Ground States of the Hydrogen Molecule and Its Molecular Ion in the Presence of Magnetic Field Using the Variational Monte Carlo Method

TL;DR

This paper applies the variational Monte Carlo method to compute the energies and properties of hydrogen molecules and ions in magnetic fields up to 10 atomic units, demonstrating the method's effectiveness in magnetic environments.

Contribution

It introduces and validates the use of VMC with new trial wave functions for molecules in magnetic fields, extending its application scope.

Findings

VMC accurately calculates energies in magnetic fields.

Results agree with recent high-precision data.

Method successfully extends to magnetic field scenarios.

Abstract

By Using the variational Monte Carlo (VMC) method, we calculate the 1s{\sigma}_g state energies, the dissociation energies and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 a.u. and 10 a.u. The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of VMC method can be extended successfully to cover the case of molecules under the effect of the magnetic field.