Visualizing molecular wavefunctions using Monte Carlo methods

Abstract

Using explicitly correlated wavefunctions and variational Monte Carlowe calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree-Fock wavefunction and then comparing these values with our explicitly correlated values.

Quantum Monte Carlo and Related Approaches

“…RQMC was used to study a variety of ground-state properties of a water molecule, such as dipole moment, components of the quadrupole moment tensor, and The influence of electron correlation on the expectation values of the electron density, the intracule density, the extracule density, their respective Laplacians, and the two forms of kinetic energy density was revealed in a VMC study of hydrogen molecule. 295 VMC calculations with explicitly correlated wave functions were performed for three values of the interatomic separation and clearly confirmed the traditional description of this system as a combination of covalent and ionic structures. Substantial differences between the properties studied and the HF calculations were found.…”

“…The influence of electron correlation on the expectation values of the electron density, the intracule density, the extracule density, their respective Laplacians, and the two forms of kinetic energy density was revealed in a VMC study of hydrogen molecule . VMC calculations with explicitly correlated wave functions were performed for three values of the interatomic separation and clearly confirmed the traditional description of this system as a combination of covalent and ionic structures.…”

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.…”

Single electron densities: A new tool to analyze molecular wavefunctions

“…Alexander and Coldwell22 have recently published a similar Monte Carlo based method to visualize electron densities. A related work on electron probability volumes has recently been published by Cancès et al23 A strong relation exists to the well established electron localization function (ELF) that allows the identification of lone pairs and bond electrons 24, 25.…”