On the relationship between molecular state and single electron pictures in simple electrochemical junctions

We consider a molecular conduction junction that comprises a redox molecule bridging between metal electrodes, in the limit of weak coupling and high temperature where electron transport is dominated by Marcus electron transfer kinetics. We address the correspondence between the Marcus description in terms of nuclear potential energy surfaces associated with different charging states of the molecular bridge, and the single electron description commonly used in theories of molecular conduction. The relationship between the energy gap, reorganization energy and activation energy parameters of the Marcus theory and the corresponding energy parameters in the single electron description is elucidated. We point out that while transport in the normal Marcus regime involves activated (therefore relatively slow) transitions between at least two charging states of the molecular bridge, deep in the inverted regime only one of these states is locally stable and transitions into this state are activationless. The relatively slow rates that characterize the normal Marcus transport regime manifest themselves in the appearance of hysteresis in the system transport behavior as a function of gate or bias potentials for relatively slow scan rates of these potentials, but not bistability in the junction conduction behavior. We also consider the limit of fast solvent reorganization that may reflect the response of the electronic environment (electronic polarization of a solvent and of the metal electrodes) to the changing charging state of the bridge. In this limit, environmental reorganization appears as renormalization of the bridge electronic energy levels. We show that the effect of this reorganization on the junction conduction properties is not universal and depends on the particular bridge charging states that are involved in the conduction process.