  We consider in this work the numerical computation of transport coefficients
for Brownian dynamics. We investigate the discretization error arising when
simulating the dynamics with the Smart MC algorithm (also known as
Metropolis-adjusted Langevin algorithm). We prove that the error is of order
one in the time step, when using either the Green-Kubo or the Einstein formula
to estimate the transport coefficients. We illustrate our results with
numerical simulations.
