  The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that
the rotational correlation times $\tau_{l}$ vary as $[l(l+1)]^{-1}$, where $l$
is the rank of the orientational correlation function (given in terms of the
Legendre polynomial of rank $l$). One often finds significant deviation from
this prediction, in either direction. In supercooled molecular liquids where
the ratio $\tau_{1}/\tau_{2}$ falls considerably below three (the Debye limit),
one usually invokes a jump diffusion model to explain the approach of the ratio
$\tau_{1}/\tau_{2}$ to unity. Here we show in a computer simulation study of a
standard model system for thermotropic liquid crystals that this ratio becomes
much less than unity as the isotropic-nematic phase boundary is approached from
the isotropic side. Simultaneously, the ratio $\tau_2/\eta$ (where $\eta$ is
the shear viscosity of the liquid) becomes {\it much larger} than hydrodynamic
value near the I-N transition. We have also analyzed the break down of the
Debye model of rotational diffusion in ratios of higher order rotational
correlation times. We show that the break down of the DSE model is due to the
growth of orientational pair correlation and provide a mode coupling theory
analysis to explain the results.
