  We evaluate the density of states of the quenched normal modes of ST2 water,
and their statistical fluctuations, for a range of densities spanning three
regimes of behavior of a hydrogen bonded liquid: a lower-density regime of
random tetrahedral network formation; in the vicinity of a liquid-liquid
critical point; and in a higher-density regime of fragile glass-forming
behavior. For all cases we find that the fluctuations around the mean spectral
densities obey the predictions of the Gaussian orthogonal ensemble of random
matrix theory. We also measure the participation ratio of the normal modes
across the entire frequency range, and find behavior consistent with the
majority of modes being of an extended nature, rather than localized.
