NUMERICAL CALCULATION OF THE GROUND STATE ENERGIES OF THE HYDROGEN MOLECULE AND THE HELIUM ATOM USING QUANTUM MONTE CARLO METHODS
NUMERICAL CALCULATION OF THE GROUND STATE ENERGIES OF THE HYDROGEN MOLECULE AND THE HELIUM ATOM USING QUANTUM MONTE CARLO METHODS
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Date
2012-02
Authors
SULEIMAN, ABDUSSALAM BALARABE
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Abstract
The ground state energies of Hydrogen molecule and the Helium atom are numerically evaluated
using the Variational Quantum Monte Carlo [VQMC] and the Path Integral Monte Carlo
[PIMC]. These analysis are done under the context of the accuracy of Born-Oppenhiemer
approximation [fixed nuclei restriction]. The ground state energies of hydrogen molecule for
different interproton separations (0.4 – 1.0Å) are computed using the two different methods
mentioned [VQMC and PIMC] and compared with previous numerical and empirical results
(results obtained by other reviewers in the field) that are essentially exact. The results from the
Path Integral Monte Carlo method of calculation were found to be precisely approaching the
required order of accuracy i.e. -31.92eV in the case of hydrogen molecule. The VQMC and
PIMC were applied to the helium atom at different values of the variational parameter b while
the interproton separation was set to zero. The corresponding average values of the ground state
energy is found to be -78.94eV and compared with the standard values and also with values
obtained from other reviewers in the field. This also shows that results obtained from PIMC are
much reliable and approaches the exact values i.e. -78.96eV. The standard errors in both cases
were calculated and the effect of time step [PIMC] as per the ground state energies is also
observed.
Description
A DISSERTATION SUBMITTED TO THE
POST GRADUATE SCHOOL,
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE AWARD OF THE DEGREEOF DOCTOR OF PHILOSOPHY IN PHYSICS
(THEORETICAL CONDENSED MATTER PHYSICS)
DEPARTMENT OF PHYSICS,
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
FEBRUARY, 2012
Keywords
NUMERICAL,, CALCULATION,, GROUND,, STATE,, ENERGIES,, HYDROGEN,, MOLECULE,, HELIUM,, ATOM,, USING,, QUANTUM,, MONTE,, CARLO,, METHODS,