Numerical Calculation of the Ground State Energies of the Hydrogen Molecule and the Helium Atom Using Quantum Monte Carlo Methods

Description

Download Numerical Calculation of the Ground State Energies of the Hydrogen Molecule and the Helium Atom Using Quantum Monte Carlo Methods. Physics students who are writing their projects can get this material to aid their research work.

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 þ while the interproton separation was set to zero.

Introduction

Hydrogen is the simplest element in the periodic table; it forms a diatomic gas at standard conditions of room temperature and atmospheric pressure. While not yet widely used as an energy carrier, new interest in hydrogen gas revolves around its potential as an alternative energy fuel.

The attraction to hydrogen arises partly, because it contains the highest energy content of any common fuel by weight and partly becomes the by-products’ of the combustion which consists of water not the green house emission [Dubravko, 2007].

Since it is quite difficult to undertake an experiment in this context, it is of particular urgency to consider a theoretical prediction of some properties of Hydrogen [H₂] molecule.

However, there is an extremely restricted choice of non-empirical methods of predicting the properties of hydrogen. Methods based on the Direct Quantum- mechanical computer simulations e.g. the Path Integral Monte Carlo are very demanding for computational resources and have not yet attained the necessary accuracy.

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