| The purpose of this thesis is to relate the structure and dynamics of glass-forming liquids by using pathways in configuration space to explain the diffusion. To quantify the structure in configuration space, we evaluate the local curvature of the potential energy from instantaneous samples of the liquid, better known as the instantaneous normal mode spectrum. Prior work has established that some fraction of the unstable modes are responsible for the diffusion, but separating the specific diffusive modes has proved challenging. We develop a localization test that allows us to determine exactly the fraction of delocalized unstable modes, fuDL, which we show that it directly relates to the diffusion coefficient. We do so by relating fuDL with the configurational entropy, a quantity that enumerates the number of stable states available to the liquid. This also provides specific restrictions on the geometry of the configuration space. We find similarities between the results for our binary Lennard-Jones system and supercooled water, supporting the potential universality of our findings. |
