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