WJCMP  Vol.3 No.4 , November 2013
A Quantum Monte Carlo Study of Lanthanum
Abstract: Pseudopotential calculations of the ground state energies of the Lanthanum neutral atom, first and second corresponding cations by means of the variational Monte Carlo (VMC) and the diffusion Monte Carlo (DMC) methods are performed. The first and the second ionization potentials have been calculated for Lanthanum. The obtained results are satisfactory and comparable with the available experimental data. Studying the DMC energy of the La atom at different time steps, gave us a time step error of the order 0.0019 Hartree for the smallest time step, τ = 0.0001 Hartree-1, and -0.0104 Hartree for the largest time step, τ = 0.01 Hartree-1. This paper demonstrates the ability of extending the QMC method for lanthanides and obtaining highly accurate results.
Cite this paper: Elkahwagy, N. , Ismail, A. , Maize, S. and Mahmoud, K. (2013) A Quantum Monte Carlo Study of Lanthanum. World Journal of Condensed Matter Physics, 3, 203-206. doi: 10.4236/wjcmp.2013.34034.

[1]   M. D. Brown, J. R. Trail, P. LoPez Rios and R. J. Needs, “Energies of the First Row Atoms from Quantum Monte Carlo,” The Journal of Chemical Physics, Vol. 126, No. 22, 2007, Article ID: 224110.

[2]   J. Toulouse and C. J. Umrigar, “Full Optimization of Jastrow-Slater Wave Functions with Application to the First-Flow Atoms and Homonuclear Diatomic Molecules,” The Journal of Chemical Physics, Vol. 128, No. 17, 2008, Article ID: 174101.

[3]   K. E. Schmidt and J. W. Moskowitz, “Correlated Monte Carlo Wave Functions for the Atoms He through Ne,” The Journal of Chemical Physics, Vol. 93, No. 6, 1990, p. 4172.

[4]   S. D. Kenny, G. Rajagopal and R. J. Needs, “Relativistic Corrections to Atomic Energies from Quantum Monte Carlo Calculations,” Physical Review A, Vol. 51, No. 3, 1995, pp. 1898-1904.

[5]   E. Buendia, F. J. Galvez and A. Sarsa, “Correlated Wave Functions for the Ground State of the Atoms Li through Kr,” Chemical Physics Letters, Vol. 428, No. 4-6, 2006, pp. 241-244.

[6]   L. Wagner and L. Mitas, “A Quantum Monte Carlo Study of Electron Correlation in Transition Metal Oxygen Molecules,” Chemical Physics Letters, Vol. 370, No. 3-4, 2003, pp. 412-417.

[7]   X. P. Li, D. M. Ceperley and R. M. Martin, “Cohesive Energy of Silicon by the Green’s-Function Monte Carlo Method,” Physical Review B, Vol. 44, No. 19, 1991, pp. 10929-10932.

[8]   A. Ma, N. D. Drummond, M. D. Towler and R. J. Needs, “All-Electron Quantum Monte Carlo Calculations for the Noble Gas Atoms He to Xe,” Physical Review E, Vol. 71, No. 6, 2005, Article ID: 066704.

[9]   J. B. Anderson, “Quantum Monte Carlo. Origins, Development, Applications,” Oxford University Press, Oxford, 2007.

[10]   M. P. Nightingale and C. J. Umrigar, “Quantum Monte Carlo Methods in Physics and Chemistry,” Kluwer Academic Publishers, Berlin, 1999.

[11]   L. M. Sobol, “A Primer for the Monte Carlo Method,” CRC Press, Boca Raton, 1994.

[12]   C. J. Cramer, “Essentials of Computational Chemistry: Theories and Models,” John Wiley & Sons Ltd, England, 2004.

[13]   W. M. C. Foulkes, L. Mitas, R. J. Needs and G. Rajagopal, “Quantum Monte Carlo Simulations of Solids,” Reviews of Modern Physics, Vol. 73, No. 1, 2001, pp. 33-83.

[14]   J. B. Anderson, “Quantum Chemistry by Random Walk. H 2P, H+3 D3h 1A′1, H2 3Σ+u, H4 1Σ+g, Be 1SJ,” The Journal of Chemical Physics, Vol. 65, No. 10, 1976, p. 4121.

[15]   A. Alkauskas, P. Deàk, J. Neugebauer, A. Pasquarello and C. Van de Walle, “Advanced Calculations for Defects in Materials,” Wiley-VCH Verlag & Co. K GaA, Weinheim, 2011.

[16]   L. K. Wagner, M. Bajdich and L. Mitas, “Qwalk: A Quantum Monte Carlo Program for Electronic Structure,” Journal of Computational Physics, Vol. 228, No. 9, 2009, pp. 3390-3404.

[17]   M. W. Schmidt, J. A. Boatz, K. K. Baldridge, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. windus, M. Dupuis and J. A. Montgomery, “General Atomic and Molecular Electronic Structure System,” Journal of Computational Chemistry, Vol. 14, No. 11, 1993, 1347-1363.


[19]   C. E. Moore, “Ionization Potential and Ionization Limits Derived from the Analyses of Optical Spectra,” National Bureau of Standards, Washington, 1970.