] Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. M.; Teller, E., Equations of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092 (1953) · Zbl 1431.65006
[18] Jones, M. D.; Ortiz, G.; Ceperley, D. M., Released-phase quantum Monte Carlo method, Phys. Rev. E, 55, 5, 6202-6210 (1997)
[19] Kent, P. R.C.; Needs, R. J.; Rajagopal, G., Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions, Phys. Rev. B, 59, 12344-12351 (1999)
[20] Lüchow, A., Quantum Monte Carlo methods, Comput. Mol. Sci., 1, 388-402 (2011)
[21] Reboredo, F. A., Many-body calculations of low-energy eigenstates in magnetic and periodic systems with self-healing diffusion Monte Carlo: steps beyond the fixed phase, J. Chem. Phys., 136, 204101 (2012)
[22] Schimeczek, C., 2D Hartree-Fock-Roothaan calculations for atoms and ions in neutron star atmospheres (2013), Universität Stuttgart, (Ph.D. thesis)
[23] Schiff, L. I.; Snyder, H., Theory of quadratic Zeeman-effect, Phys. Rev., 55, 59-63 (1939) · Zbl 0020.17903
[24] Engel, D.; Klews, M.; Wunner, G., A fast parallel code for calculating energies and oscillator strengths of many-electron atoms at neutron star magnetic field strengths in adiabatic approximation, Comp. Phys. Comm., 180, 2, 302-311 (2009) · Zbl 1198.85003
[25] Engel, D., Hartree-Fock-Roothaan-Rechnungen für Vielelektronen-Atome in Neutronenstern-Magnetfeldern (2007), Universität Stuttgart, (Ph.D. thesis)
[26] Kato, T., On the eigenfunctions of many-particle systems in quantum mechanics, Comm. Pure Appl. Math., 10, 151-177 (1957) · Zbl 0077.20904
[27] Coulson, C. A.; Neilson, A. H., Electron correlation in the ground state of helium, Proc. Phys. Soc., 78, 831-837 (1961) · Zbl 0104.23702
[28] Pack, R. T.; Brown, W. B., Cusp conditions for molecular wavefunctions, J. Chem. Phys., 45, 556-559 (1966)
[29] Fisher, D. R.; Kent, D. R.; Feldmann, M. T.; Goddard III, W. A., An optimized initialization algorithm to ensure accuracy in quantum Monte Carlo calculations, J. Comput. Chem., 29, 14, 2335-2343 (2008)
[30] Huang, C.; Umrigar, C. J.; Nightingale, M. P., Accuracy of electronic wave functions in quantum Monte Carlo: the effect of high-order correlations, J. Chem. Phys., 107, 8, 3007-3013 (1997)
[31] Nightingale, M. P.; Melik-Alaverdian, V., Optimization of ground- and excited state wave functions and van der Waals clusters, Phys. Rev. Lett., 87, 4, 043401 (2001)
[32] Drummond, N. D.; Towler, M. D.; Needs, R. J., Jastrow correlation factor for atoms, molecules, and solids, Phys. Rev. B, 70, 235119 (2004)
[33] Umrigar, C. J.; Toulouse, J.; Filippi, C.; Sorella, S.; Hennig, R. G., Alleviation of the fermion-sign problem by optimization of many-body wave functions, Phys. Rev. Lett., 98, 110201 (2007)
[34] Toulouse, J.; Umrigar, C. J., Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules, J. Chem. Phys., 128, 174101 (2008)
[35] Luo, H., Complete optimisation of multi-configuration Jastrow wave functions by variational transcorrelated method, J. Chem. Phys., 135, 024109 (2011)
[36] Umrigar, C. J.; Nightingale, M. P.; Runge, K. J., A diffusion Monte Carlo algorithm with very small time-step errors, J. Chem. Phys., 99, 4, 2865-2890 (1993)
[37] Bignami, G. F.; De Luca, A.; Caraveo, P. A.; Mereghetti, S.; Moroni, M.; Mignani, R. P.; Marconi, M., 1E1207.4-5209—a unique object, Mem. S. A. It., 75, 3, 448 (2004)
[38] D. van Heesch, Doxygen-generate documentation from source code, http://www.stack.nl/ dimitri/doxygen/index.html; D. van Heesch, Doxygen-generate documentation from source code, http://www.stack.nl/ dimitri/doxygen/index.html
[39] bwGRiD, Member of the German D-Grid initiative, funded by the Ministry of Education and Research (Bundesministerium für Bildung und Forschung) and the Ministry for Science, Research and Arts Baden-Wuerttemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg), http://www.bw-grid.de; bwGRiD, Member of the German D-Grid initiative, funded by the Ministry of Education and Research (Bundesministerium für Bildung und Forschung) and the Ministry for Science, Research and Arts Baden-Wuerttemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg), http://www.bw-grid.de
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