Additive Electron Pathway and Nonadditive Molecular Conductance

Article pubs.acs.org/JPCC

Additive Electron Pathway and Nonadditive Molecular Conductance by Using a Multipodal Bridging Compound Manabu Kiguchi,*,† Yuuta Takahashi,† Shintaro Fujii,† Masayoshi Takase,‡ Tomoyuki Narita,‡ Masahiko Iyoda,*,‡ Masayo Horikawa,§ Yasuhisa Naitoh,§ and Hisao Nakamura*,§ †

Department of Chemistry, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 W4-10 Ookayama, Meguro-ku, Tokyo 152-8551, Japan ‡ Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan § Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology, Central 2, Umezono 1-1-1, Tsukuba, Ibaraki 305-8568, Japan S Supporting Information *

ABSTRACT: We designed and synthesized a new quadrivial anchoring unit 4-TEB, to construct a stable single-molecule junction with gold electrodes, which should have equivalent conducting electron pathways between two electrodes. The conductances of single-molecule junctions comprising 4-TEB and its bidirectional counterpart 2-TEB were determined to be 2.7 × 10−4G0 (2e2/h) and 5.0 × 10−5G0, respectively, by using scanning tunneling microscope break junction (STM-BJ) techniques. The single 4-TEB molecule junction had higher stability and conductivity compared to those of the single 2-TEB molecule junction. Although the number of electron pathways from/to the electrode to/from the molecule was additive using the equivalent multianchoring, the conductance of the singlemolecule junction was not additive. From first-principles electronic transport calculations, the mechanism for the new quadrivial 4-TEB single-molecule junction involved an overlap resonance effect to the HOMO conducting orbital, giving rise to tunneling. Using fixed nanogap electrodes, we constructed stable molecular junctions of 4-TEB and observed symmetric peaks in the derivative of the conductance−voltage (G−V) curves, which were assigned to electron transport through the HOMO on the basis of theoretical calculations.

1. INTRODUCTION Fabricating molecular electronic devices in which individual molecules are utilized as active electronic components is a promising approach for the ultimate miniaturization and integration of electronic devices.1,2 The design of a metal− molecule contact in the single molecular junction is critically important to realize the molecule electronic devices since the metal−molecule contact plays a decisive role in determining the mechanical stability of the device and tunes its conductivity. While various anchoring units have been investigated, most of the molecular junctions only have two anchoring units; i.e., a single anchor is attached to each side of the electrode.3−14 Here, we are interested in the multipodal anchoring units due to the improvement of the mechanical stability and conductivity and the appearance of the quantum interference effects. Actually, the robust surface attachment and high conductivity were achieved using the pyridine-based tripodal anchoring unit.15 As the scale of the electric device approaches to the atomic scale, quantum effects begin to appear in the electric transport process.16−25 Vazequet et al. found the experimental evidence of constructive quantum interference by investigating the © 2014 American Chemical Society

molecular systems that contain two intramolecular electron transfer paths with a common linker at each end.16 Guedon et al. found that the degree of interference can be controlled by simple chemical modifications of the molecular wire by investigating the self-assembled monolayers of π-conjugated molecular wires.18 Quantum interference effects and Fano resonances have also been investigated by the theoretical calculation.20−25 The quantum interference effect should also appear in the single molecular junction with multipodal anchoring units, while there are few studies in regard to this subject. A simple classical picture shows us that conductance increases additively by increasing the spatially equivalent electron pathway by introducing multipodal anchors. However, conductance can be nonadditive, if the quantum interference effect appears. In our previous study of the pyridine-based unit, all tripodal anchors appeared not to be equivalently connected to the electrodes, and thus, the quantum interference effect has not been clarified Received: October 9, 2013 Revised: January 9, 2014 Published: February 18, 2014 5275

dx.doi.org/10.1021/jp4100262 | J. Phys. Chem. C 2014, 118, 5275−5283

The Journal of Physical Chemistry C

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yet in the single molecular junction with multipodal anchoring units.15 In this study, we have newly designed and investigated a quadrivial anchoring unit in terms of not only constructing a stable single molecular junction with a gold electrode but also providing equally connected multiple conduction pathways between two electrodes to investigate the quantum interference effect. Although a large number of oligo(phenylene ethynylene)s (OPEs) have been reported involving the attachment to one or two electrodes via Au−S linkages,26−28 quadrivial analogues29 have not been studied in detail for conductive molecular junction. Herein a 1,2,4,5-tetrakis(2mercaptothienylethynyl)benzene derivative 4-TEB and its bidirectional counterpart 2-TEB have been investigated (Chart 1).30 The limited conformational flexibility of the

Scheme 1. Synthesis of 2Ac-TEB and 4Ac-TEB

Chart 1

using a two-step procedure, starting from 3,4-dibutylthiophene, in 75% overall yield. 2Ac-TEB and 4Ac-TEB are highly soluble in common organic solvents and stable for at least one year at room temperature in air.

multianchoring units of quadrivial 4-TEB should allow (1) the formation of an equally connected robust and conductive molecular junction with gold electrodes and (2) the enhancement of the conductivity attributable to 2-fold para-substituted conduction pathways compared to that of 2-TEB. Since 4-TEB and 2-TEB have essentially identical molecular lengths and πconjugations between the electrodes, we focus here on the effect of number of anchoring units, conduction pathways, and conductance. Comparison of the junction formation probability as well as conductance and current−voltage (I−V) characteristics of the molecular junctions using the scanning tunneling microscope (STM) break junction technique and fixed planar electrodes are discussed. Furthermore, the first-principle electric transport calculations were conducted to analyze the mechanism of the new quadrivial 4-TEB and its bidirectional counterpart 2-TEB.

3. SINGLE CONDUCTANCE MEASUREMENTS Conductance measurements of single molecular junctions were performed using a scanning tunneling microscopic break junction technique on an electrochemical scanning tunneling microscope (STM) (Pico-SPM, Molecular Imaging Co.) with a Nano Scope IIIa controller (Digital Instruments Co.). Details of the experimental design used in this study have previously been reported by some of the present authors.7,8,10−14 Briefly, the STM tip was made of a Au wire (diameter ≈ 0.25 mm, purity >99%). The Au(111) substrate was prepared by flame annealing, followed by quenching. The concentrations of solutions of 4Ac-TEB or 2Ac-TEB in tetraethyleneglycol dimethyl ether (tetraglyme) or mesitylene were adjusted to 1 mM, and just before conductance measurements, a few drops of aqueous NH3 were added to the solutions for the in situ deprotection of acetylthio groups. The STM tip was repeatedly moved in and out of contact with the substrate in the solution at a rate of 50 nm/s at room temperature. Conductances were measured during the breaking process with an applied bias of 20 mV between the tip and the substrate. All statistical data were obtained using a large number (>20 000) of individual conductance traces. The experiments were performed on three distinct samples. We prepared each sample (solution, Au sample, and Au tip) from the beginning. Figure 1a−d shows typical conductance traces when the Au contacts were broken in solutions containing 2-TEB or 4-TEB (see 2D conductance histogram in Figure S2, Supporting Information). Most of the conductance traces showed a 1G0 (2e2/h) plateau, indicating the formation of Au atomic contacts before the Au contacts were broken (not shown in the figure).

2. SYNTHESIS We considered the limited conformational flexibility of multipodal bridging molecules adsorbed on Au electrodes when designing 4-TEB. A tetrakis(3,4-dibutylthienylethynyl)benzene bridge should maintain a sufficient electron density of states to form electron pathways between the electrodes. Furthermore, the eight butyl groups on the thiophene rings increase the solubility and decrease the π−π stacking interaction between the molecules. Since 4-TEB is unstable due to the instability of 2-ethynyl-5-mercaptothiophene units, 4Ac-TEB with acetylthio protecting groups was synthesized because molecular junctions easily form upon deprotection via successive formation of Au−S linkages on the Au electrodes. 4Ac-TEB and 2Ac-TEB were synthesized via Sonogashira coupling of 1,4-di- (2) and 1,2,4,5-tetraethynylbenzene (6) with 3,4-dibutyl-5-2-cyano(ethyl)thio-2-iodothiophene (3), followed by deprotection and acetylation, in 90% and 36% overall yields, respectively (Scheme 1). Key iodide 3 was prepared by 5276



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which could prevent the formation of multiple molecular bridges between Au electrodes. Compared with the last plateau due to the formation of the single molecular bridge, a plateau due to the formation of double molecular bridges is less certain for the conductance traces of 4-TEB (Figure 1a). A similar trend can be seen for the conductance traces of 2-TEB (Figure 1b). We believe that, despite the bulky shape of 4-TEB, 4-TEB has finite probability to form double molecular bridges between Au electrodes. This is possibly due to its planar structure that faces parallel to each other in the junction. The stabilities of the single-molecule junctions were evaluated by using the last plateau length of the conductance traces during breaking of the contacts, which corresponded to the single-molecule junction. Figure 2a shows a distribution of

Figure 2. Distribution of (a) the plateau length and (b) break distance of the single-molecule junctions. The red and black curves are the results for the 4-TEB and 2-TEB junctions, respectively. The distribution was obtained from 1000 conductance traces without data selection. The maximum break distances were obtained by linear least-squares fitting of the curve at the break distance regime of 1.5− 1.9 nm (4-TEB) and 0.8−1.2 nm (2-TEB).

Figure 1. (a−d) Typical conductance traces and (e,f) histograms when the Au contacts were broken in a tetraglyme solution containing (a,c,e) 4-TEB or (b,d,f) 2-TEB. The conductance traces are plotted on linear and semi log scales for (a,b) and (c,d), respectively. Dotted lines are guides for the eye. The conductance histogram was obtained from 1000 conductance traces without data selection. The tunneling background was subtracted (see Supporting Information for details). Each histogram was normalized to the number of traces used to construct the histogram. The bin sizes were 10−6 and 10−7G0 for (c) and (d), respectively.

the last plateau lengths for the 2-TEB and 4-TEB molecular junctions (detailed discussion in Supporting Information). The average lengths of the last plateau were 0.24 and 0.04 nm for the 4-TEB and 2-TEB molecular junctions, respectively. The longer last plateau indicated that the 4-TEB junction had higher stability and that the 4-TEB molecule was bound to Au electrodes via all four anchor units. The formation probability and atomic configuration of the molecular junctions were estimated from detailed analysis of the conductance traces (see detailed discussion in the Supporting Information). The formation probabilities were 99% and 59% for the 4-TEB and 2-TEB molecular junctions, respectively. The formation of the 4-TEB and 2-TEB molecular junctions was supported by the analysis of the gap size obtained by the conductance traces during breaking of the contacts. Figure 2b shows distributions of the break distances for the 2-TEB and 4TEB molecular junctions. The peak at 0.2 nm for the 2-TEB molecular junction corresponds to the tunnel gap, where molecules are not trapped between the gap when the contact is broken. The maximum values were 1.2 and 1.9 nm for the 2TEB and 4-TEB molecular junctions, respectively, which meant that the corresponding gap sizes were 1.6 and 2.3 nm, respectively. The distances between the sulfur atoms of the thiol groups on the opposite sides of the chain (i.e., para position of the central benzene) are 1.9 nm in the case of 2TEB. On the other hand, in the case of 4-TEB, the distances between the sulfur atoms parallel and perpendicular to the long axis of the molecule (i.e., meta or ortho position of the central benzene) are 1.8 and 0.7 nm, respectively. Considering the structural features of 4-TEB, a two-point linkage of 1.9 nm or a

In solutions containing 2-TEB or 4-TEB, the conductance decreased in a stepwise fashion (dotted lines in Figures 1a,b). The conductance value of the plateau was an integer multiple of ∼3 × 10−4G0 for 4-TEB and 5 × 10−5G0 for 2-TEB. Most of the steps showed a positive or negative slope, which originates from a slight structural change in the molecular junction during breaking of the junction. The corresponding conductance histograms (Figures 1e,f) showed distinctive features around 3 × 10−4G0 for 4-TEB and 5 × 10−5G0 for 2-TEB. Neither a clear plateau with preferential conductance values nor the corresponding preferential conductance distribution was observed below 5 × 10−5G0 in the conductance traces and histograms. In the absence of the bridging molecules, neither plateaus nor peaks were observed below 1G0 in both the conductance traces and histograms. These experimental results indicate that the plateau in the traces and distinctive features in the conductance histograms, which occur at 3 × 10−4G0 (5 × 10−5G0) and 2 × 3 × 10−4G0 (2× 5 × 10−5G0), are due to the bridging of one and two 4-TEB (2-TEB) molecules between the Au electrodes, respectively. The conductances of the single 4-TEB and 2-TEB molecule junctions were determined to be 2.7 × 10−4G0 and 5.0 × 10−5G0, respectively, by repeated measurements, showing that the conductance of the single 4-TEB molecule junction was about five times larger than that of the 2-TEB molecular junction. It should be noted here that 4-TEB is in the bulky shape of the rectangular plate consisting of a π-conjugated molecular backbone (see Figure S3, Supporting Information), 5277



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I−V characteristics were measured in a vacuum at room temperature using an electrometer (Keithley 2612A). Current− voltage characteristics of the 2-TEB molecular junctions could not be discussed due to the small formation probability of the molecular junction. Figure 3c shows the I−V characteristics before and after immersion of the fixed nanogap electrodes into a solution containing 4-TEB. The current increased due to the immersion process, indicating that 4-TEB molecules bridged between the fixed nanogap electrodes. By comparing the conductance value with that of the single-molecule conductance, about 50 4-TEB molecules were found to bridge between the metal electrodes. The I−V characteristics did not change with time, showing that the molecular junction had high stability. The increase in current due to the immersion process was observed for 12 of 83 samples, and the formation probability of the molecular junction was 14% (see Figure S4, Supporting Information). The formation probability of the molecular junction was 2% for 2-TEB molecules (2 of 95 samples). The formation probability improved by increasing the number of anchoring units on the target molecules, which agreed with that of using the STM break junction. The formation probability of the molecular junction using the fixed nanogap electrodes was much lower than that using the STM break junction, reflecting the different fabrication technique. The surface of the fixed nanogap electrode was flatter than that of the nanogap electrodes fabricated with the break junction technique (pyramidal structure). The reactivity of the surface was high for the rough surface, and thus, molecules easily adsorbed for the nanogap electrodes fabricated with the break junction technique. In addition, space around the nanogap was smaller for the fixed planar nanogap electrode reflecting its structure (parallel flat electrodes), in contrast with the nanogap fabricated with the break junction technique (two pyramids contact via the apex). Molecules hardly accessed the nanogap area for the fixed nanogap electrodes. Therefore, the formation probability of the molecular junction using the fixed nanogap electrodes was much lower than that using the STM break junction. To show statistical evidence, we analyzed 2D histograms of I−V characteristics. Figure 3e shows 2D histograms constructed from a total of 93 I−V characteristics, in which reproducible shape (i.e., point of inflection of the curve) is visible. Figure 3e shows the differential conductance as a function of the voltage (G−V curve) for the 4-TEB molecular junction. A conductance peak was observed around ±0.7 V. We could see the peaks in the G−V curves for most of the junctions (see Figure S5, Supporting Information), where the conductance increased after the immersion process. The average bias voltages of the peaks were 0.89 ± 0.04 and −0.83 ± 0.06 V, the values of which were obtained from 20 G−V curves. Although a simple comparison between the peak positions in the G−V curves and the molecular level is not appropriate for single-molecule junctions,18,19 there is a relationship between the peak position in the G−V curves and the energy alignment of the molecular junction. We will discuss this point below.

four-point linkage of 1.8 nm can be regarded as the sizes of the molecules (S−S distances) between the two electrodes (see Figure S3, Supporting Information). We will further discuss the molecular structures of the junctions later in the Theoretical Calculation Section. Roughly, the order of the gap size agrees with the molecule size (S−S distances), supporting the formation of 2-TEB or 4-TEB molecular junctions. During junction stretching, the single-molecule junction can break before the molecule bridges in the fully stretched configuration. Therefore, the gap length could be smaller than the actual size of the molecule, especially for 2-TEB.

4. MOLECULAR JUNCTION USING FIXED NANOGAP ELECTRODES The fixed planar nanogap electrodes (gap size ≈ 1 nm) were fabricated using oblique metal evaporation with a shadow mask, followed by an electromigration technique (detailed discussion in the Supporting Information).31−33 Figure 3a,b shows SEM images of the fixed planar nanogap electrodes. The Au nanogap electrodes were immersed in a 1 mM 4-TEB solution at room temperature for a period of 12−24 h. After removal from the solution, the Au nanogap electrodes were rinsed with ethanol.

Figure 3. (a) SEM image of the Au fixed nanogap electrodes fabricated using oblique metal evaporation with a shadow mask, followed by electromigration. (b) Magnification of SEM image in (a) around the nanogap regime. (c) Example of current−voltage characteristics of nanogap electrodes before (black) and after (red) the immersion of the fixed nanogap electrodes into a solution containing 4-TEB. (d) 2D histogram of normalized current−voltage characteristics for nanogap electrodes after the immersion of the fixed nanogap electrodes into a solution containing 4-TEB. The histogram is constructed from 96 current−voltage characteristics. Currents are normalized at the current values at −1.0 V. (e) Normalized differential conductance curve. The conductance is normalized to the zero-bias conductance of 1.66 × 10−6 S.

5. THEORETICAL ANALYSIS OF ELECTRON TRANSPORT 5.1. Method. All of the DFT calculations were carried out using the SIESTA package,34 and the transport calculations were performed by using the HiRUNE subroutines.35,36 We used the PBE exchange-correlation (XC) functional37 and 5278



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adopted the double-ζ plus polarized function (DZP) level basis set for all atoms of the molecule and the single-ζ plus polarized function (SZP) basis set for the Au atoms. To determine the junction structures of the present model systems, geometry optimization via DFT calculations was performed while relaxing the atoms of the bridging molecule and the three Au atoms nearest to the adsorption sites on the left and right electrodes. Since the terminal atom in each anchor is a thiol S atom, the hollow sites were used as adsorption sites for the initial conformations to search for stable junction structures. The distance between the electrodes was also optimized with the above conditions. The k points were taken as the 3 × 3 by Monkhorst−Pack method. The adsorption energy, Eads, was defined as

where the vector uAB ⃗ was the unit vector between atoms A and B and Hμν represented Hamiltonian matrix elements. The functions f L, f R, and feq were the Fermi function sets describing EF of the left and right electrodes and the zero-bias (equilibrium) cases, respectively. We used two possible conformations for each 2-TEB and 4TEB molecular junction as theoretical models, and they were constructed as follows. First, the Au electrode was placed on a clean Au(111) surface. We did not use an apex model to avoid an arbitrary conformation of the anchor units and adsorbed structures. We performed the transport calculations on the p(4 × 4) structure as the unit cell parallel to the surface. 5.2. Theoretical Calculation Results. For 4-TEB, two templates for the conformations were considered. One had all four anchors symmetrically attached to the electrodes (Figure 4a), which we denoted as 4ANC, and the other had only two

Eads = Etot − (EeleR + Emol‐eleL)

where Etot and EeleL were the energy of the entire molecular junction and the right-side electrode, respectively. The last term Emol‑eleL was the energy of the adsorbed molecule and the leftside electrode. Note that each conformation of these fragment systems was also optimized as the case of Etot. Since we adopted an atomic orbital basis set for DFT calculations, numerical accuracy to calculate Etot, EeleR, and Emol‑eleL was different due to the nonequivalent Hilbert space to define the wave functions and electron density. This is often called basis set superposition error (BSSE).38 BSSE sometimes gives serious inaccuracy to evaluate adsorption energy because the calculation procedure includes addition/subtraction of energies of different systems. To correct BSSE, we put a ghost atomic basis on the positions removed atoms of eleR and mol-eleL systems. The conductance in the zero-bias limit was defined as 2g0T(EF), where g0 was the (spin-separated) constant of the conductance unit; T(EF) was the transmission coefficient at the Fermi level (EF); and 2 was a spin factor. The transmission function is expressed as

Figure 4. Structures of junctions used for the first-principles transport calculations: (a) 4ANC, (b) 4−2ANC, (c) 2ANC, and (d) 2nANC models. ∠β is shown in (a).

anchors on opposite ends of the molecule connected to the electrodes (Figure 4b), which was denoted as 4−2ANC. The angle between the S−C bond and surface plane of the electrode, defined as ∠β, was close to 90° in 4ANC, whereas the angle was tilted (∼80°) in 4−2ANC. On the basis of the above two models, we considered two conformations for 2TEB. The first was labeled 2ANC in Figure 4c and had a structure similar to the subchain of the 4ANC bridging molecule, where the anchor units were connected to opposite ends of the straight molecule between the electrodes. In the other (2nANC), the molecular axis (chain) was normal to the surface of the electrodes. In this junction, ∠β was ∼30° (Figure 4d). The Au−S distance was determined to be 2.36 Å which was obtained by minimizing energy with relaxing conformation of the molecule and varying the gap distance of the electrodes. Three aromatic rings were connected in a straight chain by C≡C bonds for 2ANC. On the contrary, the connected aromatic rings were slightly twisted in 2nANC, and the Au−S distance was determined to be 2.20 Å. Although the Au−S distance of 2nANC was shorter than that of 2ANC, 2ANC was more stable than 2nANC. The adsorption energy of 2ANC was 0.34 eV larger than that of 2nANC. For 4-TEB, 4ANC was 0.31 eV more stable than 4−2ANC. In both 4ANC and 4− 2ANC, the bridging molecules were planar. The Au−S distance of 4ANC was 2.20 Å. Although the Au−S distance for the two anchor units of 4−2ANC connected to the electrodes was close to that of 4ANC, i.e., 2.36 Å, the other two anchors were not effectively attached to the electrodes. The Au−S distances were 3.72 Å for the nonadsorbed anchor units. The calculated

T (E) = g0 Tr[ΓL(E)Gr (E)ΓR (E)Ga(E)]

where Gr/a is retarded (advanced) Green’s function and ΓL/R is defined by the retarded and advanced self-energy terms of the left (right) electrode as ΓL/R = i(∑rL/R − ∑aL/R). Let us focus on the backbone of 2-TEB and 4-TEB molecules by dividing the center benzene ring (dot) and each carbon backbone (wire) of anchor moieties. Then the dot is connected to left/right Au by a single lead wire for 2-TEB, while the dot can be connected by the two equivalent lead wires to each side for 4-TEB. Thus, it is interesting to check whether the current density vector is also equivalent in the wire (and simply the number of the charge injection/ejection route is twice) or not. For this purpose, we evaluate the local current vector on each atomic site. We note that there are other approaches to analyze the electron pathway by using chemical bond order and/or orbital interaction,39,40 and these approaches will be useful to analyze the role of each valence orbital to the conductance though it is not our focus of the present pathway analysis. The electron pathway at atom A was calculated by using the local current vectors between atomic orbitals, and, as follows41 JA⃗ = g0

∑ ∑

uAB ⃗

∫ dE Im{Hμν* (GΓLG†)μν (fL − feq )

B ≠ A μ ∈ A, ν ∈ B

* (G ΓR G†)μν (f − f )} + Hμν R eq 5279



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as that of (111). The calculated conductance of 4ANC (001) was 1.52 × 10−2G0, and it reduced to 5.40 × 10−2G0 when the correction T(EF + (ΔEhyb − ΔEGGA)/2) was used. On the contrary to the tripodal pyridine anchor of ref 15, the present 4ANC was less dependent on surface index: thus we concluded that main difference between the experiments and theory was XC dependence. Recall that the conductance ratio of 2ANC and 4ANC was almost independent to the use of T(E) or T(EF + (ΔEhyb − ΔEGGA)/2), and thus our computational model, i.e., the flat Au(111) surface and NEGF-DFT within the GGA, was acceptable for the present purpose. On the basis of the above considerations, we listed the results of our computational model as follows: (1) 2ANC and 4ANC were suitable models for junctions containing 2-TEB and 4-TEB, respectively, from the viewpoint of the stability of the junctions, (2) the conductance of 4ANC was about five times higher than that of 2ANC, which agreed with the experimental results, and (3) the ratio of the conductance of the other (unstable) structures, 4−2ANC and 2nANC, was larger than that of 4ANC and 2ANC, respectively. From now on, we adopt NEGF-DFT/GGA results for analysis. We calculated the I−V characteristics as a function of bias voltage, and they are shown in Figure 5. The I−V curves

adsorption energies of 2ANC and 4ANC were 0.35 and 0.62 eV for each anchor, respectively. This is almost proportional to the number of anchoring points, and hence, the stability is simply additive. The calculated conductances for 2ANC and 4ANC, which corresponded to 2-TEB and 4-TEB molecular junctions, respectively, were 3.40 × 10−2G0 and 1.85 × 10−1G0, respectively. The plots of T(E) for 2ANC and 4ANC model systems are shown in the Supporting Information. For comparison, we also calculated 2nANC and 4−2ANC and obtained 0.56 × 10−2G0 and 0.55G0, respectively. Our theoretical results overestimated the experimental ones, and the two reasons could be considered. One is use of the generalized gradient approximation (GGA) level XC functional in the DFT calculations. It is well-known that the XC of the local density approximation (LDA) and GGA generally underestimate the HOMO−LUMO gap of a bridging molecule.42 Furthermore, slow decay of the transmission coefficient peak is often observed during LDA/GGA calculations, and the anchoring point consists of Au−S moieties.43 The transmission coefficient curves of the present systems have peaks closer to the Fermi level than those of the simple thiolate benzene or alkane molecules, hence the error by slow decay of T(E) enhances the difference of absolute value of conductance. NEGF-DFT calculations by using a hybrid XC functional or a beyond-DFT approach, such as GW, will systematically improve the accuracy, although the computational cost becomes more expensive.44 Hence, we performed the following simple model calculations only for rough estimation of potential error of conductance by LDA/GGA and to check the validity of our analysis. First we calculated the HOMO−LUMO gap of the free 2ANC and 4ANC molecules by using the same XC used for the transport calculation and by hybrid XC functional, which were denoted as ΔEGGA and ΔEhyb, respectively. Assuming that the Fermi level of the electrodes (EF) is the center of the HOMO and LUMO levels, the XC dependence of conductance may be estimated roughly as T(EF + (ΔEhyb − ΔEGGA)/2, where T(E) and EF are the results of NEGF-DFT of the GGA XC. We examined the B3LYP function as the hybrid XC and found that the conductance could be corrected as 1.10 × 10−2G0 and 6.90 × 10−2G0 for 2ANC and 4ANC, respectively. When the position of EF was changed, the order of conductance decreased gradually as expected. However, the ratio of conductance between 2ANC and 4ANC was almost the same as that of experimental results throughout shifting EF. The second possible reason for the difference in experimental values is due to highly idealized surface structures of the electrodes. One of the computational approaches is introducing an arbitrary apex or plateau into the model. However, it is much more difficult to model reasonable apexes for multipodal anchors than for the single-leg anchor since there are many to place the relative apex positions on each electrode side. In addition the internal molecular conformation such as the angle between the two molecular legs in 4-TEB depends on arbitrary apex potions. Here, we adopted a more qualitative analysis based on the strategy given in ref 10 to check the effect of surface structure, i.e., examined another surface index and then compared the results. We performed the completely same computational procedure, while the electrodes have (001) structure. For the 2ANC molecule, we could not find a stable adsorbed structure; i.e., the adsorption energy was negative. On the contrary, 4ANC contact of the (001) surface was as stable

Figure 5. Calculated I−V characteristics of 4ANC and 2ANC. The red thick line is the I−V curve for the 4ANC model system, and the blue dotted line represents the I−V curve for the 2ANC one.

show non-Ohmic behavior in the low bias region. From a comparison of Figures 6 and 3c, we found that the slopes of the I−V curves of 4ANC agree qualitatively with the observed one. On the basis of the above results, we concluded that the

Figure 6. Electron pathway in the anchor molecule in the 4ANC junction (upper panel) and that in the anchor molecule in the 2ANC junction (lower panel). Large currents on the atoms are represented by the bright arrows; that is, brighter arrows mean a larger current intensity. 5280



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theoretical models 2ANC and 4ANC could be used to analyze the experimental data. Furthermore, our theoretical calculations indicated that all four anchor units made contact by forming a bond with Au atoms of the top layer, and the bond length (Au−S) was almost the same as each other. In other words, the four anchors attached to the electrodes almost equivalently. The distance between Au electrodes was 2.2 nm for the optimized structure, which was close to the experimentally obtained gap sizes of 1.6 and 2.4 nm for 2-TEB and 4-TEB, respectively. In Figure 6, the electron pathways for 2ANC and 4ANC are presented. When we focused on the center thiophene molecule, we found that the electrons entered at each anchoring point along the “leg” of the C≡C chain and then exited the opposite leg (see Figure 6). Hence, increasing the number of connected anchors increased the number of electron pathways. However, the increase in the conductance was not proportional to the number of electron pathways. To estimate the number of dominant eigenchannels, we decomposed the transmission coefficient into the eigenchannel values (tn).45 The value of the primary channel t1 of 2ANC was 0.034, and that of the secondary channel t2 was less than 0.001. For 4ANC, t1 was 0.144, whereas t2 was 0.0037. In other words, t2 was much smaller than t1. Note that a spin factor (i.e., 2) should be included as a multiplication factor to get the conductance. Eigenchannel analysis showed that both 2ANC and 4ANC were dominated by a single eigenchannel. Instead of calculating the eigenchannel wave functions, we applied the effective molecular projected state Hamiltonian (MPSH) analysis,46 from which the orbital energy shift could be obtained. The electronic coupling between the molecular projected state and electronic states of the left/right electrodes was rigorously calculated using the Feshbach effective Hamiltonian formalism.47 Using the effective MPSH formalism, the f irst-order contribution of each projected molecular orbital (PMO) to the conductance can be estimated by calculating τ(E) τ (E ) =

Table 1. PMO Energies and the Molecule−Electrode Couplings for 2ANC (Two Anchor Molecules) and 4ANCa 2ANC Eα γαL γαR

HOMO

HOMO-1

−0.56 0.15 0.40

−1.14 0.33 0.52

4ANC Eα γαL γαL

HOMO

HOMO-1

HOMO-2

HOMO-3

−0.66 0.26 0.36

−1.01 0.58 0.62

−1.20 0.33 0.57

−1.48 0.80 0.96

a

Results of HOMO and HOMO-1 for 2ANC and HOMO−HOMO-4 for 4ANC are listed in the table as potential conducting orbitals, respectively. The Fermi level is set to zero. The units of energy (coupling strength) are eV.

in 4ANC were determined to be conductive, whereas only HOMO-1 contributed to the conductance of 2ANC. PMOs HOMO-1 and HOMO-3 coupled more effectively with the left and right electrodes than the HOMO did, although the HOMO had an advantage from the viewpoint of the resonance energy position. Furthermore, the resonance of HOMO-1 overlapped with the resonance of the HOMO in 4ANC because the difference in the PMO energies was close to the broadening width (i.e., γL + γR). As a result, the tail value of the transmission coefficient function at EF became large (see Figure S6, Supporting Information), and the ratio of the conductance for 4ANC and 2ANC was larger than the value expected from the property of the conducting HOMO, the number of possible conducting MOs, and additive electron pathways. Finally, we briefly discuss the derivative of the conductance. Figure 7 shows a plot of the derivative of the conductance as a

∑ τα α

=

∑ α

4γα Lγα R {E −

(Eα0

+ ΔEα L + ΔEα R )}2 + (γα L + γα R )2 (1)

where the PMO α is the eigenstate of MPSH, whose eigenenergy is E0α. The energy shift terms, ΔEαL and ΔEαR, result from the interactions between the left and right electrodes, respectively. Thus, the actual PMO energy (Eα) is equal to E0α + ΔEαL + ΔEαR. The terms γL and γR are defined as the imaginary parts of the effective Hamiltonian, which relate to coupling of the continuum of the electronic states of the left and right electrodes, respectively. Though these “dressed” terms of the PMO depend on the energy E, the values at E = EF are sufficient for analyzing the transport properties in the lowbias-voltage regime. We want to emphasize that eq 1 contains both the sum and product terms of γL and γR . Hence, one should estimate γL and γR separately to analyze the conductance using the PMO picture. The calculated parameters are listed in Table 1. The first conducting MO was determined to be the HOMO for both 2ANC and 4ANC. The resonance function, τHOMO, of 4ANC was 1.3 times larger than that of 2ANC at EF. This was much smaller than the ratio of conductance of the two systems. However, as shown in Table 1, the other three PMOs

Figure 7. Calculated plot of the derivative of the conductance of model 4ANC as a function of bias voltage. The conductance is normalized to the value of zero-bias conductance. The inset is the structure of 4ANC, which is also given in Figure 5.

function of bias voltage, where the conductance is normalized by zero-bias conductance to eliminate overestimation of the absolute value in PBE calculations. By comparing Figures 3d and 7, we found that the derivative of conductance curve agreed with the observed one. For instance, the experimental and calculated peak positions of the plots were ±0.85 and ±1.10 V, respectively. Roughly, the peak position of the derivative of the conductance is related to the energy level of the conducting MO. In usual NEGF calculations with bias voltage V, the EF of 5281



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grateful to the Cooperative Research Program of “Network Joint Research Center for Materials and Devices” and for the financial support provided by the Scientific Research on Innovative Areas, a MEXT Grant-in-Aid Project: “Material esign through Computics” (#25104724). We thank Dr. Fatema Sultana for her assistance in the experiments.

each electrode is shifted to EF ± V/2. Since the energy level of the first conducting MO (i.e., HOMO) of 4ANC was 0.66 eV lower than EF, we concluded that the peak of the derivative of the conductance plot corresponded to the position of the conducting HOMO.

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6. CONCLUSION A quadrivial anchoring unit, 4-TEB, was designed and synthesized to construct a stable single-molecule junction with multiple equivalent conduction pathways between two electrodes. From STM break junction measurements in solution at room temperature, the conductance and probability of the formation of the 4-TEB molecular junction were determined to be higher than those of the 2-TEB molecular junction. The conductances of the 4-TEB and 2-TEB molecular junctions were 2.7 × 10−4G0 and 5.0 × 10−5G0, respectively. The conductances of the single 4-TEB and 2-TEB molecule junctions were discussed by comparing the results of first-principle calculations. As shown by first-principles calculations of current vectors later, we found two equivalent electron pathways in the 4-TEB, while the 2-TEB had only one pathway. The number of carbon backbones in the 4-TEB is just twice of that in the 2-TEB, and hence, the electron pathway is additive. On the contrary, the conductance of the 4-TEB molecular junction was much larger than that of the 2-TEB, i.e., nonadditively increased. First-principles electronic transport calculations were conducted to analyze the mechanism for the 4-TEB molecule junction, and from the results, there is an overlap resonance effect involving the HOMO conducting orbital, causing tunneling. Detailed analysis of the conductance traces revealed that there was a high probability for the formation of a single-molecule junction, that the bridging molecules were strongly bound to the metal electrodes, and that 4-TEB bound symmetrically between the Au electrodes. On the basis of single-molecule conductance measurements, the 4-TEB molecule junctions with fixed nanogap electrodes were stable. Symmetric peaks were observed in the G−V curves of the 4-TEB molecule junction, which were assigned to electron transport through the HOMO on the basis of theoretical calculations.

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ASSOCIATED CONTENT

S Supporting Information *

Details of conductance measurements, synthetic procedures, and characterization data of all new compounds used in the present study. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by a Grant-in-Aids for Scientific Research in Innovative Areas (No. 23111706) and Grants-in-Aid for Scientific Research (A) and (B) (No. 21340074 and No. 24245027) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT). HN is also 5282



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Additive Electron Pathway and Nonadditive Molecular Conductance

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