  The vibrational modes of water get significantly modified by external
solutes; this becomes particularly important when the solute is hydrophobic. In
this work, we examine the effects of a tiny hydrophobe, methane, on the normal
modes of water, using small cluster-based harmonic normal mode analysis of
aqueous methane system. We estimate the vibrational density of states and also
the infrared spectral density. We compare the methane-water data with the bulk
water response. We decompose these modes based on different vibrational
characters. The stretch-bend decomposition reflects a pronounced coupling
between the methane asymmetric stretch mode and the water symmetric stretch
mode. We examine the methane-water data in terms of the symmetry of the central
water molecule's vibrations and find that asymmetric modes do not contribute.
We also find that the vibrational modes having non-zero contributions from
methane molecule are extremely localized in nature.
