Quantum Mechanics of the H2–H2 Interaction. I. A Restricted Valence-Bond Approach

Abstract

The short-range intermolecular interaction of two hydrogen molecules in their ground state has been approached by a rigorous valence-bond calculation using a minimal set of four symmetrically orthogonalized 1s atomic orbitals with the orbital exponent fixed to the best variational value for the isolated molecule. All the covalent, singly polar and doubly polar ``formal'' structures which are expected to be relevant in the case of relatively large intermolecular distances have been included in the calculation. Within a given range of separation distances four relative orientations of the two molecules have been considered in order to study the angular dependence of the intermolecular interaction. All the occurring three- and four- center integrals have been evaluated to six significant figures using a three-dimensional numerical integration in confocal elliptic coordinates. Although the quantitative value of the intermolecular potential resulting from this calculation is expected to be as good as it could be for a minimal basis approach, many interesting features of the interaction in the short-range region have been emphasized through a population analysis of the valence-bond (VB) molecular wavefunction made in terms of the original set of nonorthogonal atomic orbitals which allows to describe unambiguously the bonding or antibonding situations within the system. It is found that the charge distributed according to the overlap densities between orbitals belonging to different molecules escapes from the intermolecular region and piles up as an extra charge on the two molecules. A small charge transfer showing a strong angular dependence on the dihedral angle is observed to occur in each molecule along the bond direction. The general discussion suggests that the introduction of localized wavefunctions could be appropriate for understanding the details of the correlation between charge distribution and intermolecular energy and for a partitioning of the energy into significant contributions.