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Estimation of Boron Ground State Energy by Monte Carlo Simulation
American Journal of Applied Mathematics
Volume 3, Issue 3, June 2015, Pages: 106-111
Received: Apr. 2, 2015; Accepted: Apr. 23, 2015; Published: May 6, 2015
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K. M. Ariful Kabir, Department Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Amal Halder, Department of Mathematics, University of Dhaka, Dhaka, Bangladesh
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Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.
Monte Carlo Simulation, Boron, Ground State Energy, Schrödinger Equation
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K. M. Ariful Kabir, Amal Halder, Estimation of Boron Ground State Energy by Monte Carlo Simulation, American Journal of Applied Mathematics. Vol. 3, No. 3, 2015, pp. 106-111. doi: 10.11648/j.ajam.20150303.15
B. L. Hammond, W. A. Lester Jr and P. J. Reynolds, Monte Carlo methods in ab initio quantum chemistry, pp.1-10,(1994).
E. Buendía, F. J. Gálvez, A. Sarsa, Chem. Phys. Lett., Explicitly correlated energies for neutral atoms and cations ,465: pp.190-192 (2008).
S. A. Alexander, R. L. Coldwell, Int. J. Quantum Chem, Atomic wave function forms, 63,pp.1001-1022 (1997).
K. E. Riley, J. B. Anderson, Chem. Phys. Lett., A new variational Monte Carlo trial wave function with directional Jastrow functions 366: pp.153-156 (2002).
S. A. Alexander, R. L. Coldwell, Int. J. Quantum Chem, Ro-vibrationally averaged properties of H2 using Monte Carlo methods, 107: pp.345-352 (2007).
S. Datta, S. A. Alexander, R. L. Coldwell, Int. J. Quantum Chem. The lowest order relativistic corrections for the hydrogen molecule, pp.731-739 (2012).
Buendı´a, F.J. Ga´lvez, A. Sarsa, Chem. Phys. Lett., Correlated wave functions for the ground state of the atoms Li through Kr, 428: pp.241-244 (2006).
Ruiz, M.B and Rojas,M. Computational Method in Science and Technology, Variational Calculations on the 2P1/2 Ground State of Boron Atom using Hydrogenlike orbitals.9(1-2), 101-112 (2003)
A. M. Frolov, Eur. Phys. J. D, Atomic Excitations During the Nuclear β− Decay in Light Atoms, 61: pp. 571-577 (2011).
N. L. Guevara, F. E. Harris, A. Turbiner, Int. J. Quantum Chem., An Accurate Few-parameter Ground State Wave Function for the Lithium Atom, 109: pp.3036-3040 (2009).
S. B. Doma and F. El-Gamal, Monte Carlo Variational Method and the Ground-State of Helium, pp-78-83.
C. Schwarz, Many-body methods in quantum chemistry: proceedings of the symposium (1989).
W. Kutzelnigg and J. D. Morgan III, Explicitly Correlated Wave Functions in Chemistry and Physics. Phys. pp. 96-104,(1992).
D. Ruenn Su, Theory of a Wave Function within a Band and a New Process for Calculation of the Band Energy, pp. 17-28 (1976)
P. J. Reynolds, D. M. Ceperley, B. J. Alder, and W. A. Lester, Jr., The Journal of Chemical Physics, 77(12), 1982 pp. 5593–5603. doi:10.1063/1.443766.
J. B. Anderson, The Journal of Chemical Physics, 73(8), 1980 pp. 3897–3899. doi:10.1063/1.440575
D. M. Ceperley and B. J. Alder, “Quantum Monte Carlo,” Science, 231(4738), 1986 pp. 555–560. doi:10.1126/science.231.4738.555.
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