  Signatures of solvated excess protons in infrared difference absorption
spectra, such as the continuum band between the water bend and stretch bands,
have been experimentally known for a long time, but the theoretical basis for
linking spectral signatures with the microscopic proton-transfer mechanism so
far relied on normal-mode analysis. We analyze the excess-proton dynamics in ab
initio molecular-dynamics simulations of aqueous hydrochloric acid solutions by
trajectory-decomposition techniques. The continuum band in the 2000 - 3000
cm$^{-1 }$ range is shown to be due to normal-mode oscillations of temporary
H$_3$O$^+$ complexes. An additional prominent peak at 400 cm$^{-1}$ reports on
the coupling of excess-proton motion to the relative vibrations of the two
flanking water molecules. The actual proton transfer between two water
molecules, which for large water separations involves crossing of a barrier and
thus is not a normal mode, is characterized by two characteristic time scales:
Firstly, the waiting time for transfer to occur in the range of 200 - 300 fs,
which leads to a broad weak shoulder around ~100 cm$^{-1}$, consistent with our
experimental THz spectra. Secondly, the mean duration of a transfer event of
about 14 fs, which produces a rather well-defined spectral contribution around
1200 cm$^{-1}$ and agrees in location and width with previous experimental
mid-infrared spectra.
