  Path reweighting is a principally exact method to estimate dynamic properties
from biased simulations - provided that the path probability ratio matches the
stochastic integrator used in the simulation. Previously reported path
probability ratios match the Euler-Maruyama scheme for overdamped Langevin
dynamics. Since MD simulations use Langevin dynamics rather than overdamped
Langevin dynamics, this severely impedes the application of path reweighting
methods. Here, we derive the path probability ratio $M_L$ for Langevin dynamics
propagated by a variant of the Langevin Leapfrog integrator. This new path
probability ratio allows for exact reweighting of Langevin dynamics propagated
by this integrator. We also show that a previously derived approximate path
probability ratio $M_{\mathrm{approx}}$ differs from the exact $M_L$ only by
$\mathcal{O}(\xi^4\Delta t^4)$, and thus yields highly accurate dynamic
reweighting results. ($\Delta t$ is the integration time step, $\xi$ is the
collision rate.) The results are tested and the efficiency of path-reweighting
is explored using butane as an example.
