Nonequilibrium electrochemistry raises new challenges for atomistic simulation: we need to perform molecular dynamics for the nuclear degrees of freedom with an explicit description of the electrons, which in turn must be free to enter and leave the computational cell. Here we present a limiting form for electron open boundaries that we expect to apply when the magnitude of the electric current is determined by the drift and diffusion of ions in a solution and which is sufﬁciently computationally efﬁcient to be used with molecular dynamics. We present tight-binding simulations of a parallel-plate capacitor with nothing,a dimer, or anatomic wire situated in the space between the plates. These simulations demonstrate that this scheme can be used to perform molecular dynamics simulations when there is an applied bias between two metal plates with, at most, weak electronic coupling between them. This simple system captures some of the essential features of an electrochemical cell, suggesting this approach might be suitable for simulations of electrochemical cells out of equilibrium.