Reconstructing the structure and dynamics of density fluctuations in water near a moving proton

~~~~~~The structure and dynamics of water on femtosecond timescales is relevant to many topics in physical chemistry such as ion solvation. We computationally reconstruct the angstrom-scale spatial and femtosecond-scale temporal evolution of density fluctuations in water using high-resolution inelastic x-ray scattering (IXS). The imaginary part of density propagator $\chi $(q,$\omega )$ is directly extracted from the IXS data, and the real part recovered using Kramers-Kronig relations.~ The resultant complex-valued $\chi $(q,$\omega )$ is the Fourier transform of the real-space density-density response function $\chi $(r,t) which measures the dynamical density fluctuations of water due to a point-like instantaneous pulse.~ We use this density propagator from IXS data and linear-response theory to reconstruct the hydration behavior of a proton moving at different speeds through water.