$H_2$ and $(H_2)_2$ molecules with an ab initio optimization of wave functions in correlated state: Electron-proton couplings and intermolecular microscopic parameters

TL;DR

This study performs an ab initio analysis of $H_2$ and $(H_2)_2$ molecules, explicitly accounting for electronic correlations, electron-proton couplings, and zero-point motion, providing detailed microscopic parameters relevant for molecular hydrogen systems.

Contribution

It introduces a variational method combining orbital optimization and Hamiltonian diagonalization to accurately analyze correlated hydrogen molecules and their intermolecular interactions.

Findings

Explicit electron-proton coupling constants are calculated.

Zero-point motion energy with anharmonic corrections is evaluated.

Microscopic parameters for solid molecular hydrogen are estimated.

Abstract

The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron--ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to the solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for $2 \times H_2$ rectangular configurations.