In Situ Scanning Tunneling Microscopy of a Redox Molecule as a Vibrationally Coherent Electronic Three-Level Process

Abstract

We provide a theoretical frame for in situ scanning tunneling microscopy (STM) of adsorbate molecules with low-lying redox levels strongly coupled to the environmental nuclear motion. The STM process is viewed as a coherent two-step electron transfer (ET) involving electron exchange between the local redox level and the manifolds of electronic levels in the substrate and tip. The notion coherence is here taken to imply that the intermediate electron or hole state after the first ET step does not fully relax vibrationally before the second ET step. These views and the theoretical formalism are appropriate to in situ STM of large transition metal complexes and redox metalloproteins. The formalism offers two kinds of spectroscopic features. One is the relation between the tunnel current and the bias voltage at fixed overvoltage of either the tip or the substrate relative to a reference electrode. The other one is the tunnel current dependence on the overvoltage, at fixed bias voltage. Recent data on tunneling current patterns for adsorbed or covalently tethered metalloporphyrins and the blue single-copper protein azurin are discussed in terms of the formalism.

Mechanisms of molecular electronic rectification through electronic levels with strong vibrational coupling

“…The formalism follows that for STM of redox molecules, [32][33][34][35][36]58 but addresses one level higher complexity. Focus has been on current rectification as this device function in molecular electronics is coming within reach.…”

“…Such intermediate single-level resonance tunneling is most suitably addressed by ET theory of three-level systems with dynamically populated intermediate states [32][33][34]36,43,44 which has also become a theoretical frame for STM of redox molecules. [32][33][34][35] STM of electronically resonating molecules has some resemblance to the molecular rectifier but is simpler by having only a single level between the two electrodes. As a reference we therefore first provide some recent observations in the theory of in situ STM of redox molecules.…”

“…E r is significantly smaller in the tunnel gap, say E r Ϸ0.2 eV, than in the semi-infinite configuration of electrochemical ET. 33 The features are characteristic resonances in the current-and derivative currentvoltage relations. The position and width reflect electronic-vibrational coupling ͑the reorganization Gibbs free energy͒, the potential distribution in the tunnel gap, and interactions with the metallic electrodes.…”

“…4 and from other recent theoretical approaches to molecular conductivity, [20][21][22][23][24][25][26][27][28][29][30][31] but warranted by the recently discovered actual metal/ donor-acceptor-molecule/metal systems. Our approach also rests on recent broader theoretical [32][33][34][35][36] and experimental basis [37][38][39][40][41][42] for scanning tunneling microscopy ͑STM͒ of immobilized redox molecules with low-lying redox levels both in the ex situ, vacuum or air ambient, and in situ electrochemical modes. These disclose in fact close similarities to asymmetric current flow in donor-acceptor molecules.…”

Electric double layer effect on observable characteristics of the tunnel current through a bridged electrochemical contact

“…This was recognized in the first theoretical studies of electron tunneling through a single molecular redox group [10][11][12] where one of the electron tunneling mechanisms in such systems was described, viz., stepwise sequential electron transfer ͑ET͒ through a relaxed intermediate state when the coupling of the bridge group with both electrodes is weak ͑further elaborated͒. 13 The current was expressed through the rate constants ͑transition probabilities͒ for the individual ET steps, and the limit of diabatic ET ͑employing the Fermi golden rule͒ 14,15 and the high-temperature limit were in focus. The strong interaction of the redox group with the vibrational subsystem results in the appearance of the FranckCondon factor in the expressions of the transition probabilities.…”