Dynamics of supercooled water in configuration space

We study the potential energy surface (PES) sampled by a liquid modeled via the widely studied extended simple point charge (SPC/E) model for water. We characterize the curvature of the PES by calculating the instantaneous normal mode (INM) spectrum for a wide range of densities and temperatures. We discuss the information contained in the INM density of states, which requires additional processing to be unambiguously associated with the long-time dynamics. For the SPC/E model, we find that the slowing down of the dynamics in the supercooled region—where the ideal mode coupling theory has been used to describe the dynamics—is controlled by the reduction in the number of directions in configuration space that allow a structural change. We find that the fraction $f_{\mathrm{dw}}$ of the double-well directions in configuration space determines the value of the diffusion constant $D,$ thereby relating a property of the PES to a macroscopic dynamic quantity; specifically, it appears that $\sqrt{D}$ is approximately linear in $f_{\mathrm{dw}}.$ Our findings are consistent with the hypothesis that, at the mode coupling crossover temperature, dynamical processes based on the free exploration of configuration space vanish, and processes requiring activation dominate. Hence, the reduction of the number of directions allowing free exploration of configuration space is the mechanism of diffusion implicitly implemented in the ideal mode coupling theory. Additionally, we find a direct relationship between the number of basins sampled by the system and the number of free directions. In this picture, diffusion appears to be related to geometrical properties of the PES, and to be entropic in origin.