الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 32 |  |  |
| | | from | 32 | | |
Abstract
The aim of this thesis is to investigate the ground state characteristics of the hydrogen molecule, the confined hydrogen molecule, the hydrogen molecular ion and the confined hydrogen molecular ion in the absence and in the presence of aligned magnetic field. For these purposes we have applied the variational Monte Carlo method, which has been previously applied successfully for the ground and excited states of the helium and lithium atoms. The Metropolis algorithm has been adopted in our calculations with the well known Born-Oppenheimer approximation. Accurate and compact trial wave functions have been used for this purpose. The present thesis consists of five chapters and is organized as follows: Chapter One In this chapter we introduced the essential outlines of the topics investigated in the present thesis, especially the history of the Monte Carlo methods which are dealing with the atomic and molecular systems. Also, we presented a historical review about the Schrodinger equation and its applications in these two branches. This chapter is ended by the literature review. Chapter Two In chapter two we have introduced the formulation of the variational Monte Carlo (VMC) method which is based on a combination of the variational principle and the Monte Carlo evaluation of integrals, using importance sampling based on the Metropolis algorithm. Furthermore, we have explained the Metropolis algorithm, its logical steps and its acceptance and rejection ideas. Also, we have introduced the important role of the trial wave function in the variational method generally and in the variational Monte Carlo method especially. Chapter Three In this chapter we have used the variational Monte Carlo method to calculate the ground state energies of the hydrogen molecular ion H2+ and the hydrogen molecule H2 at different interproton separation distance. The calculations were carried out in framework of the principles of the Born-Oppenheimer approximation, the approximation which considers the case of an infinitely heavy nucleus. We also presented in this chapter a survey of the trial wave functions which are used in our calculations of the energy eigenvalues of the different molecular systems tackled in this thesis. Our calculations gave good results in comparison with the most recent data and the comparison showed that the accuracy and efficiency of the VMC method in calculating different molecular properties of hydrogen molecule ..2 and its molecular ion H2+ are very clear. Chapter Four This chapter is devoted to investigate the applications of the variational Monte Carlo method to the calculations of the ground state energy of the hydrogen molecule ..2 and the hydrogen molecular ion ..2+ confined by a hard prolate spheroidal cavity. In these investigations the case where the nuclear positions are clamped at the foci (on-focus case) is considered. Also, the case of off-focus nuclei in which the two nuclei are not clamped to the foci is studied. Accurate trial wave functions depending on many variational parameters are used for these purposes. The results were extended also to include the ......++ molecular ion. The obtained results are in good agreement with the most recent results. In all cases our results exhibit a good accuracy comparing with previous values using different methods and different forms of the trial wave functions. Chapter Five In chapter five we have applied the variational Monte Carlo method to calculate the 1...... state energies, the dissociation energies, and the binding energies of the hydrogen molecular ion ..2+ and the hydrogen molecule ..2 in the presence of an aligned magnetic field regime between 0 a.u. and 10 a.u. Our calculations are based on using compact and accurate trial wave functions. The obtained results are compared with the most recent accurate values and have shown excellent agreement with these results.