  We have constructed maximally-localized Wannier functions for prototype
structures of solid molecular hydrogen under pressure, starting from LDA and
tight-binding Bloch wave functions. Each occupied Wannier function can be
associated with two paired protons, defining a ``Wannier molecule''. The sum of
the dipole moments of these ``molecules'' always gives the correct macroscopic
polarization, even under strong compression, when the overlap between nearby
Wannier functions becomes significant. We find that at megabar pressures the
contributions to the dipoles arising from the overlapping tails of the Wannier
functions is very large. The strong vibron infrared absorption experimentally
observed in phase III, above ~ 150 GPa, is analyzed in terms of the
vibron-induced fluctuations of the Wannier dipoles. We decompose these
fluctuations into ``static'' and ``dynamical'' contributions, and find that at
such high densities the latter term, which increases much more steeply with
pressure, is dominant.
