Activated conduction in microscopic molecular junctions

We analyze the connection between the electron transfer (ET) rate through a given molecular bridge, and the conduction of a junction based on the same bridge between two metals. The Landauer relation between the conduction of a junction and its transmission properties is generalized to yield a relation between conduction and ET rate, including transfer processes dominated by thermal activation. The relation between the orders of magnitude of these observables involves an additional length parameter of the order of the range of the donor wave function. We find that the functional dependence of these observables on the bridge length (N) and on the temperature (T) changes from the exponential and temperature independent, exp(-beta N) for small N, to algebraic and thermally activated form, (alpha(1) + alpha(2)/N)(-1) exp(-Delta E/k(B)T), as N increases. An intermediate range of apparent independence on N exists if alpha(1) much greater than alpha(2). This behavior is the analogue to the quantum Kramers (barrier crossing) problem, analyzed with respect to the barrier length.