  In this paper, we address exponential ergodicity for L\'{e}vy driven Langevin
dynamics with singular potentials, which can be used to model the time
evolution of a molecular system consisting of $N$ particles moving in $\R^d$
and subject to discontinuous stochastic forces. In particular, our results are
applicable to the singular setups concerned with not only the
Lennard-Jones-like interaction potentials but also the Coulomb potentials. In
addition to Harris' theorem, the approach is based on novel constructions of
proper Lyapunov functions (which are completely different from the setting for
Langevin dynamics driven by Brownian motions), on invoking the H\"{o}rmander
theorem for non-local operators and on solving the issue on an approximate
controllability of the associated deterministic system as well as on exploiting
the time-change idea.
