Local self-motion of water through the Van Hove function*

We report that the self-part of the Van Hove functions of water can be determined through inelastic X-ray scattering (IXS) experiments at high-Q. Usually, a limited Q range prevents one from obtaining the real-space information from the Van Hove Functions without the termination errors that are associated with Fourier transformation. This difficulty can be mitigated if we focus on the time range in which the intermediate scattering function decays to zero within the accessible Q range. The self-part of the Van Hove functions is extracted from the short-range correlations. We found that the diffusivity estimated from the short-range dynamics of water is different from the long-range diffusivity measured by other methods, possibly due to developing intermolecular dynamic correlation. This information will bridge the gap between the hydrodynamic behavior and the phononic behavior at very short times.