Application of the Random Phase Approximation to the condensed phases of hydrogen

Density functionals based on the Random Phase Approximation (RPA) present a high accuracy/computational cost ratio, making them interesting tools for studying complex systems such as solid hydrogen at megabar pressures. In this work, we first show that the interaction energy across the potential energy surface of the (H₂)₂ dimer is more consistently described by RPA than common Density Functional Theory methods [1]. We then show, by comparing to Quantum Monte Carlo calculations, that accurate results are obtained on the molecular solid phases around the II-III phase transition [2]. A new phase II structure is revealed, highlighting the crucial role of exchange-correlation (xc) effects for determining the atomic structure. In this regard, obtaining accurate ionic forces is essential. Within the plane wave and pseudopotential approach, we found that an extra force term needs to be evaluated for methods, like RPA, that solves the Optimized Effective Potential equation to yield the xc potential. We implemented this term within the Quantum ESPRESSO code [3], obtaining forces with high accuracy [4].



[1] D. Contant, M. Casula, M. Hellgren, arXiv:2410.03410[physics.chem-ph] (2024).

[2] M. Hellgren, D. Contant, T. Pitts, M. Casula, Physical Review Research, 4, L042009 (2022).

[3] P. Giannozzi et al., Journal of Physics: Condensed Matter, 29, 465901 (2017).

[4] D. Contant, M. Hellgren, Physical Review B, 110, 125110 (2024).