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Important Insight into Electron Transfer in Single-Molecule Junctions Based on Redox Metalloproteins from Transition Voltage Spectroscopy Ioan Bâldea* Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany Institute of Space Sciences, National Institute of Lasers, Plasmas and Radiation Physics, RO 077125, Bucharest, Romania S Supporting Information *

ABSTRACT: In a recent experimental work, results of the first transition voltage spectroscopy (TVS) investigation on azurin have been reported. This forms a great case to better understand the electron transfer through bacterial redox metalloproteins, a process of fundamental importance from chemical, physical, and biological perspectives, and of practical importance for nano(bio)electronics. In the present paper we challenge the tentative interpretation put forward in the aforementioned experimental study and propose a different theoretical interpretation. To explain the experimental TVS data, we adopt an extended Newns−Anderson framework, whose accuracy and robustness is demonstrated. We show that that this framework clearly meets the need to obtain a consistent description across experiments. Most importantly, the presently proposed theoretical approach permits unraveling novel aspects on the impact of the electrochemical scanning microscope environment on the charge transport through single(bio)molecule junctions based on redox units. The usefulness of TVS as a versatile method of investigation, also able to provide important insight into the charge transport through metalloproteins, is emphasized.

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INTRODUCTION Transition voltage spectroscopy (TVS)1 is a method becoming increasingly popular, extensively used to characterize electronic single-molecule devices.2−10 In a recent experiment,11 TVS has been applied for the first time to wet single-molecule junctions based on azurin, a prototypical blue copper-containing bacterial redox protein. This forms a great case to better understand the electron transfer (ET) through redox metalloproteins, a fundamental process both from a biological perspective (respiration, photosynthesis) and (bio)technological applications (redox (bio)sensors, biofuel cells, memories, logic gates).12−14 Azurin from Pseudomonas æruginosa is a soluble protein, which very efficiently shuttles electrons between two molecular partners (cytochrome c551 and nitride reductase) by reversibly changing the oxidation state (Cu1+ ⇌ Cu2+). The wet environment (50 nM ammonium acetate) employed11 attempts to best exploit the efficient natural ET properties of azurin from P. æruginosa in physiologic-like conditions. Like other experimental investigations on the charge transport through junctions of single redox molecules,15−19 the TVS study under present consideration11 exploited the advantage of the electrochemical scanning tunneling microscopy (ECSTM) environment.15 Such studies employ an electrochemical cell under bipotentiostatic control. The STM substrate and tip potentials Vs,t are separately controlled versus a reference [e.g., Ag/AgCl (SSC)] electrode placed in solvent. © 2013 American Chemical Society

Measurements are usually carried out either in constant bias mode or variable bias mode, that is, by varying Vs at constant bias V ≡ Vb = Vt − Vs or by varying Vb at constant Vs, respectively. Reference 11 reported full I−V curves for molecular junctions based on an individual redox protein in ECSTM setup.15 In the tunneling configuration considered below, the experiments11 were carried out in an electrochemical cell with the azurin molecule covalently bound to the gold substrate and close (but without physical contact) to the tip. The TVS data for azurin11 have been analyzed within an adiabatic vibrationally coherent two-step ET model (2sETM).20 The aim of the present work is 3-fold. First, we will demonstrate that the 2sETM, also used to quantitatively analyze other valuable transport experiments through redox molecules,18,19 is inadequate for this purpose. Second, we will show that the TVS11 as well as other17 transport data for azurin can be quantitatively understood within a different, robust approach. Third and most importantly, the present approach permits us to unravel novel aspects on the impact of the ECSTM environment on the ET in azurin. Received: September 4, 2013 Revised: October 17, 2013 Published: October 21, 2013 25798

dx.doi.org/10.1021/jp408873c | J. Phys. Chem. C 2013, 117, 25798−25804

The Journal of Physical Chemistry C

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RESULTS In the present paper we will present and discuss results for TVS in azurin obtained within two different models: the 2sETM model and an extended Newns−Anderson model. We will show that the former model, which has been employed in ref 11 to interpret the experimental data reported there, is inadequate, while the latter can excellently reproduce not only those TVS data but also transport data in azurin of a different kind reported by another group of experimentalists16,17 using a different ECSTM instrument. TVS Results in Azurin and the Charge Conjugation Symmetry. Reference 11 reported current (I) measurements done in variable bias mode (i.e., by varying Vb at constant Vs) red for two situations: Vs = V̅ ox s = 0.2 V and Vs = V̅ s = −0.3 V. They correspond to oxidized and reduced states of azurin, respectively. The transition voltages Vtr deduced for these Vsred values are Vox tr ≈ −0.42 V and Vtr ≈ 0.38 V, respectively. Vtr is defined as the bias at the minimum of the Fowler-Nordheim quantity ln(I/V2b).1 Vtr serves to quantify the energy offset εr = ELUMO −μs from the substrate’s Fermi energy μs = −eVs of the molecular orbital that dominates the charge transfer through molecule; in azurin, this is the LUMO redox level related to the active Cu ion site. In nonredox molecules, the relationship εr − Vtr is expressed by simple analytical formulas.21−23 Such formulas are not yet available for redox molecules, wherein reorganization upon charge transfer is significant. Still, as shown in the present work, Vtr unravels valuable information on the charge transport through such molecules. For an azurin molecule immersed in a solvent, the LUMO energy offset can be expressed as (see the Supporting Information (SI) for more details)24,25 εr(Q , η , Vb) = λ(1 − 2Q ) − eξη − eγVb

Figure 1. (a) Experimental smoothed I−Vb curves for Vs = +0.2 V and Vs = −0.3 V,11 which are nearly symmetric and suggest that the two Vsvalues approximately correspond to mates of a pair of states related by a charge-conjugation transformation. To emphasize this symmetry, the signs of the current and bias voltage of the curve for Vs = +0.2 V have been reversed, and the current values have been multiplied by c ≃ 0.7. To improve visibility, the curve for Vs = 0.2 V has been shifted upward by 20 pA. (b) TVS curves obtained by redrawing the experimental I− Vb curves for Vs = 0.2 V and Vs = −0.3 V.11

(1)

The reorganization is described by an effective coordinate Q, λ is the total (inner/intramolecular- and outer/solvent-) reorganization energy, η = Veq − Vs the overpotential, and Veq the equilibrium potential. The voltage division factor γ and solvent gating efficiency ξ are coefficients ranging between 0 and 1. Equation 1 embodies an important charge conjugation symmetry εr(1 − Q , −η , −Vb) = −εr(Q , η , Vb)

on the validity of the 2sETM for azurin and calls for a further clarification of the TVS data.11 The aforementioned fact represents only one severe challenge to the 2sETM, which is directly related to the experimental TVS findings.11 We do not aim here at an exhaustive critical analysis of the 2sETM. Still, the presentation of two further drawbacks of the 2sETM is useful, because it makes it clear why a different framework is needed to correctly interpret the TVS and related transport data in azurin. A further important challenge to 2sETM concerns the behavior of the on-resonance current Ipeak(Vb) = maxη|I(Vb; η)| established in earlier experiments on azurin.16 The experimental data revealed an almost linear dependence of Ipeak vs Vb.16 This dependence severely contrasts with the pronounced superlinear dependence predicted by the 2sETM, which is expressed by

(2)

It expresses the fact that, whatever the transport mechanism (e.g., nonadiabatic or adiabatic), the n-(electron-)type conox duction through an oxidized molecule (ηox < 0, Vox s > Veq, Q = 0) and the p-(hole-)type conduction through a reduced red molecule (ηred > 0, Vred = 1) whose active level is s < Veq, Q ox red located symmetrically (η = −η ) should yield currents of the same magnitude I(−Vb; −η) = −I(Vb; −η). Vtr is a property of the I−Vb curve. If the equilibrium potential lay midway between the Vs-values used in experiment,11 that is, V̅ sym eq = (0.2 − 0.3)/2 V = −50 mV, the corresponding Vtr’s should be of equal magnitude. The fact that ox the above values satisfy Vred tr ≈ −Vtr ≈ 0.4 V as well as the overall appearance of the full experimental curves for V̅ red = s −0.3 V and V̅ ox = 0.2 V (cf. Figure 1a and b) can be taken as a s strong indication that the actual value of Veq should be very close to V̅ sym eq = −50 mV. Drawbacks of the Two-Step Electron Transfer Model. The experimental TVS data have been analyzed within the 2sETM by employing Veq = +0.16 V,11 a value substantially different from V̅ sym eq . This large difference raises serious doubts

⎡ β⎛ eV ⎞2 ⎤ Ipeak(Vb) = (Vb exp⎢ − ⎜λ − b ⎟ ⎥ 2 ⎠⎦ ⎣ 4λ ⎝ ⎤ ⎡β ≈ (Vb exp⎢ ( −λ + eVb)⎥ ⎦ ⎣4

(3) (4)

Here β−1 = kBT = 25.7 meV at the room temperature T = 298.16 K, and the prefactor ( is expressed by eq S14 (throughout the label S refers to the SI). Equation 3 follows from the general formula of the current I within the 2sETM, expressed by eq S12 of the SI, which predicts a peak in the current at η = ηmax = −(γ − 1/2)Vb/ξ. 25799



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one gets a level density (α ≡ 2(2m)1/2/ℏ = 1.025)1/2 Å−1 eV−1/2)

Figure 2, which depicts the experimental dependence measured in azurin (taken from the inset in Figure 3 of ref

ρ3D =

a3α 3 1/2 ε 32π 2

= ε = εF

a3α 2kF 16π 2

≃ 0.54 eV −1 (9)

For the one-dimensional case (more appropriate for atomically sharp STM tips), the value of the level density is ρ1D =

16) along with that obtained by using eqs 3 and 4, demonstrates the invalidity of 2sETM for azurin discussed in the main text even when using the implausibly large value ( = 910 nA/V (see eq 6 and the discussion presented below). The last issue, which we note here, is even more critical, because it is general and not limited to azurin, like the two aforementioned. As demonstrated below, the prefactor ( is drastically overestimated. With realistic parameters, the theoretical currents are more than 3 orders of magnitudes smaller than those measured. By ignoring possible difference between the density of states ρs,t and microscopic transmissions κs,t of two electrodes (a common assumption in the field), κsρs = κtρt = κρ, eqs S14 and S15 yield

e2 ωphκρ 4π

To end this issue, it is also worth pointing out that the basic idea used for justifying eq S12 is that a large number 5 of electrons (a “boost” of electrons, up to hundreds) is coherently transferred across the redox center in a single oxidation− reduction cycle.20 This number can be expressed as20 5≈

which has been taken over from ref 27. Typical times for longitudinal solvent relaxation 2π τrel = ωph

(5)

(6)

(7)

are tens of picoseconds. So, ωph ≈ 0.1 meV, and eq 6 amounts to assume an electrode’s density of states (κ ≲ κad ≡ 1 for the perfect adiabatic case) ρ ≲ 470 eV −1

⎪ eVbκρ /2 for κsρs = κ t ρt = κρ e|Vb| ⎧ =⎨ ⎪ Δε ⎩ eVbκ tρt for κ tρt ≪ κsρs

(12)

One can easily convince oneself that, with the typical estimates of eqs 9 and 10, the occurrence of a “boost” of electrons that amplifies the tunneling current by 2−3 orders of magnitudes can by no means be substantiated even for voltages as large as |Vb| ≈ 1 V. Results Based on the Newns−Anderson Model. The foregoing picture documents an inadequate qualitative and quantitative description of the charge transport in a prototypical redox metalloprotein. We will now consider an alternative transport approach and show that it quantitatively explains the experimental data. This approach is based on an extended Newns−Anderson model for a redox level coupled a bath of classical harmonic (nuclear solvent and intramolecular) phonons, whose effect is embodied in an effective mode Q.24,25 The fully adiabatic picture24,25 adopted here is justified by a hierarchy of three different time scales (τET ≪ τfluct ≪ τmeas) to be discussed below. Within the Newns−Anderson model,24,25,28 the instantaneous tunneling current j mediated by a redox level whose energy offset from the substrate’s Fermi energy is εr at fixed configuration Q can be expressed as29−31

To quantitatively describe the measured currents, refs 11, 18, 19, and 26 employed the following value of the prefactor entering eq S12 ( = 910 nA/V

(10)

So, by comparing eq 8 with eqs 9 and 10, one can see that the value used to quantitatively interpret the transport measurements11,18,19,26,27 has been severely overestimated. From this perspective it is also noteworthy that, for a highly asymmetric situation (κtρt ≪ κsρs), it is the lower density of states that determines the prefactor ( , and this makes the overestimation of ( even more drastic (cf. eqs S14 and S15)

Figure 2. Nearly linear dependence of the on-resonance current Ipeak on Vb found experimentally in azurin16 clearly contrasted with the pronounced superlinear dependence predicted by the 2sETM (eqs 3 and 4). The value λ = 0.66 eV employed for curves based on eqs 3 and 4 have been obtained by constraining the slope at low Vb to that of the experimental curve (( = 910 nA/V, β−1 ≃ 25.7 meV).

(=

aα −1/2 1 aα 2 ε = ≃ 0.07 eV −1 8π 16π kF ε = εF

(8)

Let us compare the above value with those typical for gold electrodes, as those used in the experiments considered here.11,16 Gold electrodes are characterized by the lattice constant a ≃ 4.07 Å and the values of the Fermi velocity, wave vector, and energy vF ≃ 1.4 × 106 m/s, kF ≃ 1.2 Å−1, and εF ≃ 5.6 eV, respectively. For a metal with nearly free electrons (free electron mass m) and an isotropic three-dimensional conduction band with parabolic dispersion εk = ℏ2k2/(2m)

j(Vb; η , Q ) =

ε + eVb ε⎞ 2e ⎛ Γa⎜arctan r − arctan r ⎟ ⎝ h Γ Γ⎠

(13)

Above, Γ= 25800

1 (Γs + Γt) 2

and

2 1 1 = + Γa Γs Γt

(14)



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are the arithmetic and harmonic averages of the broadening functions Γs,t, respectively. Here Γs,t = 2πρs,t = 2s,t

is expressed in terms of the adiabatic (Gibbs free) energy < ad (Q;η,Vb) given by25 0) that contributes to electron tunneling (flat band, or wide-band approximation). In eq 13 and whenever appropriate, the arguments of εr = εr(Q;η,Vb) have been/are omitted for simplicity. Considering an instantaneous current j(Vb;η,Q) at a given (frozen) coordinate Q is meaningful if the two characteristic times described below satisfy the condition τET ≪ τfluct. τET is the characteristic time of the two coherent ETs

τET ≈

+ εrnrs(Q ; η , Vb) +

(20)

Since the Coulomb interaction between two electrons of opposite spins is usually strong, the LUMO’s double occupancy can be neglected, and this justifies the usage of a spinless model.32 For a redox unit embedded in a biased molecular junction (Vb ≠ 0), the instantaneous level occupancy nr(Q;η,Vb) can be expressed as25 nr(Q ; η , Vb) = nrt(Q ; η , Vb) + nrs(Q ; η , Vb)

ℏ 2ℏ = Γ Γs + Γt

1 ωph

τ kBT = rel 2λ 2π

kBT 2λ

(17)

I(Vb; η) = ⟨j(Vb; η , Q )Q ⟩Q ∞

∞

(22)

nrs(Q ; η , Vb) =

Γs ⎛ ε⎞ 2 ⎜1 − arctan r ⎟ ⎝ 2Γ π Γ⎠

(23)

DISCUSSION The present results are important for several reasons. They validate the description of the adiabatic transport in azurin within the Newns−Anderson extended to include an effective reorganizable phonon mode.24 Like any phenomeno-

(18)

The thermal weight 7(Q ; η , Vb) = exp[−β kBT), τfluct ≪ τrel. Notice that the instantaneous current j(Vb;η,Q) results from the redox-mediated coherent tunneling at frozen Q, which occurs within a time scale τET determined by the sum Γs + Γt, wherein the two (electrode-redox and redox-tip) coherent ETs can not be considered as two separate processes. This implies that τET can be shorter than τfluct even if Γt ≪ Γs, as we found to be the case for the experiments in azurin11 (see below). If the two ETs proceed coherently, it is not allowed to consider the tip−redox electron transfer separated from the redox−substrate electron transfer and describe them, say, by separate transfer times τt ≈ h̅/Γt and τt ≈ h̅/Γs. With the presently estimated parameter values for azurin one gets τET ≈ 10 fs and τfluct ≈ 2 ps; so, the condition τET ≪ τfluct is satisfied. The instantaneous current is of little practical relevance because τfluct is much shorter than measurement times τmeas(>1 μs).17,32 The theoretical current I(Vb;η) to be compared with the experimental current should be computed as a temporal average within a time ∼τmeas. Because τmeas is long compared to τfluct, instead of temporal averaging, one can perform ensemble averaging

=

(21)

where

(16)

It is determined by the finite level width Γ = (Γs + Γt)/2 due to the redox couplings to electrodes Γs,t. τfluct is the time wherein thermal fluctuations in the coordinate Q yield an energy shift of the redox level δεr ≈ kBT. It can be estimated as25 τfluct ≈

⎞ Γs ⎛ εr2 ln⎜ 2 + 1⎟ 4π ⎝ Γ ⎠

(19) 25801



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V) coincide, and there are only minor differences for the description of a dif ferent kind of experiments16 performed by a dif ferent group with a dif ferent instrument. The contrast with the description based on the 2sETM is noteworthy; for Vb- and Vs-ranges that significantly overlap, based on the 2sETM refs 17 and 11 found λ = 0.13 eV and λ ≈ 0.6 eV, respectively. The fact that the couplings Γt,s of the redox molecule to the substrate and tip are highly asymmetric (Γt ≪ Γs) represents a new finding reported here. Previous studies assumed Γt = Γs = Γ.11,16−19,24,25 The absence of a direct tip−azurin contact in ref 11, and the fact that the hopping integral = t (cf. eq 14) is determined by the overlap between the electronic wave functions of azurin and tip, which is very sensitive to the spatial separation, makes a value Γt much smaller than Γs plausible. However, potential drops at (polarizable) electrodes may be a significant cause that diminishes the effective bias on the azurin molecule.17 For this reason the presently evaluated δ may be underestimated. The fact that the azurin−tip electron tunneling may be mediated by surface states35,36 may be an important source of reducing Γt. The asymmetry in the molecular couplings to electrodes Γs,t found here is by far larger than that of the voltage division factor γ. Although our value γ = 0.44 ≲ 0.5 ≡ γsym indicates that the substrate−azurin potential difference is slightly smaller than that between azurin and tip, this asymmetry is less pronounced than that found within the 2sETM (γ ≈ 0.1−0.2).11 Most importantly, we have demonstrated that the ECSTM environment has a substantial impact on azurin. As expected from the preliminary analysis of the TVS data11 presented in the beginning, the equilibrium potential Veq = −28 mV turned out to be very close to the midpoint V̅ sym eq = −50 mV between Vs values used in experiment.11 It significantly differs from the value Veq = +160 mV11 used in the TVS analysis based on the 2sETM, which is even larger than the standard redox potential Vredox = +120 mV deduced form the redox midpoint of cyclic voltammograms.17 Transport data acquired in constant bias mode in azurin also suggested a difference between Veq and Vredox.16,17 The fact that the equilibrium potential in ECSTM environment may in principle differ from standard redox potential has been noted, but convincing experimental evidence on this difference37 was missing. The TVS data11 provides the first clear experimental evidence of this fact based, as discussed in the beginning, on a general model- and mechanismindependent argument, namely, the charge conjugation symmetry. It is known32,34,38 that the molecular electroaffinity (LUMO energy with reversed sign via Koopman’s theorem) in solvents is significantly reduced with respect to vacuo. From this perspective, the above result that Veq < Vredox can be rationalized: solvent molecules have more freedom to rearrange in order to stabilize a reduced redox species if they have a (practically) semi-infinite spatial region at their disposal (cyclic voltammetry) than a very limited spatial region (tunneling nanogap in ECSTM setup). This means that the bare LUMO energy ε0r of eq S6 in the former case should be lower than in the latter case. Via eq S9, this implies Vredox > Veq, as is the case in experiments. This indicates that solvent effects on ET in a nanogap are significantly reduced as compared to a (semi)infinite solution, and for this fact we can present a further confirmation. The presently deduced value λ = 0.18 eV is very close to the value Λi = 0.19 eV for the inner-sphere reorganization deduced from resonance Raman intensities,39 but much smaller than the total value Λi + λo ≈ 0.7 eV for

Figure 3. Experimental and theoretical I−Vb curves for Vs = −0.3 V and Vs = 0.2 V (Vtr = 0.412 V, nr = 0.963, and Vtr = −0.3986 V; nr = 0.040, respectively). Parameter values: λ = 0.18 eV, Γ = 70 meV, ξ = 1, γ = 0.44, Veq = −28 mV, δ = Γt/Γ = 1.1 × 10−4. One could note that the relatively large experimental errors, which give the experimental curves of both panels a blurry aspect, leave a certain ambiguity in determining the parameter values that produce the “best” fitting.

Figure 4. Unlike the 2sETM (cf. Figure 2), the present theoretical approach predicts a behavior of the on-resonance current Ipeak which agrees with the nearly linear behavior found in experiment.16

logical approach, the present approach inherently resorts to model parameters, which have to be determined by fitting some data. To be able to rationalize experimental findings, it is important that these model parameters can be transferable from one situation to another. It is of very limited use if, like often the case in studies on charge transfer through redox molecules within the 2sETM, substantial differences in the values of model parameters (especially λ) are needed to describe, for example, experiments conducted in constant bias or variable bias mode, or measurements in variable bias mode at several Vs’s. Importantly, we found that the present transport approach for azurin is robust: the parameter sets needed to explain experiments11 in variable bias mode corresponding to azurin in an oxidized state (Vs = 0.2 V) and a reduced state (Vs = −0.3 25802



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azurin placed in bulk solution.40 From the fact that λ ≈ Λi one should not necessarily conclude that the reorganization in ECSTM environment is almost entirely inner reorganization. Out of the numerous intramolecular phonons,41 only lowfrequency (ωi) modes compatible to eq 17 contribute to λ. Such modes (ωi ≃ 2−3 meV) have been observed in azurin,42 but an analysis of the partial contributions of the various modes to Λi, similar to other cases,32,34 is missing. Nevertheless, the above values reveal a drastic suppression of the solvent reorganization in the nanogap, which is beneficial for ET. Driving forces for biologically relevant reactions are often small (∼0.1 eV), and rapid long-range ET over distances dazurin ∼3−4 nm is possible only for small reorganization energies.40

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The experimental data employed in Figures 1 and 3 represent results of ref 11 generously provided by P. Gorostiza and J. M. Artés, who kindly reprocessed them to facilitate the comparison with the present theory. Financial support by the Deutsche Forschungsgemeinschaft (grant BA 1799/2-1) is gratefully acknowledged.

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CONCLUSION The present theoretical investigation has been motivated by an observation based on a very general argument: whatever the transport mechanism, the transition voltages of (nearly) equal 11 ox magnitude (Vred tr ≈ −Vtr ≈ 0.4 V) found in the experiment must correspond to two (reduced and oxidized) states of azurin (approximately) related to each other by a charge conjugation transformation. The failure of the 2sETM, the model employed in ref 11, demonstrated in the first part naturally calls for an alternative framework. As shown above, the fully adiabatic picture relying upon the Newns−Anderson model represents a viable alternative to the 2sETM, able to excellently describe TVS and other transport data in azurin. We have worked out this transport approach, whose robustness was demonstrated by the transferability of the employed parameters to quantitatively reproduce measurements done in dif ferent modes by dif ferent groups with dif ferent instruments. It allowed revealing important solvent effects on ET in a typical redox metalloprotein placed in a nanogap: (i) a significant change of the equilibrium potential as compared to the standard redox potential, (ii) a very pronounced asymmetry of the couplings between the redox unit and the two (STM-tip and substrate) electrodes (Γt ≠ Γt), and (iii) a drastic reduction of the solvent reorganization energy. The experimental TVS results11 suggested, for example, intriguing possibilities of gating between different conductance regimes through the proximity of redox centers and protein− protein recognition. They are per se sufficiently interesting to motivate the present theoretical work. Considering some other experimental transport data for azurin16,17 in addition to the TVS data11 has been merely done to emphasize the robustness of the extended Newns−Anderson model as compared to the 2sETM. This model appears to clearly meet the need to obtain consistent fittings across experiments. An extensive comparison between the two aforementioned models, which has much wider implications than the discussion of TVS and available experimental transport data for azurin, will make the object of a separate publication.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

Details on the redox level under bipotentiostatic control, on the vibrationally coherent two-step electron transfer model (2sETM), and the computation of the adiabatic transport within the Newns−Anderson model, and remarks on the parameter values. This material is available free of charge via the Internet at http://pubs.acs.org. 25803



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(18) Pobelov, I. V.; Li, Z.; Wandlowski, T. Electrolyte Gating in Redox-Active Tunneling Junctions. An Electrochemical STM Approach. J. Am. Chem. Soc. 2008, 130, 16045−16054. (19) Li, Z.; Liu, Y.; Mertens, S. F. L.; Pobelov, I. V.; Wandlowski, T. From Redox Gating to Quantized Charging. J. Am. Chem. Soc. 2010, 132, 8187−8193. (20) Kuznetsov, A. M.; Ulstrup, J. Mechanisms of in Situ Scanning Tunnelling Microscopy of Organized Redox Molecular Assemblies. J. Phys. Chem. A 2000, 104, 11531−11540. (21) Bâldea, I. Revealing Molecular Orbital Gating by Transition Voltage Spectroscopy. Chem. Phys. 2010, 377, 15−20. (22) Bâldea, I. Ambipolar Transition Voltage Spectroscopy: Analytical Results and Experimental Agreement. Phys. Rev. B 2012, 85, 035442. (23) Bâldea, I. Effects of Stochastic Fluctuations at MoleculeElectrode Contacts in Transition Voltage Spectroscopy. Chem. Phys. 2012, 400, 65−71. (24) Schmickler, W. A Theory of Adiabatic Electron-Transfer Reactions. J. Electroanal. Chem. 1986, 204, 31−43. (25) Medvedev, I. G. Tunnel Current through a Redox Molecule Coupled to Classical Phonon Modes in the Strong Tunneling Limit. Phys. Rev. B 2007, 76, 125312. (26) Li, C.; Mishchenko, A.; Li, Z.; Pobelov, I.; Wandlowski, T.; Li, X. Q.; Würthner, F.; Bagrets, A.; Evers, F. Electrochemical GateControlled Electron Transport of Redox-Active Single Perylene Bisimide Molecular Junctions. J. Phys.: Condens. Matter 2008, 20, 374122. (27) Albrecht, T.; Guckian, A.; Ulstrup, J.; Vos, J. Transistor Effects and in Situ STM of Redox Molecules at Room Temperature. IEEE Trans. Nanotechnol. 2005, 4, 430−434. (28) Muscat, J.; Newns, D. Chemisorption on Metals. Prog. Surf. Sci. 1978, 9, 1−43. (29) Haug, H.; Jauho, A.-P. Quantum Kinetics in Transport and Optics of Semiconductors; Springer Series in Solid-State Sciences: Berlin, 1996; Vol. 123. (30) Peskin, U. An Introduction to the Formulation of Steady-State Transport through Molecular Junctions. J. Phys. B: Atom. Molec. Opt. Phys. 2010, 43, 153001. (31) Bâldea, I.; Kö ppel, H. Sources of Negative Differential Resistance in Electric Nanotransport. Phys. Rev. B 2010, 81, 193401. (32) Bâldea, I. Extending the Newns-Anderson Model to Allow Aanotransport Studies Through Molecules with Floppy Degrees of Freedom. Europhys. Lett. 2012, 99, 47002. (33) Schmickler, W. Investigation of Electrochemical Electron Transfer Reactions with a Scanning Tunneling Microscope: A Theoretical Study. Surf. Sci. 1993, 295, 43−56. (34) Bâldea, I.; Köppel, H.; Wenzel, W. (4,4′)-Bipyridine in Vacuo and in Solvents: A Quantum Chemical Study of a Prototypical Floppy Molecule from a Molecular Transport Rerspective. Phys. Chem. Chem. Phys. 2013, 15, 1918−1928. (35) Bâldea, I. Transition Voltage Spectroscopy in Vacuum Break Junction: Possible Role of Surface States. Europhys. Lett. 2012, 98, 17010. (36) Wu, K.; Bai, M.; Sanvito, S.; Hou, S. Origin of the Transition Voltage in Gold-Vacuum-Gold atomic junctions. Nanotechnology 2013, 24, 025203. (37) Kuznetsov, A. N.; Schmickler, W. Mediated Electron Exchange between an Electrode and the Tip of a Scanning Tunneling Microscope - A Stochastic Approach. Chem. Phys. 2002, 282, 371− 377. (38) Bâldea, I. Demonstrating Why DFT-Calculations for Molecular Transport in Solvents Need Scissor Corrections. Electrochem. Commun. 2013, 36, 19−21. (39) Fraga, E.; Webb, M. A.; Loppnow, G. R. Charge-Transfer Dynamics in Plastocyanin, a Blue Copper Protein, from Resonance Raman Intensities. J. Phys. Chem. 1996, 100, 3278−3287. (40) Gray, H. B.; Malmströ m, B. G.; Williams, R. Copper Coordination in Blue Proteins. J. Biol. Inorg. Chem. 2000, 5, 551−559.

(41) One should note that only slow phonons contribute to the adiabatic current expressed by eq 18. According to ref 24, all lowfrequency harmonic modes (let they be solvent modes or lowfrequency intramolecular modes) can be replaced by a single effective harmonic mode (Q). Fast intramolecular phonons of energies ℏωm > Γ do not reorganize by classical thermal activation and have to be treated quantum mechanically. Via the associated inelastic tunneling, they give rise to peaks in the second derivative d2I/dV2 at resonant voltage values eV = ℏωm, which can identified, e.g., in experiments directly acquiring the second derivative of the current,3 but are by no means observable in the presently considered experimental results, characterized by substantial errors, as depicted by the blurry curves of Figure 3. (42) Paciaroni, A.; Bizzarri, A. R.; Cannistraro, S. Low Frequency Vibrational Anomalies in Hydrated Copper Azurin: A Neutron Scattering and {MD} Simulation Study. J. Mol. Liq. 2000, 84, 3−16.

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