Electron Distributions for the Helium Atom–Hydrogen Molecule System

Abstract

A study is made of the electron distribution generated by self-consistent field wavefunctions for the hydrogen molecule–helium atom system. The electron density is studied by means of electron density contour plots and plots of the difference between the electron density for interacting hydrogen molecule and helium atom systems and the noninteracting hydrogen molecule and helium atom. A population analysis technique is applied to these wavefunctions. Though the population analysis is a rather unrealistic method of distributing the electrons among and between the nuclei, it appears to give a qualitatively correct description of the electron distribution. The wavefunction studied gives a potential surface on which the H2 molecule tends to contract when the He atom approaches. This is true even when He approaches the H2 at an angle of 90° to the internuclear axis. The population analysis reflects this effect by showing an increase in the H2 bond population as He approaches.

The calculation of intermolecular forces. A critical examination of the Gordon-Kim model

“…The following discussion of the additive density approximation is based on Hartree-Fock calculations. For H% (and He-H2), the molecular density is equal to the sum of the separate densities to within a few per cent near the minimum [54,55]. Also the molecular density has regions between the two nuclei both of increased and of reduced value relative to the additive density.…”

Density Functional Calculation of Intermolecular Potentials

“…Anyway, such data are only scarcely available from the literature. Among others some results for interactions of two helium atoms from a Hartree–Fock calculation due to Gordon et al will be considered. As mentioned from DFT calculations, structure dependent charge distributions could in principle be obtained by the use of the two well-known theorems of Hohenberg and Kohn, but a detailed method for numerical calculations of intermolecular potentials does not seem available at present.…”

“…Inert Gas Atom–Inert Gas Atom Potential First results based on a detailed calculation of the disturbed charge distribution for He–He from ref will be discussed. In ref ,Gordon et alshow that the distortion at the center of interatomic geometry is approximately Δρ ≈ −0.0025 au for an intermolecular distance of R = 3 au, compared with results obtained by using the method of summation of undisturbed charge distributions, eq . Following the method in ref it is easy from this result to calculate that the short-range potential in the LDA limit will be reduced by approximately 10% due to the distribution just mentioned.…”

“…Δρ = ρ HF – ρ sum , and Δ V = V LDA (ρ HF ) – V LDA (ρ sum ). “HF” means “Hartree–Fock”, and “sum” means summation of undisturbed charge distributions from the colliding atoms. b Data for Δρ and ρ HF from ref . c Data for Δρ and ρ HF from ref . d Data obtained by the LDA method following ref using the charge distributions shown. …”

“…First results based on a detailed calculation of the disturbed charge distribution for He–He from ref will be discussed. In ref ,Gordon et alshow that the distortion at the center of interatomic geometry is approximately Δρ ≈ −0.0025 au for an intermolecular distance of R = 3 au, compared with results obtained by using the method of summation of undisturbed charge distributions, eq .…”