Localization-delocalization transition of the instantaneous normal modes of liquid water

Despite the fact that the localization-delocalization transition (LDT) widely exists in wave systems, quantitative studies on its critical and multifractal properties are mainly focused on solids. In this work, these properties are investigated on the vibrational motions of liquid water. Simulations of up to 18000 molecules on the flexible extended simple point charge water model provide nearly 10(6) instantaneous normal modes. They are shown to undergo an LDT close to the translational transition and exhibit multifractal fluctuations while approaching the LDT. In combination with finite-size scaling, multifractal analysis predicts the critical frequency Im(ω(c))≈-131.6 cm(-1) for unstable modes at room temperature. The estimated critical exponent ν≈1.60 is close to those of other calculated systems in the same Wigner-Dyson class. At the LDT, the fractal spectrum f(α) and the most probable local vibrational intensity α(mc)≈4.04 coincide with those of the Anderson model, which might be additional universal properties of LDT in more general wave systems. The results extend the validity of the multifractal scaling approach beyond Andersonian systems to a Hessian system.