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Fragility index of a simple liquid from structural inputs

We make a first principle calculation of the fragility index $m$ of a simple liquid using the structure of the supercooled liquid as an input. Using the density functional theory (DFT) of classical liquids, the configurational entropy ${\cal S}_c$ is obtained for low degree of supercooling. We extrapolate this data to estimate the Kauzmann temperature $T_\mathrm{K}$ for the liquid. Using the Adam-Gibbs relation, we link the configurational entropy ${\cal S}_c$ to the relaxation time. The relaxation times are obtained from direct solutions of the equations of fluctuating nonlinear hydrodynamics (FNH). These equations also form the basis of the mode coupling theory (MCT) for glassy dynamics. The fragility index for the supercooled liquid is estimated from analysis of the curves on the Angell plot.