  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.

Statistical Mechanics