  Inspired by the work of Kamenev and Kohn, we present a general discussion of
the two-terminal dc conductance of molecular devices within the framework of
Time Dependent Current-Density Functional Theory. We derive a formally exact
expression for the adiabatic conductance and we discuss the dynamical
corrections. For junctions made of long molecular chains that can be either
metallic or insulating, we derive the exact asymptotic behavior of the
adiabatic conductance as a function of the chain's length. Our results follow
from the analytic structure of the bands of a periodic molecular chain and a
compact expression for the Green's functions. In the case of an insulating
chain, not only do we obtain the exponentially decaying factors, but also the
corresponding amplitudes, which depend very sensitively on the electronic
properties of the contacts. We illustrate the theory by a numerical study of a
simple insulating structure connected to two metallic jellium leads.
