Wannier-function description of the electronic polarization and infrared absorption of high-pressure hydrogen

We have constructed maximally localized Wannier functions for prototype str uctures of solid molecular hydrogen under pressure, starting from local-den sity approximation and tight-binding Bloch wave functions. Each occupied Wa nnier function can be associated with two paired protons, defining a "Wanni er molecule." The sum of the dipole moments of these "molecules" always giv es the correct macroscopic polarization, even under strong compression, whe n the overlap between nearby Wannier functions becomes significant. We find that at megabar pressures the contributions to the dipoles arising from th e overlapping tails of the Wannier functions are very large. The strong vib ron infrared absorption experimentally observed in phase III, above similar to 150 GPa, is analyzed in terms of the vibron-induced fluctuations of the Wannier dipoles. We decompose these fluctuations into "static" and "dynami cal" contributions, and find that at such high densities the latter term, w hich increases much more steeply with pressure, is dominant.