The role of van der Waals and exchange interactions in high-pressure solid hydrogen

Abstract

We investigate the van der Waals interactions in solid molecular hydrogen structures. We calculate enthalpy and the Gibbs free energy to obtain zero and finite temperature phase diagrams, respectively. We employ density functional theory (DFT) to calculate the electronic structure and Density functional perturbation theory (DFPT) with van der Waals (vdW) functionals to obtain phonon spectra. We focus on the solid molecular C2/c, Cmca-12, P 6 3 /m, Cmca, and P bcn structures within the pressure range of 200 < P < 450 GPa. We propose two structures of the C2/c and P bcn for phase III which are stabilized within different pressure range above 200 GPa. We find that vdW functionals have a big effect on vibrations and finite-temperature phase stability, however, different vdW functionals have different effects. We conclude that, in addition to the vdW interaction, a correct treatment of the high charge gradient limit is essential. We show that the dependence of molecular bond-lengths on exchange-correlation also has a considerable influence on the calculated metallization pressure, introducing errors of up to 100GPa.

A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures

“…Experimentally, no metallic phases have been observed in this pressure range, and quantum nuclear effects do not account for this discrepancy either. 4 The too low metallisation pressure can be attributed to the lacking of van der Waals interactions in PBE functional, 40 resulting in underestimation of the stability in the molecular structures. We note that Fig.…”

“…[7][8][9]13,[36][37][38][39] However, different parameterisations of the XC functional in DFT give inconsistent predictions, e.g., PBE predicts a too low metallisation pressure compared with experiments, whilst other exchange functionals produce higher pressures than DMC. 4,35,40 Instead, more accurate methods including diffusion Monte Carlo (DMC) have been employed to predict more reliable pressure temperature-phase diagrams, [2][3][4]31,32 which correct the underestimation of the metallisation pressure by DFT-PBE to a large extent. However, DMC calculations rely on the fixed-node approximation, and most of the current studies use crystal structures optimised using DFT.…”

A perspective on conventional high-temperature superconductors at high pressure: Methods and materials

“…The metalization of hydrogen has been seen as a compelling subject of study by many scientists, ranging from experimental chemists and physicists [134,135,136,137,10,463,9], to theoreticians [139,140,141]. However, despite the great advancement in high pressure-techniques and tools, the metalization of hydrogen in its solid phase has proven to be very challenging, and still debated [142,143,144,145,146,147,148,149,150,151,152]. The P − T phase diagram of hydrogen comprises many structures, including solid and molecular crystals and is so complex that it could be subject of a Review by itself [463].…”

Icosahedral (H2)13 supermolecule

“…The choice of exchange correlation functional is a highly debated topic in DFT studies of hydrogen. In a benchmarking studies on hydrogen the BLYP functional 22,23 was shown to give results closest to Quantum Monte Carlo calculations 24,25 , for transition pressures and vibrational frequencies, due mainly to the correct asymptotic behaviour at high charge density gradient 26 .…”

“…Furthermore, the hydrogen structure is the same in all compounds at the same lattice parameter, while the intermolecular distances within the supermolecule are highly dependent on density. Explicit treatment of van der Waals interactions is critical at low densities in hydrogen, but of secondary importance at pressure 26 . Here van der Waals interactions modelled by the Tkatchenko-Scheffler correction to PBE produced the same structures, further evidence that packing via the P V term in the enthalpy is more important.…”