Current Rectification through ÏâÏ Stacking in Multilayered Donor

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Current Rectification through #-# Stacking in Multilayered Donor-Acceptor Cyclophanes Yuta Tsuji, and Kazunari Yoshizawa J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp308849t • Publication Date (Web): 28 Nov 2012 Downloaded from http://pubs.acs.org on December 4, 2012

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The Journal of Physical Chemistry

Current

Rectification

through

π-π

Stacking

in

Multilayered Donor-Acceptor Cyclophanes

Yuta Tsuji and Kazunari Yoshizawa* Institute for Materials Chemistry and Engineering and International Research Center for Molecular Systems, Kyushu University, Fukuoka 819-0395, Japan

*To whom correspondence should be addressed. E-mail: [email protected]

ACS Paragon Plus Environment


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Abstract: Extended π-stacked molecules have attracted much attention since they play an essential role in both electronic devices and biological systems. In this manuscript electron transport properties of a series of multilayered cyclophanes with the hydroquinone donor and quinone acceptor units in the external positions are theoretically studied with applications to molecular rectifiers in mind. Calculations of electron transport through the π-π stacked structures in the multilayered cyclophanes are performed by using nonequilibrium Green’s function method combined with density functional theory. Calculated transmission spectra show that the conductance decreases exponentially with the length of the molecule with a decay factor of 0.75 Å-1, which lies for the values between π-conjugated molecules and σ-bonded molecules. Applied bias calculations provide current-voltage curves, which exhibit good rectifying behavior. The rectification mechanism in the coherent transport regime is qualitatively explained by the response of the frontier orbital energy levels, especially LUMO levels, to the applied bias, where the rectifying direction is expected to be opposite to the Aviram-Ratner model. The maximum value of rectification ratio increases with an increase in the number of stacking layers, due to the effective separation of the donor and acceptor parts, where effects from the opposite electrodes to the donor and acceptor are negligible. Multilayered donor-acceptor cyclophanes are suitable materials for investigating the relationship among electron transport properties, rectification properties, and molecular length (separation between the donor and acceptor parts).

Keywords: molecular electronics, π-stacked system, rectifier, nonequilibrium Green’s function, frontier orbital, density functional theory.

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1. Introduction Miniaturization of conventional silicon-based electronic devices requires the substitution of the micro-sized devices with nano-sized molecular electronic devices.1,2 A detailed understanding of nanoscale electron transport plays an essential role in the design of molecular electronic devices.3 In the past decades, the electron transport phenomena through π-π stacked systems have attracted much attention, due to their not only potential applications in nanotechnology but also biological importance. Numerous experimental and theoretical studies have been carried out on electron transport properties through columnar structures in π-stacked polycyclic aromatic hydrocarbons (PAHs)4-6 and helical π-stacked structures in double-stranded DNA molecules.7-9 The charge migration in these systems having a quasi one-dimensional character is achieved via extensive interactions between π-orbitals of the stacked aromatic rings, where the dominant mechanism is assumed to be a hopping process. Recent advances in various break junction techniques such as scanning tunneling microscope break junction (STM-BJ)10,11 and mechanically controllable break junction (MCBJ)12,13 have allowed us to access single-molecule properties in metal-molecule-metal junctions. Schematic representations of the pπ-pπ and pσ-pσ orbital interactions in metal-molecule-metal junctions are shown in Figure 1. Electron transport through the pπ-pπ interactions plays a crucial role in commonly used π-conjugated molecular wires while the pσ-pσ interactions are of great importance in π-stacked systems.

14,15

As shown schematically in

Figure 1c, electron transport properties in π-stacked systems wired to two electrodes via anchor groups have been measured by using the STM-BJ and MCBJ techniques.16-18 Theoretical studies based on Landauer’s formula19 with Green’s function techniques20 have



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been performed to provide essential insights into the mechanisms of electron transport in the π-stacked systems wired to two electrodes.15,21-25 In these systems electron injection and extraction can be achieved through the pπ-pπ orbital interactions while electron transport through the π-stacked region can be mainly dominated by the pσ-pσ orbital interactions, where the electron transport direction is nearly perpendicular to the electrode-electrode axis and the electric field acceleration effect can be suppressed. On the other hand, as shown schematically in Figure 1d, experimental measurement of electron transport properties through π-stacked systems without the pπ-pπ transport pathways at the single-molecule level is not an easy task. Wolkow and co-workers measured electron transport properties through molecular lines of π-stacked ethylbenzene produced on a Si substrate using a self-directed chemical growth process.26,27 However, a theoretical study performed by Smeu et al. reported that conduction pathways through the Si substrate are not negligible in the electron transport in the π-stacked systems aligned on the substrate.28


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(a)

(b)

p-p

p-p (c) electrode

p-p

electrode p-p

p-p (d) electrode

electrode p-p

Figure 1. Schematic representations of (a) pπ-pπ and (b) pσ-pσ orbital interactions and molecular junctions with (c) both pπ-pπ and pσ-pσ transport pathways and (d) only a pσ-pσ transport pathway. For simplicity the orbital phases are omitted.

Dulić et al. investigated electron transport properties of short DNA molecules attached to Au electrodes with propanethiols using MCBJ method, where the propanethiol spacer that introduces flexibility in the orientation of the nucleoside allows the aromatic rings of DNA bases to arrange parallel to the surface.29 Our previous study has revealed that electron transport through short DNA molecules can be achieved through the pσ-pσ orbital overlaps in the π-stacked DNA bases.14 Various anchor-less π-stacked systems in molecular junctions, where the pσ-pσ transport pathway is aligned parallel with the electrode-electrode axis, have been investigated theoretically, for instance, π-stacked benzene molecules,30 π-stacked PAHs,31 and metal-bridged cyclophanes.32 Recently Schneebeli et al. have succeeded in obtaining direct contact of Au electrodes with distorted benzene rings of



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cyclophanes without any anchor groups using the STM-BJ method.33,34 They have performed theoretical calculations to determine that the major transport pathway is not ethylene bridges but the pσ-pσ orbital interactions between the π-stacked aromatic rings. Kiguchi et al. have also succeeded in measuring conductance of π-stacked aromatic molecules intercalated in columnar coordination cages using the STM-BJ method, where the analysis of conductance traces suggests that the top and bottom aromatic panels of the cages directly bind to the Au electrodes.35,36 They performed conductance measurements of the empty cage and molecular orbital (MO) analysis to confirm, both experimentally and theoretically, the importance of the pσ-pσ transport pathways through the π-stacked aromatic rings and the strong Au-π interaction at the electrode surfaces. In previous studies we have proposed two different kinds of molecular rectifiers based on cyclophanes. One is a boron- and nitrogen-doped cyclophane,25 where the molecule is connected to the electrodes by thiol anchor groups and the electron transport can be achieved by the scheme shown in Figure 1c. The other is a double-layered cyclophane-type quinhydrone,37 where the molecule is aligned so that the planes of the quinone (acceptor) and hydroquinone (donor) rings are parallel to the electrode surface and the electron transport can be achieved by the scheme shown in Figure 1d. In this manuscript we report a trend study on multilayered donor-acceptor cyclophanes. The effect of the number of layers on the electron transport and rectification properties of multilayered π-stacked systems with pσ-pσ orbital interactions is investigated in detail. Scheme 1 illustrates the geometry of the molecules chosen for this study along with the shorthand nomenclature used throughout the remainder of this manuscript. This series of multilayered cyclophanes with the hydroquinone donor and


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quinone acceptor units in the external positions was synthesized independently by Misumi and co-workers38-40 and Staab and co-workers.41-43 They attempted to investigate the orientation- and distance-dependencies of charge transfer (CT) interactions, which are inaccessible by the investigation of regular intermolecular CT complexes. An overview of early studies on various properties of CT interactions in cyclophanes is presented in a review article written by Schwartz.44 Both Misumi and Staab suggested that a sandwiched benzene ring functions as a sort of conductor for intramolecular donor-acceptor interaction. We shed new light on the role of the intramolecular donor-acceptor interaction in the electron transport and rectification properties of multilayered π-stacked systems.

Scheme 1. Structures for the series of multilayered donor (hydroquinone)-acceptor (quinone) cyclophanes investigated in this study. O

O

O

HO

O

O

O

OH

Double layer (DL)

HO

OH

Triple layer (TL)

HO

OH

Quadruple layer (QL)

2. Theoretical background Rectifiers (or diodes) are key elements in the electrical circuits. A design principle for rectifiers based on a single organic molecule with suitable electronic asymmetry was presented by Aviram and Ratner in 1974.45 The Aviram-Ratner (AR) molecular rectifier consists of two π-conjugated segments, i.e., donor (D) and acceptor (A). The D and A parts



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are separated by σ-bonds, which serve as an insulating barrier between the two segments. Thus, the AR rectifier is expressed as a D-σ-A rectifier. We show energy-level diagrams of a D-σ-A molecule in Figure 2a, where the proposed mechanism of the AR rectifier is summarized.1,45 At the zero bias, electrons cannot transfer through the D-σ-A bridge since none of the frontier orbitals of the A and D parts aligns with the Fermi levels of the electrodes. Under a bias, the frontier orbital levels of the A and D parts follow the electrochemical potentials of the left and right electrodes, respectively, since the A and D parts have a strong coupling with the left and right electrodes, respectively. Under forward bias, if the Fermi level of the left electrode reaches the lowest unoccupied molecular orbital level of the A part, LUMO(A), and the vacant levels of the right electrode fall below the highest occupied molecular orbital level of the D part, HOMO(D), electron injection from the left electrode to the A part and electron extraction from the D part to the right electrode will occur. The electron migration from the A to D parts can be achieved by the inelastic tunneling, leading to the continuous current flow thorough the D-σ-A molecule enhanced at a small threshold voltage. On the other hand, under reverse bias, the energy level matching between the Fermi level of the right electrode and the LUMO(D) requires a large bias, which leads to a substantially larger threshold voltage than forward bias. This difference in the threshold voltage gives rise to rectifying behavior in the AR model and the electron transfer in the A to D direction is expected.


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Figure 2. Schematic representations of the mechanisms of (a) AR rectifiers and (b) rectification in the coherent transport regime for zero, forward, and reverse biases. μL(R) represents the electrochemical potential of the left (right) electrode. The filled and empty parts of the rectangles represent filled and empty levels of the electrode conduction bands. The A and D parts are assumed to be connected with the left and right electrodes, respectively. The blue and red lines represent the frontier orbital levels of the A and D parts, respectively. In (b) the frontier orbital levels of the united molecule arising from the orbital interaction between the A and D parts are shown and the bias window is shown by the dashed lines.

Ellenbogen and Love proposed a different rectification mechanism for the AR rectifier.46 In their mechanism, it is assumed that the LUMOs can provide channels for the resonant transport of electron. They reduced the complexity of the rectification mechanism to a single parameter, potential drop, which is defined as the energy difference between the LUMO(D) and LUMO(A) at zero bias. They pointed out that the MO calculation for the



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united molecule is important for the precise estimation of the potential drop, since equilibration of electron densities across the insulating barrier can affect the energy level alignment between the A and D parts. Stokbro et al.47 have investigated the rectifying properties of a D-σ-A molecule with nonequilibrium Green’s function method combined with density functional theory (NEGF-DFT),3,20,48-51 which is a state-of-the-art tool for calculation of bias-dependent electron transport. They have observed nearly symmetrical current-voltage (I-V) characteristics resulting in very limited rectification. Numerous theoretical studies on the AR rectifiers have been performed, but most of them show rectifying properties in the direction opposite to the AR rectifiers.37,52-55 This discrepancy in the rectifying direction can be explained by a rectification mechanism based on the coherent transport model shown in Figure 2b. The AR model assumes electrons residing in the D and A parts and inelastic tunneling between them, which is validated in the incoherent transport regime such as long-range electron transfer.56 For a short-range electron transport, where electrons can transport without scattering, i.e., coherent transport, the AR mechanism will break down. As a rule of thumb, the coherent transport mechanism is effective up to a transport distance of ~2.5 nm.57 The coherent transport mechanism requires molecular energy levels serving as a transmission channel to lie within the bias window.20 The MO levels of the united molecule comprised of the D and A parts should be taken into account in the coherent transport regime, due to no electron residing on either the D or A part.58 Various experimental59-61 and theoretical62-64 studies on electron transport within the coherent framework have shown that the alignment of the HOMO and LUMO relative to the electrode Fermi level is important.


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As shown in Figure 2b, the HOMO and LUMO of the united molecule are constructed from the bonding and antibonding combinations of the HOMO(D) and LUMO(A), respectively. The HOMO is primarily HOMO(D) with some fraction of LUMO(A) mixed in, whereas the LUMO is primarily LUMO(A) with some fraction of HOMO(D) mixed in. In the situation where the overlap between A and D is neglected and the difference in the orbital energy between the HOMO(D) and LUMO(A) is much larger than the interaction matrix element between A and D, the stabilization (destabilization) energy of HOMO(D) (LUMO(A)) is approximated by eq 1, according to the second-order perturbation theory.65,66

E

2 H AD ED(A) EA(D)

(1)

where HAD is the interaction matrix element and ED(A) is the orbital energy of HOMO(D) (LUMO(A)). Owing to the good separation between the A and D parts, HAD can be assumed to be so small and ED(A) - EA(D) is so large that the orbital energy of the HOMO (LUMO) is shifted from that of the HOMO(D) (LUMO(A)) by only a small amount in the forward bias case. The stabilization and destabilization energies are maximum when the energy difference between the HOMO(D) and LUMO(A) is zero in the reverse bias case, in which case they have the value approximately HAD.66 In the case of forward bias, which is defined in accordance with the AR mechanism, there is no transmission channel within the bias window, while in the case of reverse bias the HOMO and LUMO can provide transmission channels in the bias window. Thus, the electron transport in the D to A direction is expected, which is opposite to the AR mechanism. The orbital energy of the HOMO increases with an increase in



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the Fermi energy of the right electrode, whereas the orbital energy of the LUMO decreases with a decrease in the Fermi energy of the left electrode. A large HOMO-LUMO gap is expected for forward bias, while a small HOMO-LUMO gap is expected for reverse bias. Although recent experimental and theoretical investigations on hetero-doped molecular rectifiers have reported the same rectifying direction as the AR model, the rectification characteristics are explained by the bias-induced change in the MO amplitudes, leading to asymmetric metal-molecule contact coupling at the right and left ends.2,25,67,68 In this manuscript we report the rectification properties of a series of multilayered donor-acceptor cyclophanes shown in Scheme 1 on the basis of the rectification mechanism shown in Figure 2b. In the following, the case that the right electrode acts as a source and the left electrode acts as a drain, which corresponds to reverse bias in Figure 2, is referred to as the application of positive bias for descriptive purposes.

3. Computational methods We performed geometry optimizations of the multilayered donor-acceptor cyclophanes, DL, TL, and QL, shown in Scheme 1 with the Gaussian 09 program69 at the B3PW91 level of theory70 with the 6-31+G(d,p) basis set.71 According to Caramori et al. B3PW91/6-31+G(d,p) is the most suitable DFT method for describing distortion effects in strained ring systems, giving good agreement with experimental data.72,73 To investigate the I–V characteristics, we performed electron transport calculations with the NEGF-DFT method. Electron transport calculations were performed for the zero-bias optimized geometries because studies in the literature74,75 have shown that the applied electric field between the


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electrodes does not significantly alter the molecular geometry. In a previous study we confirmed that zero-bias optimized geometries of a donor-acceptor cyclophane are valid under the ±1.0 V bias electric fields.37 For the electron transport calculations we used the ATK 11.8.1 program,76 which includes the full self-consistent field (SCF) treatment of electrode–molecule–electrode junctions. The effect of the external electric field on the electronic properties of the molecules is taken into account.76 The exchange-correlation potential described by the Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA) was employed.77 The single ζ basis set (SZ) was used for gold atoms and the double ζ basis set with polarization (DZP) was used for all other atoms. The semi-infinite left and right electrodes were modeled by two Au(111)-(4 × 4) surfaces (i.e., each layer includes 16 Au atoms). Three layers from each electrode (in total 96 Au atoms) were included in the central region. The model of the central region with molecule DL is shown in Figure 3. In this model the cyclophanes are aligned so that the planes of the quinone and hydroquinone rings are parallel to the electrode surface. The relative positions of the center of the quinone and hydroquinone rings on Au(111) surface are set to be the hollow and on-top sites, respectively. We confirmed that the relative positions of the quinone and hydroquinone rings on the surface do not significantly affect the electron transport properties (see the Supporting Information, Figure S3). Ferrighi et al. performed a theoretical study of adsorption of aromatic molecules on Au(111) surface, reporting that the adsorption energy is nearly independent of the adsorption site.78 The distance of the planes of the quinone and hydroquinone rings from the electrode surface is set to be 3.1 Å, which corresponds to the distance between Au(111) surface and benzene ring adsorbed on the surface with its



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molecular plane parallel to the surface.79 Such metal-molecule-metal junctions without anchor groups were measured by using the STM-BJ method.33-36

Figure 3. Geometry of the central region with molecule DL used for the electron transport calculations. The model consists of left electrode-acceptor group (quinone)-CH2-CH2 bridge-donor group (hydroquinone)-right electrode.

4. Results and discussion Figure 4 shows top and side views of the optimized structures of molecules DL, TL, and QL. The benzene rings are stacked at almost the same interval. The ring-to-ring distances between the average planes of the deformed benzene rings fall in a range from 2.95 to 3.08 Å. These values are almost all consistent with an experimental value of 3.03 Å observed for [2.2]paracyclophane.80

These

values

are

longer

than

the

previously

investigated

cyclophane-type quinhydrone,37 where the completely rigid mutual orientation between the benzene rings is enforced by the fourfold bridging. In many cyclophanes π-electron repulsion between aromatic rings results in distortion from the parallel arrangement.72,73,80,81 The distortion angles between the rings fall in a range from 7° to 9°, which is slightly larger than


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an experimental value of 6° observed for [2.2]paracyclophane,81 due to the steric hindrance between the neighboring ethylene bridges. Although the previously investigated cyclophane-type quinhydrone indicates intramolecular hydrogen bond formation between quinone and hydroquinone,37 no hydrogen bond formation is observed in this study, due to the slightly large distortion angle and long ring-to-ring distance.

Figure 4. Top views (top) and side views (bottom) of the optimized structures of DL, TL, and QL. In the side views the left and right ends of the molecules are quinone (acceptor) and hydroquinone (donor) parts, respectively. Interlayer distances are shown in Å.

We show in Figure 5 MO energy diagrams and frontier orbital distributions of isolated molecules DL, TL, and QL calculated at the B3PW91 level of theory. In the MO energy diagrams the energy levels of the HOMO of hydroquinone, the LUMO of quinone,



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and the HOMO of benzene are shown for reference. In the three molecules, the HOMO and LUMO are localized on the donor (hydroquinone) and acceptor (quinone) parts of the molecule, respectively. This orbital localization is consistent with many charge-transfer (donor-acceptor) systems.82,83 The HOMO and LUMO of DL are derived from π-π bonding-like (in-phase) and antibonding-like (out-of-phase) orbital interactions between the HOMO of hydroquinone and the LUMO of quinone in the stacking direction, respectively.37 In the case of molecules TL and QL, the donor-acceptor interaction is weakened by the intervening benzene rings. The HOMO of TL is derived from an out-of-phase combination of the HOMOs of hydroquinone and benzene; as a result, it is slightly pushed up compared to the HOMO of hydroquinone. In a similar way, the HOMO of QL comes from an out-of-phase combination of the HOMOs of hydroquinone and benzene and it is thus slightly pushed up compared to the HOMO of hydroquinone. Owing to an out-of-phase combination of the HOMOs of the internal benzenes, the HOMO of QL is slightly pushed up compared to the HOMO of TL. The LUMOs of TL and QL are derived from an out-of-phase combination between the LUMO of quinone and the HOMO of benzene, being pushed up compared to the LUMO of quinone. No orbital interaction occurs between the LUMOs of quinone and benzene, due to the large energy difference between them and the symmetry restriction. The LUMOs of TL and QL are primarily the LUMO of quinone with the admixture of a small amount of the HOMO of benzene, due to the large energy difference between the LUMO of quinone and the HOMO of benzene. Thus, the LUMOs are more localized than the HOMOs and the energy variation of the LUMOs is smaller than that of the HOMOs.


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Figure 5. (a) MO energy diagrams and (b) frontier orbital distributions of isolated molecules DL, TL, and QL calculated at the B3PW91 level of theory. The energy levels of the HOMO of hydroquinone, the LUMO of quinone, and the HOMO of benzene are shown for reference. Frontier orbital distributions of hydroquinone, quinone, and benzene are shown in the Supporting Information.

The

NEGF-DFT calculations

provide

molecular

projected

self-consistent

Hamiltonian (MPSH) states, which are the eigenstates of the molecule placed between two electrodes.50,76 The MPSH states analysis was performed to study the frontier orbitals in the junction environment modified by the electrodes. The spatial distributions of the MPSH states corresponding to the HOMO and LUMO of molecules DL, TL, and QL for zero bias are shown in Figure 6, where the energies are relative to the Fermi level of the electrodes, which was determined from DFT calculations of the bulk gold electrodes. The energy level alignments and orbital distributions of the MPSH states are almost all consistent with those of



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the isolated molecules shown in Figure 5. The LUMO states of the three molecules have nearly the same energy and lie much closer to the Fermi level than the HOMO states. Thus, the transannular electron transport through the multilayered donor-acceptor cyclophanes can be dominated by the LUMO states. The MPSH states calculated with inclusion of the electrode atoms in the scattering region are shown in Figure S2 in the Supporting Information. Figure 6 and S2 clearly show that the LUMO states are strongly coupled with the left electrode while the HOMO states are strongly coupled with the right electrode. These asymmetrical couplings between the molecule and the electrodes in the HOMO and LUMO states are consistent with the qualitative view shown in Figure 2b, where the LUMO level follows the electrochemical potential of the left electrode while the HOMO level follows that of the right electrode.

Figure 6. The spatial distributions of the MPSH states corresponding to the HOMO and LUMO of (a) DL, (b) TL, and (c) QL for zero bias. The MPSH energies given in parentheses are relative to the Fermi level of the electrodes.


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Zero-bias transmission spectra of DL, TL, and QL calculated with the NEGF-DFT method are shown as a function of the energy of electron in Figure 7a. The Fermi level of the electrodes is located at the origin of the energy (E = 0). The three spectra exhibit remarkably a similar shape but the intensity decays exponentially with an increase in the molecular length. The three peaks with nearly the same energy are assigned to the LUMO resonance peak by the MPSH analysis. According to Landauer’s formula, the conductance G of a metal-molecule-metal junction at the zero temperature and zero bias voltage is proportional to the transmission probability at the Fermi level T(EF) as follows:19,20

G = G0T(EF)

(2)

where G0 is the quantum conductance constant (2e2/h = 77.5 μS). The conductance G decays exponentially with molecular length L within the approximation of coherent non-resonant tunneling through a rectangular barrier as follows:84-90

G = Gconexp(-βL)

(3)

where Gcon is a constant, which corresponds to the contact conductance,90 and β is the tunneling decay constant. Although the theoretical methods overestimate the contact conductance, due to the approximation in the exchange-correlation functional, a direct comparison of the tunneling decay constants between experimental and theoretical studies is permitted.35,88 Figure 7b shows the dependence of the logarithmic conductance on the



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molecular length for TL, DL, and QL. From the linear fits in the Figure 7b we can obtain a tunneling decay constant of 0.75 Å-1. It has been shown that the tunneling decay constant of π-conjugated molecules is ~0.2 Å-1 while that of σ-bonded molecules is ~1.0 Å-1.85,87 The calculated value of the tunneling decay constant that lies midway between the values for π-conjugated molecules and σ-bonded molecules is in good agreement with an experimentally observed value of 0.63 Å-1 for π-stacked cyclophanes.33

Figure 7. (a) Computed transmission spectra of DL, TL, and QL for zero bias with the NEGF-DFT method and (b) single-molecule conductance as a function of distance between quinone and hydroquinone rings.

In Figure 8a-c transmission spectra of DL, TL, and QL under the three applied biases of 0.0, 1.0, and -1.0 V are shown. According to the Landauer-Büttiker formula,20 the current is obtained after integration of a finite part of the transmission spectra called bias window as follows:


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I (V ) =

2e h

eV 2 eV 2

dET ( E,V )

(4)

The bias window includes only energies close to the Fermi level in the interval from -eV/2 to eV/2, which corresponds to the electrochemical potentials of the left and right electrodes.20,49 The peak area included in the bias window contributes to the value of the calculated current. There is no significant difference in peak width among the peaks of the transmission spectra calculated at the three applied biases. In this case peak shifts with applied bias have a crucial effect on the current. Only the tail of the transmission peak is included in the bias window under -1.0 V, whereas the most part of the peak is included in the bias window under 1.0 V. Thus, we can expect higher current for the positive bias than the negative bias, leading to the rectification function of the molecules. Figure 8d-f shows evolution of the eigenvalues of the MPSH for DL, TL, and QL under applied bias. The eigenvalues of the MPSH can be almost all consistent with the peak positions in the transmission spectra. This figure clearly shows that the LUMO level plays a key role in the electron transport and the peak in the transmission spectra stems from the LUMO channel. The peak shift with applied voltage can be rationalized by the evolution of the LUMO level. The LUMO levels of TL and QL change linearly, following the electrochemical potential of the left electrode. Although the HOMO levels are of little relevance to the electron transport, due to the large separation from the Fermi level, those of TL and QL also change linearly to follow the electrochemical potential of the right electrode. The linear evolution of the HOMO and LUMO levels of TL and QL with a change of electrochemical potentials of the left and right electrodes is consistent with



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that in the qualitative explanation of the rectification behavior shown in Figure 2b. However, the HOMO and LUMO levels of DL show a non-linear change with applied voltage. Although the LUMO level of DL linearly follows the electrochemical potential of the left electrode under the negative bias, that under the positive bias deviates from the electrochemical potential of the left electrode. This is because, as shown in Figure 6a, the LUMO of DL has not only a strong coupling with the left electrode but also a weak coupling with the right electrode. As a result, the effect of increase in the electrochemical potential of the right electrode is not negligible. The longer the molecule is, the more the effect of the right electrode on the LUMO level is negligible. Thus, the slope of the evolution of the LUMO level of QL is closer to that of the electrochemical potential of the left electrode than that of TL, which results in a smaller HOMO-LUMO gap for QL than TL under positive bias. There is little change in the HOMO-LUMO gap for DL, whereas the bias-induced reduction of the HOMO-LUMO gap is observed for TL and QL, leading to higher transmission peak intensity under positive bias than under negative bias. The bias-induced intensity enhancement can also contribute substantially to the rectification of current.


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Figure 8. Transmission spectra of (a) DL, (b) TL, and (c) QL for biases of 0.0 V (black line), 1.0 V (red line), and -1.0 V (blue line), where the bias window at ±1.0 V is shown with dotted lines, and evolution of the MPSH states under applied bias for (d) DL, (e) TL, and (f) QL, where the two dashed lines show the electrochemical potentials of the left and right electrodes. Evolution of the HOMO and LUMO levels is indicated by the blue and red lines, respectively.

In Figure 9a-c, we show computed I-V curves for DL, TL, and QL. Note that the scales on the vertical axis are different among panels. As expected from the exponential decrease in conductance, the current also decreases one order of magnitude with an increase in the number of layers. Under positive bias, the current of DL increases quickly as the bias changes, whereas under the negative bias, the current that changes slowly is smaller than that under the positive bias. On the other hand, for TL and QL, the currents increase sharply in a



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lower positive bias range and saturate in a higher positive bias range, whereas the currents under the negative bias saturate to a very low values. This difference derives from the difference in the evolution of the LUMO levels shown in Figure 8d-f. The rectification ratio, R(V), plays a key role in evaluating whether a molecular rectifier can be used for practical applications as an electronic device, being defined as follows:

R (V ) = I (V ) I (V )

(5)

where I(V) and I(-V) represent the currents under positive and negative voltages for the same voltage magnitude, respectively. Figure 9d shows the rectification ratio as a function of the applied bias. The rectification ratio increases with an increase in the number of layers. As the bias is 0.8 V, moderate rectifying behavior can be observed for DL and the maximum rectification ratio reaches 4.6, which is two times larger than that of the previously investigated cyclophane-type quinhydrone with an extremely short transannular distance, due to the fourfold bridging.37 For TL and QL, the maximum rectification ratios can be observed at lower bias than for DL. The maximum rectification ratios are 9.3 at 0.3 V and 12.5 at 0.6 V for TL and QL, respectively. Thus, in order to enhance the rectifying properties, we should keep an effective separation of the donor and acceptor parts so that the effect of the opposite electrode is negligible. In recent experimental measurements of single molecular rectifiers using the MCBJ and STM-BJ techniques, the rectification ratio values have been reported to range from 1.2 to 10 although these experimentally measured molecules are not π-stacked systems.67,91-93 The rectification ratio of the investigated π-stacked donor-acceptor systems can


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be predicted to be the same or more than that of conventional molecular rectifiers without π-stacked structures. We may approach an upper limit of rectification ratio of ~22 predicted in the coherent transport regime94 by extending the π-π stacking although the current value is expected to be very low and the effect of incoherent transport will be significant in long molecules.56

Figure 9. Calculated I-V curves for (a) DL, (b) TL, and (c) QL and (d) bias-dependent rectification ratio for DL, TL, and QL.



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5. Summary and conclusions In this manuscript we propose a rectification mechanism based on the coherent transport model, in which the rectifying direction is expected to be opposite to the Aviram-Ratner model. We employed a series of multilayered cyclophanes, i.e., double-layered (DL), triple-layered (TL), and quadruple-layered (QL) cyclophanes, with the hydroquinone donor and quinone acceptor units in the external positions as a model system for the trend study of electron transport and rectification properties in π-stacked systems. We performed NEGF-DFT calculations to investigate the effect of the number of layers on the electron transport and rectification properties in the multilayered donor-acceptor cyclophanes. MPSH analysis within the NEGF-DFT formalism revealed that the LUMO states of DL, TL, and QL have nearly the same energy very close to the Fermi level, playing a key role in the electron transport. The LUMOs of the molecules are localized on the left-hand side (acceptor part), which implies the strong coupling between the LUMOs and the left electrode. From computed zero-bias transmission spectra, we obtained a tunneling decay constant of 0.75 Å-1 for the multilayered π-stacked systems, which falls between the values for π-conjugated molecules and σ-bonded molecules. We performed applied bias calculations, which can provide transmission peak shift and variation of MPSH states under an external electric field. The peak shift with applied voltage is almost all consistent with evolution of the LUMO level. The evolution of the LUMO levels of TL and QL is linear with respect to the change of the electrochemical potential of the left electrode, whereas that of DL is non-linear, due to the presence of the non-negligible interaction between the LUMO state and the right electrode. The applied bias calculations that can provide I-V curves and rectification ratios show that the


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performance of the rectification is improved and the maximum rectification ratio increases with an increase in the number of layers. However, the current value decreases with an increase in the number of layers, due to the exponential tunneling decay. Thus, the most important thing in the design of molecular rectifiers within the coherent transport regime is to strike a balance between exponential decay of transmission probability and increase in the separation of donor and acceptor parts. The series of π-stacked multilayered cyclophanes with the hydroquinone donor and quinone acceptor units in the external positions is suitable for a systematic investigation of the relationship between the electron transport and rectification properties.



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Acknowledgments. K.Y. thanks Grants-in-Aid for Scientific Research (Nos. 22245028 and 24109014) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), the Kyushu University Global COE Project, the Nanotechnology Support Project, the MEXT Project of Integrated Research on Chemical Synthesis, and CREST of the Japan Science and Technology Cooperation. Y.T. thanks JSPS for a graduate fellowship.

Supporting Information Available: Complete ref 69, atomic Cartesian coordinates for molecules DL, TL, and QL, frontier orbitals of hydroquinone, quinone, and benzene, the MPSH states including electrode atoms, comparison of transmission spectra between different adsorption models, and detailed description of calculation condition. This material is available free of charge via the Internet at http://pubs.acs.org.


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TOC graphic for

Current Rectification through π-π

Stacking in Multilayered Donor-Acceptor

Cyclophanes

Yuta Tsuji and Kazunari Yoshizawa*


Current Rectification through ÏâÏ Stacking in Multilayered Donor

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