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

Spectral statistics of the quenched normal modes of a network-forming molecular liquid