Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

Abstract

Using variational Monte Carlo method we calculated the lowest order relativistic corrections for the ground state energies of the helium-like atoms, up to Z = 10, and also for some excited state energies of the helium atom. These relativistic corrections include: massvelocity eect, orbitorbit interaction, spin magnetic and dipole moments of the two electrons and the Darwin eect. Moreover, correction due to the nucleus motion has been also calculated. Our results were obtained by using two new types of compact and accurate trial wave functions for the helium ions. For excited states we used simple trial wave functions of good quality and accurate results. The obtained results are in good agreement with the most recent previous accurate values and also with the exact values.

Ground states of the hydrogen molecule and its molecular ion in the presence of a magnetic field using the variational Monte Carlo method

“…The aim of the present paper is to study the total energies, the dissociation energies and the binding energies of the hydrogen molecule 2 and the hydrogen molecular ion 2 + in the presence of external magnetic field in framework of the Variational Monte Carlo (VMC) method, which is used widely in Refs [12][13][14][15][16][17][18][19][20][21]. Therefore, we have extended our previous work [22] to investigate the molecular systems using the VMC method.…”

Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms

“…And finally, the fourth is the U. Kleinekathöfer et.al correlation function [3] given by @ ( ) = 1 − O PQH "# EMR (8) In the above functions S, T, U and V are non-linear variational parameters. The parameter W helps in satisfying Kato-cusp condition [34], which equals 2 for unlike spins and 4 for like spins.…”

“…Moreover, we investigate the helium atom in a strong magnetic field. The method and the technique of the variational Monte Carlo were described well in [34].…”

Ground state calculations of the confined molecular ions H2+ and HeH++ using variational Monte Carlo method

“…In the present paper we extended our previous works about the applications of the variational Monte Carlo (VMC) method to the atomic systems [15][16][17][18][19], to the investigation of the molecular systems. As a first application we studied the confined hydrogen molecular ion .…”