Assessing many-body methods on the potential energy surface of the (H$_2$)$_2$ hydrogen dimer

TL;DR

This study evaluates the performance of various many-body computational methods, including DFT and RPA, in accurately modeling the potential energy surface of the hydrogen dimer, revealing the importance of exchange effects for reliable predictions.

Contribution

It provides a comprehensive comparison of many-body methods on the hydrogen dimer's potential energy surface, highlighting the necessity of RPA for accurate descriptions across all configurations.

Findings

Most DFT functionals fail at finite compression.

RPA-based methods give qualitatively correct energy curves.

Exchange inclusion is crucial for accurate potential energy modeling.

Abstract

The anisotropic potential energy surface of the (H$_2$)$_2$ dimer represents a challenging problem for many-body methods. Here, we determine the potential energy curves of five different dimer configurations (T, Z, X, H, L) using the lattice regularized diffusion Monte Carlo (LRDMC) method and a number of approximate functionals within density functional theory (DFT), including advanced orbital-dependent functionals based on the random phase approximation (RPA). We assess their performance in describing the potential wells, bond distances and relative energies. The repulsive potential wall is studied by looking at the relative stability of the different dimer configurations as a function of an applied force acting along the intermolecular axis. It is shown that most functionals within DFT break down at finite compression, even those that give an accurate description around the potential well minima. Only by including exchange within RPA a qualitatively correct description along the entire potential energy curve is obtained. Finally, we discuss these results in the context of solid molecular hydrogen at finite pressures.