Instantaneous normal mode analysis of liquid water

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Abstract
We present an instantaneous-normal-mode analysis of liquid water at room temperature based on a computer simulated set of liquid configurations and we compare the results to analogous inherent-structure calculations. The separate translational and rotational contributions to each instantaneous normal mode are first obtained by computing the appropriate projectors from the eigenvectors. The extent of localization of the different kinds of modes is then quantified with the aid of the inverse participation ratio—roughly the reciprocal of the number of degrees of freedom involved in each mode. The instantaneous normal modes also carry along with them an implicit picture of how the topography of the potential surface changes as one moves from point to point in the very-high dimensional configuration space of a liquid. To help us understand this topography, we use the instantaneous normal modes to compute the predicted heights and locations of the nearest extrema of the potential. The net result is that in liquid water, at least, it is the low frequency modes that seem to reflect the largest-scale structural transitions. The detailed dynamics of such transitions are probably outside of the instantaneous-normal-mode formalism, but we do find that short-time dynamical quantities, such as the angular velocity autocorrelation functions, are described extraordinarily well by the instantaneous modes.