First-principles study of solid hydrogen: Comparison among four exchange-correlation functionals

Abstract

The structures of solid hydrogen under high pressures have been revisited by using first-principles electronic structure calculations. Focusing on the stability, the intramolecular bond strength of hydrogen molecules in solid hydrogen, and the cell volume, we made a comparison study on seven structures including $P21/c\text{\ensuremath{-}}24$, $C2/c\text{\ensuremath{-}}24$, $P6122\text{\ensuremath{-}}36$, $Pc\text{\ensuremath{-}}48$, $Pca21\text{\ensuremath{-}}48$, $Cmca\text{\ensuremath{-}}4$, and $Cmca\text{\ensuremath{-}}12$ with the recently proposed strongly constrained and appropriately normed (SCAN) functional and three conventional exchange-correlation functionals, namely Perdew-Burke-Ernzerhof (PBE), Becke-Lee-Yang-Parr (BLYP), and van der Waals-density functional (vdW-DF). On one hand, with the SCAN functional the $C2/c$ structure takes the minimum static lattice enthalpies in the pressure range from 150 to 450 GPa, which agrees with the recent synchrotron infrared spectroscopic study and is similar to the result of the BLYP functional. On the other hand, the vibration frequencies of hydrogen molecules calculated by the SCAN functional match well with the experimental characteristic IR and Raman peaks, which indicates that the SCAN functional gives a reasonable estimation of the bond strength or bond length of hydrogen molecules in solid hydrogen, while the BLYP and vdW-DF functionals overestimate the bond strength. All SCAN, PBE, BLYP, and vdW-DF functionals give a good estimation of the unit cell volumes. Thus, the structures optimized with the SCAN functional can be an excellent starting point for advanced works on solid hydrogen.