The Effect of the Chemical Potentials of Electrodes on Charge

Subscriber access provided by Nottingham Trent University

C: Energy Conversion and Storage; Energy and Charge Transport

The Effect of the Chemical Potentials of Electrodes on Charge Transport across Molecular Junctions Geng-Min Lin, Chih-Hsun Lin, Hao Howard Peng, Han Hsiao, TsaiHui Wang, Ching-Hwa Ho, Hsiu-Fu Hsu, and Chun-hsien Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b05927 • Publication Date (Web): 14 Aug 2019 Downloaded from pubs.acs.org on August 20, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

The Effect of the Chemical Potentials of Electrodes on Charge Transport across Molecular Junctions Geng-Min Lin,†,§ Chih-Hsun Lin,†,§ Hao Howard Peng,†,§ Han Hsiao,† Tsai-Hui Wang,‡ Ching-Hwa Ho,†,* Hsiu-Fu Hsu,‡,* and Chun-hsien Chen†,* †Department

of Chemistry and Center for Emerging Material and Advanced Device, National Taiwan University, Taipei, Taiwan 10617. ‡Department of Chemistry, Tamkang University, New Taipei City, Taiwan 25137. ABSTRACT: Charge transport across molecular junctions can be described by G = Gcontactexp(–βL), envisioned as sequential propagation through electrode-molecule contacts (Gcontact) and the molecular backbone (exp(–βL)). How Gcontact and exp(–βL) are modulated by the chemical potentials of the electrodes (EF), although essential, remains relatively unexplored because EF is typically driven by the applied Vbias and hence limited to a small range in that a large Vbias introduces complicated transport pathways. Herein, the interrelated EF and Vbias are electrochemically disentangled by fixing Vbias at a small value while potentiostatically positioning the electrode EF in a 1.5 V range. The results show that EF affects Gcontact more pronouncedly than the molecular backbone. For the covalently anchored Au–C junctions, the energy level of the frontier molecular orbital (EFMO) is found to shift nonlinearly as EF changes; |EFMO – EF| is independent of EF in the range of –0.25~0.00 V (vs. EAg/AgCl) and is narrowed by ~32% at 0.00~0.75 V. These findings are elucidated by the refined Simmons model, Newns-Anderson model, and single-level Breit-Wigner formula and quantitatively shed light on the influence of electrodes on the molecular orbitals (viz., the self-energy, Σ).

1. INTRODUCTION Single-molecule nanoelectronics that steer electric behavior via molecular orbitals (MOs) represent an ultimate miniaturization goal that the persistent quest for Moore's law can strive for.1 To master the electrical performance, the basics of how the devices respond to an external voltage must be comprehended. The typical testbed for theoretical and experimental studies is a two-terminal metal-moleculemetal (MMM) junction.2-13 Charge transport across the junction is driven by the applied bias voltage, 𝑉 , corresponding to the difference between the chemical potentials (μ) of the electrodes (viz., the Fermi level, 𝐸 ). For homologous molecules, the measured junction conductance is are, found to be 𝐺 = 𝐺 exp(−𝛽 𝑛), where n, β, and 𝐺 respectively, the number of repeat units, tunneling decay ). constant, and contact conductance (also termed 𝐺 According to literature studies that cross-examined the junction conductance for electrode materials (e.g., Au, Ag, Cu, and Pt), the exponential term is correlated to the electrode Fermi level by |𝐸 − 𝐸 |,14-16 where RL denotes the resonant level responsible for charge transport. The pre) scales the junction conductexponential factor ( 𝐺 ance,12,13,17-18 and the importance is self-evident. Studies of have focused on the strength of molecule-electrode in𝐺 teractions by pairing a variety of molecular anchoring

groups and electrode materials.10-13,19-21 Explorations of are how the chemical potential of the electrode affects 𝐺 lacking. The conductance at the molecule-electrode contact (𝐺 ) can be derived from the extrapolated intercept of the junction conductance (𝐺) plotted against the number of repeat against the molecular length).17,22-26 To units (or of 𝐺 acquire the single-molecule conductance, the applied 𝑉 is small and presumably within the ohmic range where the current is linearly proportional to 𝑉 and passes through the origin (viz., zero bias). Hence, the reported single-molecule conductance and contact conductance represent properties at zero bias. At a large bias (e.g., Scheme 1a), a mixture of transport mechanisms may collectively occur and complicate the interpretation.4,5,27 Accordingly, the incannot be extracted from the trinsic effects of 𝐸 on 𝐺 prevalent 2-electrode experimental scheme. The aforementioned problem associated with a large bias is herein overcome through the integration of conductance measurements with an electrochemical bipotentiostat, which drives the chemical potentials of the two working electrodes against that of a reference electrode (explicitly, μ = e𝑉 = 𝐸 ) and concurrently keeps 𝑉 constant (Scheme and the chemical 1b). Therefore, the contribution of 𝑉 potentials to G can be decoupled. The model compounds are

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

electrochemically inactive α,ω-alkanes and OPEn (oligo(phenylene-ethynylene)s) with anchoring groups of amino and thiol for alkanes and covalently bridged C−Au for OPEn; their respective large and small HOMO-LUMO gaps and contact strengths are suitable for studying the effect of 𝐸 on 𝐺 , and β, which is essential to characterizing the behavior of molecular junctions. The experimental results, for the first time, unambiguously reveal how the contact conductance is associated with 𝐸 and responds more strongly than β. Molecular junctions with stronger headgroup-electrode interactions are more significantly modulated by a change in 𝐸 . Scheme 1. Potential waveforms and Fermi levels of electrodes

(a) Vbias scan in a conventional two-electrode configuration. (b) EF scan with EF being varied against the chemical potential of a reference electrode using an electrochemical bipotentiostat. The bias between the two working electrodes (VSTM tip and Vsubstrate) is fixed. The lower panels illustrate how the EF of the two electrodes responds to the (a) Vbias and (b) EF scans.

This article is organized as follows. After the method section, first presented are the experimental results of Scheme 1b; junction conductance measured at a fixed 𝑉 as a function of the potentiostatted 𝐸 . Subsequently, Simmons model and Newns-Anderson model are reformulated to make clear the dependence of 𝐺 and β on 𝐸 in Sections 3.2a and 3.2b. Section 3.3 emphasizes on the interfacial molecule-electrode hybridization to pictorially manifest the effect of 𝐸 on 𝐺 . Section 3.4 shows the results of i−𝑉 scans at a series of potentiostatted 𝐸 . The shift of the energy level for the frontier molecular orbital (EFMO) due to 𝐸 is extracted by our modified single-level Breit-Wigner method derived from Newns-Anderson model. Finally, our findings are concluded in Section 4. 2. EXPERIMENTAL SECTION 2.1. Chemicals. Literature procedures were adapted to prepare oligo(phenylene-ethynylene)s, OPEn (n = 1−3), by the reaction of AuClPPh3 with the corresponding trimethylsilyl protected alkynes in MeOH containing NaOH at room temperature.28,29 Details and characterizations are described in the Supporting Information. Other reagents were used as received. 2.2. EC-STM-Based Single-Molecule Conductance. The STM (scanning tunneling microscope) tips were gold wires (99.95%, 0.25 mm in diameter, Leesan, Tainan, Taiwan)

Page 2 of 10

handmade using a pair of scissors. The substrate was 100nm-thick gold films thermally evaporated on glass slides. The tip, except for the apex, was covered by ethylene vinyl acetate (EVA, Ted Pella, Inc.) to reduce current leakage in the solution with a high ionic strength. Similarly, for the substrate, only a small portion (~2 mm in diameter) was exposed, and the rest was insulated by a sheet of EVA. EVA is stable in PC (propylene carbonate, Sigma-Aldrich),30 which has a low volatility suitable for long-duration experiments. Hence, PC was dried and employed as the solvent. The supporting electrolyte was 0.1 M (Bu4N)(ClO4) (TCI). The reference electrode was custom-made Ag/AgCl(s) containing 0.1 M (Bu4N)Cl (Alfa Aesar) in PC. The porous frit consisted of a commercial pencil core made of graphite mixed with a clay binder (grade 4B, Pilot). A Luggin capillary was utilized to cope with the small size of the EC-STM cell. EC-STM-based experiments were carried out with a NanoScopeIIIa controller. A signal access module (Veeco) was utilized to regulate the electrochemical potentials of the electrodes via a universal bipotentiostat (Veeco) and to obtain the resulting conducting current via a data acquisition system (24-bit PXI-4461, National Instruments) by using customized LabVIEW programs (National Instruments) at a rate of 40,000 points/sec. To generate molecular junctions, the STS (scanning tunneling spectroscopy) mode was adapted with the cycle mode configured for the feedback loop. The tip was set to repeatedly hit and move away from the substrate at a frequency of 1.99 Hz. The retraction of the tip was 50 nm and created a molecular junction with host molecules in the surrounding area. The currents passing across molecular junctions were acquired as a function of the tip stretching distance, i(s). For each molecule, the conductance histogram was prepared without data selection from more than 2000 recorded i(s) traces. The distributed range of the molecular conductance values was the reference values needed to maintain junctions to obtain itip–wk–𝑉wk curves, in which the waveform is illustrated in Figure 1b. To fit the SLBW model, the number of i–𝑉 curves acquired at each 𝑉wk ranged from 1027 (0.75 V) to 4067 (0.25 V). 2.3. Simulations. Transmission spectra were calculated using the Atomistix Toolkit package (QuantumATK 2017.2, Synopsys) implemented with density functional theory (DFT) and the nonequilibrium Green's function (NEGF).31,32 The exchange-correlation potential was described by the Perdew-Zunger local density approximation (LDA).33 Geometry optimization was performed with a force tolerance of 0.05 eV/Å, a mesh cutoff of 150 Ry, periodic boundary conditions with 3 × 3× 100 sampling, and an electronic temperature of 300 K. The electronic structure was obtained based on the double ζ with polarization (DZP) basis set for Au, H, C, N, and S atoms. 3. RESULTS AND DISCUSSION 3.1. β and 𝑮𝐧 𝟎 as a Function of Chemical Potentials. Figure 1a reveals that, under a small fixed 𝑉 of 50 mV, the junction conductance increases34-36 upon continuously driving 𝑉 positively from −0.5 V to +1.0 V against 𝐸 / (viz., , see Scheme 1b). farther from the vacuum level, 𝐸

2


Page 3 of 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Consistent trends were found for the conductance measurements carried out at a fixed 𝑉 of +0.5 V and −0.5 V (Figure 1b). The nominal molecular conductance at +0.5 V is larger than that at −0.5 V for the corresponding molecule. The conductance value at +1.0 V could not be determined due to the low probability of junction formation. Probably due to the difference in the preferential junction geometries, the conductance revealed from i−𝑉 scanning under fixed 𝑉 is different from those under fixed 𝑉 (Figure 1b).37 For example, the latter yields a junction conductance of 1.43 (±1.11) x 10−4 G0 at +0.5 V and 4.81 (±5.25) x 10−5 G0 at −0.5 V for OPE3. The ratio between these values is approximately three, while a difference of approximately 150% is found for the continuous 𝑉 scanning method (Figure 1a). are affected by the change in To correlate how β and 𝐺 𝑉 , typical procedures that plot G against the number of repeat units are employed (Figure 1b). For junctions of the same homologous series yet different 𝐸 with and without electrochemical control, the slopes (β) are similar, but the intercepts (𝐺 ) are quite different. The results are summarised in Table 1. The values of 𝐺 are significantly dependent on 𝑉 (viz., 𝐸 ) for S−Au and CC−Au contacts. Hence, the shape of the i–𝑉 characteristics for molecule junctions is partially described by the 𝐸 –dependent 𝐺 . 3.2. Simmons Model and Newns-Anderson Model. To describe the electrochemical effect on the molecular junctions, the present DFT-based computations introduce a modified self-energy term to shift the energy level of the molecule.34,35 Alternatively, our modeling focuses on the potentiostat-driven Fermi level of the working electrode. For α,ω-alkanes and OPEs shorter than the phase-breaking mean free path of electrons under a small bias, the consensus is that the transport occurs through direct tunneling (i.e., super-exchange). The mechanism features the negative exponential relationship between the conductance and molecular dimensions given by 𝐺 = 𝐺 𝑒𝑥𝑝(−𝛽 𝑛), consistent with our findings displayed in Figure 1b and Table 1. Accordingly, the Landauer formula (Equation 1) valid for coherent transport is suitable for modelling the present cases;38 for an electron with energy E propagating through the molecular junction, the current (I) is described by integrating the transmission probability T(E) over the bias range.

Figure 1. Effect of the electrochemical potential of the electrode on the single-molecule conductance. (a) Normalized conductance as a function of Vwk for (upper) H2N(CH2)6NH2, (middle) HS(CH2)6SH, and (lower) OPE3. (b) Junction conductance measured at a Vwk of (solid) –0.5 V and (open) +0.5 V against EAg/AgCl for (square) H2N(CH2)nNH2, (circle) HS(CH2)nSH, and (triangle) OPEn. The molecular junctions were obtained by ECSTM (electrochemical scanning tunneling microscopy).30,39-42 Instead of the silver-wire quasi-reference electrode typically used in the literature reports, the reference electrode was an organic-phase Ag/AgCl(s) electrode prepared in propylene carbonate (PC) containing 0.1 M tetrabutylammonium chloride, (Bu4N)Cl. The numbers of G–Vwk traces used to plot Panel a are 897 for H2N(CH2)6NH2, 3826 for HS(CH2)6SH, and 1824 for OPE3. Conditions: Vbias, 50 mV; solution, solute in PC with the supporting electrolyte of 0.1 M (Bu4N)(ClO4).

𝐼=

𝑇(𝐸) 𝑓 (𝐸) − 𝑓 (𝐸) 𝑑𝐸

(1)

where 𝑓 (𝐸) − 𝑓 (𝐸) represents 𝑉 , with f(E) being the Fermi function and the subscript L (R) denoting the left (right) electrode. The Fermi function is formulated as 𝑓 ( ) (𝐸) = 1 + (𝐸 − 𝜇 ( ) )/𝜏 , in which μ is the chemical potential of the electrode and τ is the fundamental temperature associated with the Boltzmann distribution factor (τ = kBT). By taking advantage of the step-function-like property of 𝑓 ( ) (𝐸) and the small 𝑉 employed in the present

Table 1. β and Gcontact at Selected Chemical Potentials. H2N(CH2)nNH2 (n = 4, 5, 6)

HS(CH2)nSHb (n = 4, 5, 6)

OPEn, L-CC(φ-CC)n-L (n = 1, 2, 3; φ = −(p-C6H4)−; L = AuPPh3)

Vwk (Volt)a

(per CH2)

β

Gn=0 (x 10–2 G0)

(per CH2)

β

Gn=0 (x 10–2 G0)

−0.50

1.02 (±0.01)c

5.05 (±0.28)

1.03 (±0.07)

10.0(±3.37)

2.18 (±0.29)

4.47(±2.83)

0.50

0.96 (±0.05)

6.67 (±1.55)

0.96 (±0.15)

13.0(±9.73)

2.19 (±0.13)

11.5 (±3.27)

NAd

1.04 (±0.03)

6.56 (±0.93)

1.01 (±0.02)

10.1(±1.09)

2.13 (±0.31)

8.97(±5.91)

β

(per φ-CC)

Gn=0 (x 10–2 G0)

a. The

potentials of the substrate were potentiostated against EAg/AgCl. The conditions were the same as those described in Figure 1. the literature,12,43-45 multiple conductance values have been reported for alkanedithiols, termed HC and LC for high and low conductance, respectively. In the present study, the reported β and Gn=0 were derived from the HC of the conductance histograms. c. The values in parentheses are the standard deviation of the Gaussian fit to the 1D conductance histograms. d. NA: without electrochemical control, viz., measured by the typical scheme of the two-electrode configuration. Other experimental conditions were identical to those of the upper rows, including the electrolyte, solvent, and EVA (ethylene vinyl acetate)-coated tip and substrate with limited exposed areas. The conductance histograms for OPEn with n = 1, 2, and 3 peaked at 10–2.05, 10–2.75, and 10–3.90 Go, respectively. b. In

3



study, the junction conductance can be properly simplified to Equation 2, where G0 is the conductance quantum (2e2/h). 𝑇(𝐸 ) = 𝐺 𝑇(𝐸 )

𝐼=

(2)

Based on Equation 2, the Simmons model and the NewnsAnderson model, two of the most prevalent approaches, are and β upon ademployed to elucidate the behaviors of 𝐺 justment of 𝐸 . We will show that both the potential barrier-based Simmons model and DOS (density of states)is more based Newns-Anderson model indicate that 𝐺 sensitive than β to the chemical potential of the electrodes. 3.2a. Simmons Model. The Simmons model considers the molecular junction to be a rectangular potential barrier at zero bias. For an electron travelling in a perfect one-dimensional manner from the left electrode through the junction to the right electrode, the wavefunctions of the three regions can be obtained by solving the time-independent Schrödinger equations. Ψ (𝑥) = 𝑒𝑥𝑝(𝑖𝑘𝑥) + 𝑟 ∙ 𝑒𝑥𝑝(−𝑖𝑘𝑥) (𝑥) = 𝐴

Ψ

𝑒𝑥𝑝(𝑖𝑘𝑥) + 𝐵

𝑒𝑥𝑝(−𝑖𝑢𝑥)

Ψ (𝑥) = 𝑡 ∙ 𝑒𝑥𝑝(𝑖𝑘𝑥) where r (t) describes the propagation of a reflecting (transmitting) electron to the left (right) electrode, and k and u are the magnitudes of the wave vectors (k = (2mE/ћ2)1/2, u = (2m(E − V0)/ћ2)1/2). For measurements conducted at a fixed and small bias, the proposed potential profile is a perfect rectangle with a barrier height of V0. The amplitude of the transmission wave, t, can be written in terms of k and u under the conditions that, at the boundaries, the wavefunction and its first derivative are continuous. 𝑡=

(

( (

(

)

)

) ) (

)

Therefore, the transmission function can be calculated. 𝑇(𝐸) = |𝑡| = 𝑡 ∙ 𝑡 ∗ = (

)

(

)

Assuming that the length of the barrier, L, is sufficiently large such that the first term of the denominator dominates, T(E) can be further approximated as an exponential function. (

𝑇(𝐸) =

)

𝑒𝑥𝑝(2𝑖𝑢𝐿)

(3)

Substituting Equation 3 into Equation 2 gives the following. 𝐺

=

(

)

𝐺

conductance is more sensitive than the tunneling decay constant to the working potential, consistent with the experimental observations displayed in Figure 1b. 3.2b. Newns-Anderson Model. The Newns-Anderson model is relatively complex yet better defined in that it includes characteristics of charge transport through molecular junctions, such as the resonant level (deduced from the unperturbed molecular Hamiltonian, Hmol), the electrodes' DOS (inherited through the Green's function, 𝔾), the molecule-electrode coupling function (Γ), and the electrode selfenergy (Σ, the influence of electrodes). Σ presumably only affects the immediate anchoring group and is described by ( ) Σ ( ) = (Δ ( ) )( ) ∓ 𝑖(Γ ( ) )( ) , where the negative (positive) sign specifies the retarded (advanced) self-energy with superscript R (A) and the subscript  (r) indicates the left (right) anchoring group in contact with the electrode. The real part (Δ) corresponds to the shift of the resonant level (𝐸 ) arising from the molecule-electrode interactions. For the imaginary part (𝑖Γ), a stronger coupling more significantly broadens the resonant level and confers on Γ ( ) a faster electron transfer rate from the left electrode to the bridging molecule (from the molecule to the right electrode). To formulate 𝑇(𝐸 ) of Equation 2, the identity operator (I) is introduced to enable matrix operation for the single-par( ) ( ) = (𝐸 ∙ 𝐼 − 𝐻 −Σ − ticle Green's function, 𝔾 ( ) Σ ) . The matrix form of the retarded molecular Green's function (𝔾 ) is presented in Equation S25. Under the tight-binding model and the present cases of off-resonance tunneling (viz., a negligible resonance integral between , explicitly, 𝑡 = |𝐸 − 𝜀 − neighboring sites 𝑡 Σ ( ),( ) |, where εRL is the on-site energy of the resonance level), 𝑇(𝐸 ) is expressed as follows. 𝑇(𝐸 ) = 𝑇𝑟(Γ 𝔾

𝛽=

) ℏ

The contact conductance is to the second order with respect to the Fermi level, while the tunneling decay constant has a square root relation with the Fermi level. The results derived from the Simmons model suggest that the contact

) = Γ , Γ

,

|𝔾

,



𝔾

,

𝐺

= 𝐺 𝑇(𝐸 ) = 𝐺

=

=

(

, )(



, | 

∙

|

(6)

|

,

∙

)(

,

(7)

)

𝑒𝑥𝑝(−𝛽 𝑛) |

|

∙

(8)

×





(4) (5)

Γ 𝔾

where Γ , (Γ , ) is the upper left (lower right) entry of ma( ) trix Γ (Γ ). 𝔾 , addresses the propagation of an electron between the molecular termini from the left (right) to the right (left) and is the entry at row  and column r of ma( ) ( ) trix 𝔾 . 𝔾 , , 𝑇(𝐸 ), and the junction conductance are calculated. Equations 9 and 10 demonstrate that and βn are 𝐸 dependent. The details are elaborated 𝐺 in the Supporting Information.

𝐺 (

Page 4 of 10

=

, | 

|

∙

,

|

|

∙



𝐺

(9)



𝛽 = 2𝑙𝑛

(10)

is to the fourth power of 𝐸 , while βn has a loga𝐺 rithmic relation with 𝐸 , consistent with the experimental is more sensitive to a change in 𝐸 . results that 𝐺 OPEs have three types of resonance integrals between is replaced by the terms neighboring carbons. Hence, 𝑡

4


Page 5 of 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a, b, and c, representing carbon-carbon interactions of triple bonds (ethynes), single bonds (ethyne-benzene), and those in the benzene ring, respectively (Chart 1). Using mathematical procedures similar to the alkane case, the conductance of OPEs is derived. 𝐺

=

,

⋅

,

,

⋅

,

(

)

Chart 1. Notations of the hopping integrals between adjacent carbon atoms of OPE1.

generally far from the electrodes' 𝐸 and thus contribute little to the transmission function. Therefore, the single-level representation of the molecular Hamiltonian is suitable for the system. Accordingly, Equation 6 yields the transmission coefficient associated with the FMO dominant in electron transport as follows, which is known as the SLBW formula:3,52-55 𝑇(𝐸, 𝐸

,Γ ,Γ ) =

(

)

(

(13)

)

where 𝐸 is the energy of the FMO and is shifted from that of the isolated form (𝐸 ) due to the coupling of the orbital to the electrodes; ΓL and ΓR denote the coupling of the orbital to the left and right electrodes, respectively, and are responsible for the electron transport rate.

Accordingly, Equations 11 and 12 give 𝐺 and βn, which exhibit the same 𝐸 dependence as those of alkanes. 𝐺

,

=

,

𝛽 = 12 𝑙𝑛

(

) /

,

𝐺

(11)

,

(12)

Both the Simmons model and the Newns-Anderson model support the experimental findings that under a fixed small responds to 𝐸 more sensitively than does βn. bias, 𝐺 This finding is consistent with that of a recent study in which the 𝐸 was adjusted by the use of Ag, Au, and Pt electrodes by Xie, Bâldea and Frisbie.46 3.3. Transmission Spectra: Headgroup-Electrode Hybridization. Equations 9 and 11 show that 𝐺 is described by 𝜀( ) , Γ, and Σ, symbolizing the on-site energy of the anchoring group, molecule-electrode coupling function, and electrode self-energy, respectively. To visualize the associated interactions at the molecule-electrode interfaces, Figure 2 illustrates the electron charge density isosurfaces with the dominant eigenstates at zero bias (𝐸 − 𝐸 = 0) of the corresponding transmission spectra. The shapes of the isosurfaces localize at the headgroup-electrode contacts and are distinct from those of the FMOs (frontier molecular orbitals). In addition, the HOMO and LUMO transmission bands are typically more than 4 eV away from 𝐸 for α,ωhexanes.47-50 Accordingly, at zero bias, the features indicated by the arrows are not attributed to the molecular frameworks but to the headgroup-electrode hybridization, specifically between the p-orbitals of the anchoring groups and d-orbitals of the contact gold atoms (also see Figure S7).51 To the best of our knowledge, protocols to simulate transmission spectra as a function of the electrochemical potentials of electrodes have not been established. Hence, a simulation of the 𝐸 -dependent headgroup-electrode hybridisation by mimicking the experimental conditions of Figure 1 (viz., scanning 𝐸 under a fixed and small 𝑉 ) is unavailable at present. 3.4. i–𝑽𝐛𝐢𝐚𝐬 Curves at Potentiostatted 𝑽𝐰𝐤 and the Single-Level Breit-Wigner Method (SLBW). The formalism of the Newns-Anderson model provides helpful insight into how the anchoring group and repeat units contribute to the transmission function of a molecule. In practice, the diagonalized molecular Hamiltonian makes available a direct representation of the energies of MOs whose energy levels are

Figure 2. Transmission spectra and isosurface plots at the electrode-anchoring group interfaces. (a) Linear-scale transmission spectra at zero bias for H2N(CH2)6NH2 (solid line), HS(CH2)6SH (dotted), and OPE3 (dashed). The frontier molecular orbitals (FMOs) of α,ω-alkanes are more than 3 eV away from EF. For the junction of OPE3, simulations (Figure S8) show that under applied bias voltages, the HOMO peak position shifts away from EF. (b) Isosurface plots associated with transmission spectra at zero bias for H2N(CH2)nNH2 (upper panel), HS(CH2)nSH (middle), and OPE3 (lower). The contribution to electron transport is not from FMOs but mainly from the interactions between the contact gold atoms and the anchoring groups. The isovalues are 0.6 for α,ω-alkanes and 0.25 for OPE3.

To unravel how 𝐸 responds to a change in 𝑉 (viz., 𝐸 /e), the experimental i– 𝑉 curves are fitted by the SLBW formula to derive 𝐸 as a function of 𝐸 , which is presently inaccessible by using commercial simulation packages. Based on the Landauer formula, the integration of Equation 13 yields Equation 14, and the analytical solution is shown in Equation 15, which is different from that of typical two-electrode junctions because only 𝑉 is swept in Equation 13 beand 𝑉 is fixed (see Figure 3a). 𝐸 comes (𝐸 + 𝛾𝑒𝑉), where the superscript denotes the energy level of the FMO at zero bias and 𝛾 describes the shift of the FMO per volt induced by the applied bias. 𝐼= 𝐼=

(

𝑡𝑎𝑛

(

)

)

𝑑𝐸 + 𝑡𝑎𝑛

(14) ( (

) )

(15)

5



To fit the modified SLBW formula for OPE3, thousands of i–𝑉 curves were acquired at each 𝑉 (see Figures 3a and S6). Fitting for alkanediamines and dithiols could not be performed due to the insufficient junction lifetimes for the curves. The same experiacquisition of unbroken i–𝑉 mental challenges limit the positive boundary of 𝑉 .

Figure 3. Vwk-dependent 𝐸 derived from the SLBW model. (a) Potential waveforms of VSTM tip and Vwk (viz., Vsubstrate) where the latter was potentiostatically fixed against EAg/AgCl. In the lower panel, the dotted line indicates the zero-bias potential. Typically, only those waveforms exhibiting two complete cycles (thick purple segments) for each junction were collected for the data analysis. Scan rate: 100 V/s. (b) Fitting results of 𝐸 (V vs. EAg/AgCl, blue) for i–𝑉 curves obtained at a series of fixed Vwk (green). The numbers in black are the difference between the fitted 𝐸 and the applied Vwk. Note that EAg/AgCl is −4.7 eV from 𝐸 and, therefore, the work function of Au(111) is at +0.6 V relative to EAg/AgCl. The electrochemical conditions were the same as those in Figure 1.

Intriguingly, at 𝑉 ≥ 0.25 V, the negative-bias currents are larger than the positive-bias currents (Panels f–h of Figure S6). For 𝑉 at 0.75 V, the rectification ratio reaches half-an order of magnitude at |𝑉 | of ±1.5 V. This finding suggests that the HOMO is the dominant FMO for electron transport (see the illustration in Figure S8). The opposite is found for 𝑉 at −0.75 V, indicative of a LUMO-dominant pathway. However, the rectification is not as apparent, the data quality is inferior to that at more positive 𝑉 due to the relatively noisy background and the difficulty in maintaining stable −CC−Au interactions at negative potentials. derived for 𝑉 ≥ −0.25 V Hence, Figure 3b presents 𝐸 and plotted with respect to 𝐸 / . For 𝑉 from −0.25 V to +0.25 V, the |𝐸 − 𝐸 | gap is reduced by 0.04 eV or by 10%. When 𝑉 goes further positively from 0.00 to 0.75 V, − 𝐸 | gap narrows steadily by 0.24 eV (viz., 32%), the |𝐸 indicative of HOMO pinning for OPE3 at the electrode. This nonlinear dependence34-36 on the potentiostatted 𝐸 (viz., Fermi level pinning) is distinct from those of monolayer − 𝐸 | gap appears to be linearly junctions where the |𝐸 proportional to the Fermi levels of Ag, Au, and Pt electrodes.2,3,46,56,57 Although interesting, the discrepancy cannot be examined in depth because of the apparent difference in the anchoring groups, molecular structures, and environments (close-packed monolayer versus single molecule surrounding by polar solvent and charged electrolytes). The fitting results also provide some experimental information that may shed light on the correlation of the electrode's self-energy (Σ) with the potential of the working electrodes, which has never been experimentally or theoretically discussed before. As mentioned above, the real to part (Δ) of Σ describes the energy shift from 𝐸

Page 6 of 10

as a result of the molecule-electrode interactions. 𝐸 Hence, the relatively small changes in |𝐸 − 𝐸 | (≤ 0.24 eV, Figure 3b) imply significant energy shifts from 𝐸 at these 𝑉 . The energy shift of MOs, however, cannot be attributed to 𝑉 , as the largest energy shift due to the variation of 𝛾 is only 0.008 eV (see page S9 of the Supporting Information for arithmetic details). Therefore, the shift should originate from Δ. Explicitly, the differences in Δ values with the four 0.25-V increments in 𝑉 from −0.25 V to +0.75 V are 0.31, 0.14, 0.20, and 0.17 eV. This result means that for the HOMO-dominant transport case, when the working potential increases, the change in Δ makes the bias window closer to the transmission peak. The opposite is true for 𝑉 decreasing from −0.25 V to −0.75 V when the LUMO is the dominant channel. With the contribution from Δ to the molecular junction, the conductance variation under a range of 𝑉 can be attributed to the bias window approaching the peak of the transmission function. This general description, however, requires more experiments and theoretical works to elucidate the fundamental principles. 4. CONCLUSIONS The efficiency of charge transport across molecular juncand by the associated headgrouptions is gated by 𝐺 electrode interactions. Although electrode Fermi levels are involved in the interactions, experimental attempts to deare limited because, for termine the effect of 𝐸 on 𝐺 conventional two-electrode platforms, 𝐸 is interrelated with 𝑉 . Upon driving the electrodes' 𝐸 , the synchrointroduces additional nised development of a large 𝑉 transport mechanisms and makes extraction of the contribution of 𝐸 to the measured junction conductance unfeasible. To decouple the effect of 𝐸 from that of 𝑉 , this study employs an electrochemical bipotentiostat to position 𝐸 of 50 mV. over a range of 1.5 V under a small fixed 𝑉 Moreover, an organic-phase Ag/AgCl reference electrode equipped with a Luggin capillary is introduced to this research field to confer stable potentials on the electrodes of the substrate and the STM tip. This study reveals the 𝐸 deat 1.0 V pendence of the contact conductance, with 𝐺 ) larger than that at –0.5 V by ca. 30%, 50%, and (vs. 𝐸 / 100%, respectively, for junctions of hexanediamine, hexanedithiol, and OPE3. The effect of 𝐸 on the value of β, in contrast, appears to be relatively insignificant. To explain and β as a function of 𝐸 this finding, equations of 𝐺 are derived from the potential barrier-based Simmons model and DOS-based Newns-Anderson model. Both modis more sensitive than β to a change els indicate that 𝐺 in the electrode 𝐸 , consistent with the conductance measurements under electrochemical control and, for the first time, mathematically unravelling the physics behind the conductance dependence on 𝑉 . Furthermore, the modified-SLBW model provides another aspect on the interpretation of the 𝑉 dependent conductance; the shift of 𝐸 under electrochemical control reveals the effect of the selfenergy from the electrodes. Simulations of zero-bias transmission spectra show that the HOMO/LUMO bands of α,ωalkanes are more than 4 eV away from 𝐸 and thus contribute negligibly to the transmission coefficient. Hence, the dominant eigenstate at 𝐸 is proposed to involve the d-orbital of the gold atom at the headgroup-electrode contact.

6


Page 7 of 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


However, developing calculation packages that can simulate junction conductance under electrochemical control remains challenging. GLOSSARY h: Planck constant E: energy of electron injected from the electrodes ħ: h/2π kB: Boltzmann constant T: temperature T(E): transmission function for a tunnelling electron with energy E fL(R)(E): Fermi function of the left (right) electrode μL(R): chemical potential of the left (right) electrode 𝐸 : Fermi level of the system k and u: magnitudes of the wave vectors V0: height of the rectangular barrier L: length of the barrier t: amplitude of the transmission wave G: Green's function Γ: molecule-electrode coupling function Σ: electrode self-energy I: identity operator tma: hopping integral between the methylene group and the anchoring group tmm’: hopping integral between two adjacent methylene groups ERL: energy shift of the resonant level ( ) 𝔾 : matrix form of the retarded (advanced) molecular Green's function R ( A) : retarded (advanced) molecular Green's function Gmol R : matrix element at row l and column r of GMR Gmol ,lr ΣRL((RA)) : retarded (advanced) self-energy from the left (right) electrode ε(r): on-site energy of the left (right) anchoring group εm: on-site energy of the methylene group ε: on-site energy of the carbon atoms in OPE series a, b, c: hopping integral of adjacent carbon atoms in OPE series : energy of the FMO in its isolated form 𝐸 : 𝐸 at zero bias 𝐸 𝐸 : dominant energy level in the modified Breit-Wigner model γ: the shift of the FMO per volt induced by the applied bias

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website. The preparation of the organic-phase Ag/AgCl reference electrode; conductance histograms; i–Vbias curves of OPE3 at Vwk of −1.00 ~ 0.75 V (vs. EAg/AgCl); SLBW fitting results; NEGF-DFT calculated transmission spectra under Vbias; derivation details of the molecular conductance.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (C.-H.H.) *E-mail: [email protected] (H.-F.H.) *E-mail: [email protected] (C.-h.C.)

Author Contributions G.-M.L., C.-H.L., and H.H.P. contributed equally.

‡

ORCID Chun-hsien Chen: 0000-0001-5507-3248

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors are grateful to Mr. Ta-Cheng Ting, Er-Chien Horng (NTU), and Dr. Yamuna Ezhumalai (TKU) for the development of this project at the early stage and to NTU, TKU and MOST (106-2119-M-002-015, 106-2113-M-002-019-MY2, 106-2113M-032-005) for financial support. The authors also thank Ms. Fung-Mei Chen for the preparation of the TOC graph.

REFERENCES (1) Moore, G. E. Cramming More Components onto Integrated Circuits. Electronics 1965, 38, 114-117. (2) Kim, B.; Choi, S. H.; Zhu, X. Y.; Frisbie, C. D. Molecular Tunnel Junctions Based on Π-Conjugated Oligoacene Thiols and Dithiols between Ag, Au, and Pt Contacts: Effect of Surface Linking Group and Metal Work Function. J. Am. Chem. Soc. 2011, 133, 1986419877. (3) Xie, Z.; Bâldea, I.; Smith, C. E.; Wu, Y.; Frisbie, C. D. Experimental and Theoretical Analysis of Nanotransport in Oligophenylene Dithiol Junctions as a Function of Molecular Length and Contact Work Function. ACS Nano 2015, 9, 8022-8036. (4) Ding, W.; Koepf, M.; Koenigsmann, C.; Batra, A.; Venkataraman, L.; Negre, C. F. A.; Brudvig, G. W.; Crabtree, R. H.; Schmuttenmaer, C. A.; Batista, V. S. Computational Design of Intrinsic Molecular Rectifiers Based on Asymmetric Functionalization of NPhenylbenzamide. J. Chem. Theory Comput. 2015, 11, 5888-5896. (5) Zhang, G.; Ratner, M. A.; Reuter, M. G. Is Molecular Rectification Caused by Asymmetric Electrode Couplings or by a Molecular Bias Drop? J. Phys. Chem. C 2015, 119, 6254-6260. (6) Nichols, R. J.; Higgins, S. J. Single-Molecule Electronics: Chemical and Analytical Perspectives. Annu. Rev. Anal. Chem. 2015, 8, 389-417. (7) Xin, N.; Guan, J.; Zhou, C.; Chen, X.; Gu, C.; Li, Y.; Ratner, M. A.; Nitzan, A.; Stoddart, J. F.; Guo, X. Concepts in the Design and Engineering of Single-Molecule Electronic Devices. Nat. Rev. Phys. 2019, 1, 211-230. (8) Higgins, S. J.; Nichols, R. J. Metal/Molecule/Metal Junction Studies of Organometallic and Coordination Complexes; What Can Transition Metals Do for Molecular Electronics? Polyhedron 2018, 140, 25-34. (9) Fu, M.-D.; Chen, I-W. P.; Lu, H.-C.; Kuo, C.-T.; Tseng, W.-H.; Chen, C.-h. Conductance of Alkanediisothiocyanates: Effect of Headgroup−Electrode Contacts. J. Phys. Chem. C 2007, 111, 1145011455. (10) Adak, O.; Korytár, R.; Joe, A. Y.; Evers, F.; Venkataraman, L. Impact of Electrode Density of States on Transport through Pyridine-Linked Single Molecule Junctions. Nano Lett. 2015, 15, 37163722. (11) Li, Z.; Li, H.; Chen, S.; Froehlich, T.; Yi, C.; Schonenberger, C.; Calame, M.; Decurtins, S.; Liu, S. X.; Borguet, E. Regulating a Benzodifuran Single Molecule Redox Switch via Electrochemical Gating and Optimization of Molecule/Electrode Coupling. J. Am. Chem. Soc. 2014, 136, 8867-8870. (12) Ko, C.-H.; Huang, M.-J.; Fu, M.-D.; Chen, C.-h. Superior Contact for Single-Molecule Conductance: Electronic Coupling of Thiolate and Isothiocyanate on Pt, Pd, and Au. J. Am. Chem. Soc. 2010, 132, 756-764.

7



(13) Huang, M.-J.; Hsu, L.-Y.; Fu, M.-D.; Chuang, S.-T.; Tien, F.-W.; Chen, C.-h. Conductance of Tailored Molecular Segments: A Rudimentary Assessment by Landauer Formulation. J. Am. Chem. Soc. 2014, 136, 1832-1841. (14) Engelkes, V. B.; Beebe, J. M.; Frisbie, C. D. Length-Dependent Transport in Molecular Junctions Based on Sams of Alkanethiols and Alkanedithiols: Effect of Metal Work Function and Applied Bias on Tunneling Efficiency and Contact Resistance. J. Am. Chem. Soc. 2004, 126, 14287-14296. (15) Peng, Z.-L.; Chen, Z.-B.; Zhou, X.-Y.; Sun, Y.-Y.; Liang, J.-H.; Niu, Z.-J.; Zhou, X.-S.; Mao, B.-W. Single Molecule Conductance of Carboxylic Acids Contacting Ag and Cu Electrodes. J. Phys. Chem. C 2012, 116, 21699-21705. (16) Wang, Y.-H.; Hong, Z.-W.; Sun, Y.-Y.; Li, D.-F.; Han, D.; Zheng, J.-F.; Niu, Z.-J.; Zhou, X.-S. Tunneling Decay Constant of Alkanedicarboxylic Acids: Different Dependence on the Metal Electrodes between Air and Electrochemistry. J. Phys. Chem. C 2014, 118, 1875618761. (17) Zang, Y.; Pinkard, A.; Liu, Z.-F.; Neaton, J. B.; Steigerwald, M. L.; Roy, X.; Venkataraman, L. Electronically Transparent Au-N Bonds for Molecular Junctions. J. Am. Chem. Soc. 2017, 139, 1484514848. (18) Magoga, M.; Joachim, C. Conductance and Transparence of Long Molecular Wires. Phys. Rev. B 1997, 56, 4722-4729. (19) Chen, F.; Li, X.; Hihath, J.; Huang, Z.; Tao, N. Effect of Anchoring Groups on Single-Molecule Conductance: Comparative Study of Thiol-, Amine-, and Carboxylic-Acid-Terminated Molecules. J. Am. Chem. Soc. 2006, 128, 15874-15881. (20) Park, Y. S.; Whalley, A. C.; Kamenetska, M.; Steigerwald, M. L.; Hybertsen, M. S.; Nuckolls, C.; Venkataraman, L. Contact Chemistry and Single-Molecule Conductance: A Comparison of Phosphines, Methyl Sulfides, and Amines. J. Am. Chem. Soc. 2007, 129, 15768-15769. (21) Shih, K.-N.; Huang, M.-J.; Lu, H.-C.; Fu, M.-D.; Kuo, C.-K.; Huang, G.-C.; Lee, G.-H.; Chen, C.-h.; Peng, S.-M. On the Tuning of Electric Conductance of Extended Metal Atom Chains Via Axial Ligands for [Ru3(μ3-dpa)4X2]0/+ (X = NCS−, CN−). Chem. Commun. 2010, 46, 1338-1340. (22)Prieto-Ruiz, J. P.; Miralles, S. G.; Großmann, N.; Aeschlimann, M.; Cinchetti, M.; Prima-García, H.; Coronado, E. Design of Molecular Spintronics Devices Containing Molybdenum Oxide as Hole Injection Layer. Adv. Electron. Mater. 2017, 3, 1600366. (23) Kaliginedi, V.; Rudnev, A. V.; Moreno-Garcia, P.; Baghernejad, M.; Huang, C.; Hong, W.; Wandlowski, T. Promising Anchoring Groups for Single-Molecule Conductance Measurements. Phys. Chem. Chem. Phys. 2014, 16, 23529-23539. (24) Su, T. A.; Li, H.; Klausen, R. S.; Kim, N. T.; Neupane, M.; Leighton, J. L.; Steigerwald, M. L.; Venkataraman, L.; Nuckolls, C. Silane and Germane Molecular Electronics. Acc. Chem. Res. 2017, 50, 1088-1095. (25) Zhao, X.; Huang, C.; Gulcur, M.; Batsanov, A. S.; Baghernejad, M.; Hong, W.; Bryce, M. R.; Wandlowski, T. Oligo(Aryleneethynylene)S with Terminal Pyridyl Groups: Synthesis and Length Dependence of the Tunneling-to-Hopping Transition of Single-Molecule Conductances. Chem. Mater. 2013, 25, 4340-4347. (26) Moreno-García, P.; Gulcur, M.; Manrique, D. Z.; Pope, T.; Hong, W.; Kaliginedi, V.; Huang, C.; Batsanov, A. S.; Bryce, M. R.; Lambert, C.; Wandlowski, T. Single-Molecule Conductance of Functionalized Oligoynes: Length Dependence and Junction Evolution. J. Am. Chem. Soc. 2013, 135, 12228-12240. (27)Beebe, J. M.; Kim, B.; Gadzuk, J. W.; Frisbie, C. D.; Kushmerick, J. G. Transition from Direct Tunneling to Field Emission in MetalMolecule-Metal Junctions. Phys. Rev. Lett. 2006, 97, 026801. (28) Khairul, W. M.; Porrès, L.; Albesa-Jové, D.; Senn, M. S.; Jones, M.; Lydon, D. P.; Howard, J. A. K.; Beeby, A.; Marder, T. B.; Low, P. J. Metal Cluster Terminated “Molecular Wires”. J. Cluster Sci. 2006, 17, 65-85. (29) Simpson, C. D.; Brand, J. D.; Berresheim, A. J.; Przybilla, L.; Räder, H. J.; Müllen, K. Synthesis of a Giant 222 Carbon Graphite Sheet. Chem.–Eur. J. 2002, 8, 1424-1429.

Page 8 of 10

(30) Ting, T.-C.; Hsu, L.-Y.; Huang, M.-J.; Horng, E.-C.; Lu, H.-C.; Hsu, C.-H.; Jiang, C.-H.; Jin, B.-Y.; Peng, S.-M.; Chen, C.-h. EnergyLevel Alignment for Single-Molecule Conductance of Extended Metal-Atom Chains. Angew. Chem. Int. Ed. 2015, 54, 15734-15738. (31) Smidstrup, S.; Stradi, D.; Wellendorff, J.; Khomyakov, P. A.; Vej-Hansen, U. G.; Lee, M.-E.; Ghosh, T.; Jónsson, E.; Jónsson, H.; Stokbro, K. First-Principles Green's-Function Method for Surface Calculations: A Pseudopotential Localized Basis Set Approach. Phys. Rev. B 2017, 96, 195309. (32) Brandbyge, M.; Mozos, J.-L.; Ordejón, P.; Taylor, J.; Stokbro, K. Density-Functional Method for Nonequilibrium Electron Transport. Phys. Rev. B 2002, 65, 165401. (33) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B 1991, 43, 1993-2006. (34) Li, Z.; Smeu, M.; Rives, A.; Maraval, V.; Chauvin, R.; Ratner, M. A.; Borguet, E. Towards Graphyne Molecular Electronics. Nat. Commun. 2015, 6, 6321. (35) Brooke, R. J.; Jin, C.; Szumski, D. S.; Nichols, R. J.; Mao, B.-W.; Thygesen, K. S.; Schwarzacher, W. Single-Molecule Electrochemical Transistor Utilizing a Nickel-Pyridyl Spinterface. Nano Lett. 2015, 15, 275-280. (36) Díez-Pérez, I.; Li, Z.; Guo, S.; Madden, C.; Huang, H.; Che, Y.; Yang, X.; Zang, L.; Tao, N. Ambipolar Transport in an Electrochemically Gated Single-Molecule Field-Effect Transistor. ACS Nano 2012, 6, 7044-7052. (37) Bai, J.; Daaoub, A.; Sangtarash, S.; Li, X.; Tang, Y.; Zou, Q.; Sadeghi, H.; Liu, S.; Huang, X.; Tan, Z.; Liu, J.; Yang, Y.; Shi, J.; Meszaros, G.; Chen, W.; Lambert, C.; Hong, W. Anti-Resonance Features of Destructive Quantum Interference in Single-Molecule Thiophene Junctions Achieved by Electrochemical Gating. Nat. Mater. 2019, 18, 364-369. (38) Datta, S., Quantum Transport: Atom to Transistor. Cambridge University Press: Cambridge, UK, 2005. (39) Xiang, L.; Palma, J. L.; Li, Y.; Mujica, V.; Ratner, M. A.; Tao, N. Gate-Controlled Conductance Switching in DNA. Nat. Commun. 2017, 8, 14471. (40) Li, Y.; Haworth, N. L.; Xiang, L.; Ciampi, S.; Coote, M. L.; Tao, N. Mechanical Stretching-Induced Electron-Transfer Reactions and Conductance Switching in Single Molecules. J. Am. Chem. Soc. 2017, 139, 14699-14706. (41) Nichols, R. J.; Higgins, S. J. Single Molecule Nanoelectrochemistry in Electrical Junctions. Acc. Chem. Res. 2016, 49, 26402648. (42) Baghernejad, M.; Zhao, X.; Ørnsø, K. B. l.; Füeg, M.; MorenoGarcia, P.; Rudnev, A. V.; Kaliginedi, V.; Vesztergom, S.; Huang, C.; Hong, W.; Broekmann, P.; Wandlowski, T.; Thygesen, K. S.; Bryce, M. R. Electrochemical Control of Single-Molecule Conductance by Fermi-Level Tuning and Conjugation Switching. J. Am. Chem. Soc. 2014, 136, 17922-17925. (43) Guo, S.; Hihath, J.; Díez-Pé rez, I.; Tao, N. Measurement and Statistical Analysis of Single-Molecule Current-Voltage Characteristics, Transition Voltage Spectroscopy, and Tunneling Barrier Height. J. Am. Chem. Soc. 2011, 133, 19189-19197. (44) Leary, E.; Zotti, L. A.; Miguel, D.; Márquez, I. R.; PalominoRuiz, L.; Cuerva, J. M.; Rubio-Bollinger, G.; González, M. T.; Agrait, N. The Role of Oligomeric Gold–Thiolate Units in Single-Molecule Junctions of Thiol-Anchored Molecules. J. Phys. Chem. C 2018, 122, 3211-3218. (45) Nichols, R. J.; Higgins, S. J. Single Molecule Electrochemistry in Nanoscale Junctions. Curr. Opin. Electrochem. 2017, 4, 98-104. (46) Xie, Z.; Bâldea, I.; Frisbie, C. D. Determination of EnergyLevel Alignment in Molecular Tunnel Junctions by Transport and Spectroscopy: Self-Consistency for the Case of Oligophenylene Thiols and Dithiols on Ag, Au, and Pt Electrodes. J. Am. Chem. Soc. 2019, 141, 3670-3681. (47) Frederiksen, T.; Munuera, C.; Ocal, C.; Brandbyge, M.; Paulsson, M.; Sanchez-Portal, D.; Arnau, A. Exploring the Tilt-Angle Dependence of Electron Tunneling across Molecular Junctions of SelfAssembled Alkanethiols. ACS Nano 2009, 3, 2073-2080.

8


Page 9 of 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(48) Hüser, F.; Solomon, G. C. From Chemistry to Functionality: Trends for the Length Dependence of the Thermopower in Molecular Junctions. J. Phys. Chem. C 2015, 119, 14056-14062. (49) Foti, G.; Sánchez-Portal, D.; Arnau, A.; Frederiksen, T. Role of K-Point Sampling in the Supercell Approach to Inelastic Electron Tunneling Spectroscopy Simulations of Molecular Monolayers. Phys. Rev. B 2015, 91, 035434. (50) Brisendine, J. M.; Refaely-Abramson, S.; Liu, Z.-F.; Cui, J.; Ng, F.; Neaton, J. B.; Koder, R. L.; Venkataraman, L. Probing Charge Transport through Peptide Bonds. J. Phys. Chem. Lett. 2018, 9, 763767. (51) Quek, S. Y.; Choi, H. J.; Louie, S. G.; Neaton, J. B. Length Dependence of Conductance in Aromatic Single-Molecule Junctions. Nano Lett. 2009, 9, 3949-3953. (52) Isshiki, Y.; Fujii, S.; Nishino, T.; Kiguchi, M. Fluctuation in Interface and Electronic Structure of Single-Molecule Junctions Investigated by Current versus Bias Voltage Characteristics. J. Am. Chem. Soc. 2018, 140, 3760-3767.

(53) Komoto, Y.; Fujii, S.; Nakamura, H.; Tada, T.; Nishino, T.; Kiguchi, M. Resolving Metal-Molecule Interfaces at Single-Molecule Junctions. Sci. Rep. 2016, 6, 26606. (54) Frisenda, R.; van der Zant, H. S. J. Transition from Strong to Weak Electronic Coupling in a Single-Molecule Junction. Phys. Rev. Lett. 2016, 117, 126804. (55) Frisenda, R.; Perrin, M. L.; Valkenier, H.; Hummelen, J. C.; van der Zant, H. S. J. Statistical Analysis of Single-Molecule Breaking Traces. Phys. Status Solidi B 2013, 250, 2431-2436. (56) Smith, C. E.; Xie, Z.; Baldea, I.; Frisbie, C. D. Work Function and Temperature Dependence of Electron Tunneling through an NType Perylene Diimide Molecular Junction with Isocyanide Surface Linkers. Nanoscale 2018, 10, 964-975. (57) Xie, Z.; Bâldea, I.; Frisbie, C. D. Why One Can Expect Large Rectification in Molecular Junctions Based on Alkane Monothiols and Why Rectification is so Modest. Chem. Sci. 2018, 9, 4456-4467. .

9



Page 10 of 10

Insert Table of Contents artwork here

10 ACS Paragon Plus Environment

The Effect of the Chemical Potentials of Electrodes on Charge

Recommend Documents