The accurate description of vibrational spectra of isolated dye molecules such as quinones has become a standard task in computational chemistry due to the progress of density functional theory. This is by no means the case for solution spectra. To contribute to this issue, we have carried out a QM/MM hybrid molecular dynamics (MD) simulation of p-benzoquinone in water, so as to derive its IR spectra. We have explored two different computational procedures that allow the calculation of an IR spectrum from such a dynamics simulation. One is based on Fourier transforms of autocorrelation functions and the other on instantaneous normal-mode analyses of snapshots. We show that both approaches are valid and yield similar vibrational frequencies. For a detailed comparison of computed bandwidths and intensities, however, our 17.5 ps QM/ MM-MD trajectory turned out to be too short. The analysis of the trajectory also demonstrates that, on the average, three water molecules form distinct solvation shells around each of the quinone C=O groups. These hydrogen bonded water molecules exchange on a time scale of about 2.5 ps. Computations on small, rigid quinone-water clusters compare reasonably well with the dynamics approach concerning the spectral positions of the quinone IR bands. Of course, the inhomogeneous broadening of IR bands, which is covered by the dynamics calculations, is inaccessible to the static cluster approach.