Ab initio calculation of optical-mode frequencies in compressed solid hydrogen

Vibrational optical-mode frequencies have been calculated for some of the structures recently proposed by theoretical and experimental studies of compressed solid hydrogen, by means of first principles band theoretical treatments using the plane wave basis set, in the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation energy. The results of the GGA are compared with those of the LDA, and both results are compared with recent Raman scattering and infrared absorption experiments. The possible structures of the compressed molecular solid hydrogen at megabar pressures have been discussed in light of vibrational optical modes and their frequencies. The total energy is also calculated in the GGA for some of the candidate structures in the molecular phase as well as those in the atomic phase. The molecular phase persists over 400 GPa, which can result in the metallization prior to the molecular dissociation. The effects of the band gap closure on the frequencies are studied together with the effects of the GGA. The GGA decreases the bond length and hence increases the vibron frequencies, by which the calculated frequencies show excellent agreement with the experiments for the (Formula presented) structure, while the phonon frequencies are less affected by the GGA. The shorter bond length leads to wider band gaps. The GGA favors the molecular phase more than the atomic phase. Our results of the frequencies suggest that the (Formula presented) structure is most probable in phase II if the molecules are oriented there and the (Formula presented) is in phase III at pressures under (Formula presented).