The impact of Hubbard and van der Waals corrections on the DFT calculation of epsilon-zeta transition pressure in solid oxygen.

In this study, we aim to clarify the physics that governs the unique properties of the transition between epsilon and zeta phases in solid oxygen observed at 96 GPa by using density functional theory (DFT) calculations. We first conduct the calculation using various functionals, namely, LDA, PBE, BLYP, and TPSS. The results show that LDA and TPSS predict the epsilon-zeta transition pressure at 30 GPa, while PBE and BLYP show the transition at 40 GPa. Then we include the van der Waals correction (either vdW functionals or semi-empirical methods) to improve the nonlocal effects in epsilon oxygen. The transition pressure is improved to 50 GPa. Finally, the Hubbard correction is added to enhance the localization and short-range interactions. The final epsilon-zeta transition pressure is significantly improved to 80 GPa. This demonstrates that the contribution from the local interaction is higher than the nonlocal London dispersion term at the metallization point. Moreover, this approach suggests that the van der Waals correction may correctly capture the nonlocal interaction in solid oxygen. The nonlocal effect is expected to be dominant below 20 GPa. A correct treatment of the local and nonlocal interactions on an equal footing is important to study solid oxygen.