  We study Langevin dynamics of $N$ particles on $R^d$ interacting through a
singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show
that the system converges to the unique invariant Gibbs measure exponentially
fast in a weighted total variation distance. The proof of the main result
relies on an explicit construction of a Lyapunov function. In contrast to
previous results for such systems, our result implies geometric convergence to
equilibrium starting from an essentially optimal family of initial
distributions.
