Spectroscopic constants of H₂ using Monte Carlo methods

Abstract

ABSTRACT:We have computed the spectroscopic constants w e , w e x e , ␣ e , and B e of the ground state of H 2 using two methods. In the first method, a highly accurate potential energy surface was generated using explicitly correlated wave functions and variational Monte Carlo techniques. We calculated the vibrational-rotational energies from this surface and then obtained the spectroscopic constants by fitting these energies to a simple equation. In the second method, the spectroscopic constants were determined from local derivatives of the energy with respect to the internuclear distance. These derivatives have also been calculated using variational Monte Carlo techniques. For this system we find that the first method yields spectroscopic constants that are in excellent agreement with experiment. We also find that the second method, although slightly less accurate, is extremely well suited to Monte Carlo calculations.

Visualizing molecular wavefunctions using Monte Carlo methods

“…In Refs. 12 and 13 we showed that the trial wavefunction form produces rapidly convergent energies for the H 2 ground state. Here P 12 is the operator which interchanges the two electrons, P AB is the operator which interchanges the two nuclei and q x = r x /(1 +cr x ) is a coordinate transformation which allows terms in the exponent to go smoothly to the separated atom limit.…”

“…In Ref. 12 we optimized a separate N = i + j + l + m + n = 4 wavefunction at 24 internuclear distances using variance minimization and 4,000 Monte Carlo integration points. With these wavefunctions we then computed the Born–Oppenheimer energy, the diagonal correction to the Born–Oppenheimer energy and the lowest‐order relativistic energy 13.…”

“…In several recent studies, we have used standard numerical difference formulas to evaluate the derivatives of the energy and the wavefunction 12, 13, 24. For H 2 this approach produces the following expressions for the Laplacians of the electron, intracule and extracule densities: …”

Rovibrationally averaged properties of H2 using Monte Carlo methods

“…In Refs. 22 and 23, we showed that the trial wave function form produces rapidly convergent energies for the H 2 ground state. Here P 12 is the operator that interchanges the two electrons; P AB is the operator that interchanges the two nuclei and q x = r x /(1 + cr x ) is a coordinate transformation that allows terms in the exponent to go smoothly to the separated atom limit.…”

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.…”