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J. Phys. Chem. C 2009, 113, 14474–14477
Effect of Aromatic Coupling on Electronic Transport in Bimolecular Junctions Li-Li Lin,† Jian-Cai Leng,† Xiu-Neng Song,†,‡ Zong-Liang Li,† Yi Luo,‡ and Chuan-Kui Wang*,† College of Physics and Electronics, Shandong Normal UniVersity, Jinan 250014, China, and Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, AlbaNoVa, S-10691 Stockholm, Sweden ReceiVed: January 30, 2009; ReVised Manuscript ReceiVed: April 29, 2009
We have performed a systematic first-principles study on conductance-voltage characteristics of bioligo(phenylene ethynylene)-monothiol molecular junctions as recently reported by Wu et al.[Nature Nanotech. 2008, 3, 569]. It is found that the molecular conductance is very sensitive to the vertical distance between two molecules as well as the titled angle between two molecular planes. By comparing with experimental results, key structure parameters for bimolecular junction are determined, indicating that in the experimental devices, the vertical distance between two molecules is around 0.30 nm, the two planar molecules have a cofacial arrangement, and the length of the molecular bridge is about 2.88 nm. The underlying mechanism for electron transport in these aromatically coupled bimolecular junctions has also been discussed. I. Introduction With the development of new experimental techniques that allow the controlled formation of nanometre-sized gaps between pairs of metal electrodes, the preparation of single molecular junctions has become possible in the last decades.1-4 Among these techniques, the construction of mechanical break junctions has attracted much attention.5-8 Various kinds of single-molecule junctions or molecular monolayer junctions, such as atomic wires,9 short organic molecule wires,5 long-chain polymers,10 carbon nanotubes,11 and fullerenes,12 have been reported. Phenylene ethynylene oligomer, a so-called “Tour wire”, consisting of phenyl rings separated by triplet-bonded carbon atoms that form a long rigid molecule with π-conjugated delocalized frontier orbitals, has been intensely studied as a prototype molecular device with a negative differential resistance (NDR) behavior both in experiment and theory.13,14 Thiols (-SH) have been widely used as terminal anchor groups of a molecule for constructing a single-molecular junction thanks to the formation of the strong covalent bonds between gold and sulfur atoms. For those molecules with only one anchor group, the metal-molecular-metal junctions are usually unstable. However, the molecular junctions based on two molecules, where each molecule has one thiol anchor group and the two molecules have strong coupling, are predicted to be formed stably. Recently, using the oligo(phenylene ethynylene) (OPE) molecules with one thiol anchor group, Wu et al. have prepared a series of molecular junctions by using the approach of mechanical break junctions. They observed pronounced conductance peaks similar to those measured for the OPE-dithiol molecule. With careful analysis, they concluded that aromatic π-π coupling between adjacent molecules is efficient enough to allow for the controlled formation of molecular junctions between nearby electrodes.15 A new technique is thus experimentally realized for constructing molecular junctions. It is noted that the aromatic bonding in molecules * To whom correspondence should be addressed. E-mail: ckwang@ sdnu.edu.cn. † Shandong Normal University. ‡ Royal Institute of Technology.
was also found to be important for electric conductivity of molecular junctions.16 To understand the mechanism of formation of molecular junctions and their electronic transport properties, we present a systematic study for the current-voltage characteristics of the bi-OPE-monothiol molecular junctions using the quantum chemical elastic-scattering Green’s function approach at the hybrid density functional theory level. The paper is organized as follows. The introduction is given in section I and the theoretical model and computational details are described in section II. Section III contains our results and discussion. Finally, a conclusion is given in section IV. II. Theoretical Model and Computational Details On the basis of the general Green’s function formalism of Mujica et al.,17 our approach has been applied for elucidating electronic transport properties of several kinds of molecular junctions successfully.18 It considers a system that consists of two semi-infinite electron reservoirs, namely the source (S) and the drain (D), connected by a molecule (M). The transition matrix element from the source to the drain is written as
T(E) )
∑ ∑ VJSVDK ∑ (E 〈J|η〉〈η|K〉 - εη) + iΓη J
K
(1)
η
where J and K run over all the atomic sites, which are denoted as 1, 2,..., N, and sites 1 and N are the two end sites of the molecule that connect with two electron reservoirs. VJS (VDK) represents the coupling between atomic site J (K) and reservoirs S (D) and VJS are written as follows:
VJS ) 〈J|H|S〉 )
∑ CηRJ 〈JR|H|Si〉CηiS
(2)
η,R,i
Orbital |η〉 is the eigenstate of the Hamiltonian (H) of a finite system that consists of the molecule sandwiched between two clusters of metal atoms. The product of two overlap matrix
10.1021/jp900908w CCC: $40.75 2009 American Chemical Society Published on Web 07/17/2009
Effect of Aromatic Coupling on Electronic Transport
J. Phys. Chem. C, Vol. 113, No. 32, 2009 14475
Figure 1. Stacking configuration of the bi-OPE-monothiol junction in our simulation. The dashed frame contains the extended molecular system.
elements 〈J|η〉〈η|K〉 represents the delocalization of the orbit |η〉. For a three-dimensional electrode, when the external bias VD is applied, the net current density of junction from the source to the drain can be written as
iSD )
4em*kBT p3
∫eV∞ ln
(
Ef + eVD - EZ kBT Ef - EZ 1 + exp kBT
1 + exp
(
)
)
|T| 2nS(EZ)nD(EZ) dEZ
(3)
where m*is the electron effective mass, Ef is the Fermi level, and nS and nD are the density of states of the source and drain, respectively. For the three-dimension system, ISD ) AiSD, where A is the effective injection area. The conductance is obtained by
G ) ∂ISD/∂VD
(4)
In our simulations, two cofacial molecules are sandwiched between two semi-infinite gold electrodes. As a possible configuration (see Figure 1), the contact geometry is a triangle structure with three gold atoms, and the terminal thiol anchor for each molecule locates at a hollow site, where a strong chemical bond is formed between each sulfur atom and the gold atoms. These three gold cluster systems have been found to be adequate for describing sulfur-gold contacts.19-21 The two molecules and the two gold clusters thus constitute our extended molecular system, where d represents the vertical distance between the two molecular planes, a represents the translation distance of one molecule relative to the other molecule, and β is the tilted angle of one molecular backbone where the other molecule is fixed. The optimized OPE-monothiol molecule remains in a planar configuration. The bond lengths of S-Au and Au-Au are set to be respectively 0.285 and 0.288 nm. The choice of the Fermi level is a major problem for the modeling of single molecular transport. In our calculations, the middle of HOMO and LUMO of the metal-molecule cluster is chosen as the Fermi level, and the nonequilibrium transport is considered by simply lining up the Fermi energy of the extended molecule and the bulk metals.22 The geometry optimization and the electronic structure calculation are performed at the hybrid density-functional theory (DFT) B3LYP level with Lanl2DZ basis set in the GAUSSIAN 03 package,23 where the effective core potential (ECP) is used for the gold atoms. The electron transport properties are obtained from the QCME program.24
Figure 2. (a) Conductance-voltage curves of the bi-OPE-monothiol molecular junctions with different vertical distance and (b) conductancevoltage curves of the OPE-dithiol molecular junctions.
III. Results and Discussion A. Dependence on Vertical Distance d. For the case of β ) 0, we study the dependence of molecular conductance between two molecules in the junction. Here the translation distance a is chosen as 0.838 nm, thus the distance b between the two sulfur atoms for the bi-OPE-monothiol is 2.88 nm, which is close to the experimentally estimated value of 2.91 nm. The conductance-voltage curves of the bi-OPE-monothiol junctions at different vertical distance are shown in Figure 2a. At about 0.8 V bias, the first conductance plateau appears. It is clearly seen that the values of the conductance plateau are increased when d is decreased. When the vertical distances are taken to be 0.36, 0.33, 0.31, and 0.28 nm, the conductance plateaus are G ) (9.7 × 10-7)G0, (3.1 × 10-6)G0, (4.4 × 10-6)G0, and (1.2 × 10-5)G0, respectively, where G0 ) 2e2/h is the quantum conductance unit. The calculated conductance values at about 0.30 nm is highly comparable with G )(5.9((2.4) × 10-6)G0 given by the measurement.15 From the simulation, it is clearly shown that the molecular junction based on aromatic coupling is gradually formed as the vertical distance becomes narrower. As a comparison, we also calculate the conductance of the OPE-dithiol molecular junction as shown in Figure 2b. The conductance plateau is G ) (3.2 × 10-4)G0, which is in the same order as G ≈ (1.2 × 10-4)G0 in the experiment. The OPE-dithiol junction has a better electronic transport behavior compared to the bi-OPE-monothiol junction because the electronic tunneling distance for the OPE-dithiol junction is shorter. This consistency between the simulation and the measurement for the OPE-dithiol junction further demonstrates the reliability of our theoretical model. As we know, for the bimolecular system, there exist two possible electron transport pathways, namely, (1) electrons directly tunnel through one molecule to the right electrode from the left electrode and (2) electrons first move to one molecule, then hop to the other molecule that is covalently bonded to the other electrode, and finally go to the electrode. For a pair of parallel atomic wires, Lang et al. have shown that the conductance is strongly dependent on the wire separation, which indicates the importance of both pathways.9 For the 1,4dithiolbenzene molecular junction, the intermolecular interaction and molecule-electrode coupling have a large effect on the molecular electronic conductance.25 In our case, because the
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J. Phys. Chem. C, Vol. 113, No. 32, 2009
Lin et al.
TABLE 1: Coupling Energy between Molecules and HOMO and LUMO Energies of Extended Molecular System with Configuration B as the Vertical Distance between Molecules Is Modified d ) 0.28 nm d ) 0.31 nm d ) 0.33 nm d ) 0.36 nm coupling energy (eV) HOMO (eV) LUMO (eV)
7.95
2.78
1.34
0.39
-5.51 -3.82
-5.53 -3.82
-5.54 -3.82
-5.55 -3.82
two molecules in question are covalently linked to different electrodes and one end of one molecule is quite a long distance away from an electrode, the first pathway is negligible. The coupling energy between the two molecules and the energies of the highest occupied molecular orbit (HOMO) and the lowest unoccupied molecular orbit (LUMO) of the extended molecule are listed in Table 1. As d is increased, the coupling energy is decreased, and the energy gap between HOMO and LUMO is wider, which results from the weaker interaction between the two OPE molecules. Furthermore, it is seen that the bi-OPE-monothiol junction is difficult to form at d ) 0.36 nm, where the coupling energy is just 0.39 eV. The charge distributions of the two delocalized molecular orbits, HOMO and LUMO+2, are plotted in Figure 3. The behavior of the molecular orbits is modified as the vertical distance d is varied. In general, when d is smaller than 0.33 nm, there exists overlapping of the wave functions attributed to a single molecule, and the molecular orbits display a unitary behavior related to the two molecules. Here the π-π stacking interaction between the monothiol molecules is strong enough to induce the formation of molecular junctions. When d is quite large, for instance, d ) 0.36 nm, the molecular orbits have some of the character of a single molecule’s orbit, which is responsible for the weaker π-π interaction. B. Dependence on Different Horizontal Distance a. In the above section, the electronic transport properties of one reason-
Figure 3. Charge distribution of two delocalized molecular orbits, HOMO and LUMO+2, of the extended molecular junctions with different vertical distances. All orbits are drawn with the same isovalue.
Figure 4. Conductance-voltage curves of the three bimolecular junctions. Inset figures are configurations of three extended molecular junctions noted as A, B, and C.
TABLE 2: Coupling Energy between Molecules, HOMO and LUMO Energies, and Conductance at 1.0 V for Bimolecular Junctions with Three Configurations, A, B, and C stacking configuration
G (G0)
A B C
1.84 × 10-4 1.22 × 10-5 9.23 × 10-7
coupling HOMO (eV) LUMO (eV) energy (eV) -5.30 -5.51 -5.57
-3.83 -3.82 -3.82
12.74 7.95 3.33
able stacking configuration suggested by the experimental counterpart are demonstrated. In this section, taking other stacking configurations into consideration, we study their conductance behavior. The horizontal distance a is taken as 0.142, 0.838, and 1.529 nm, thus, three stacking configurations are formed with three (A), two (B), or one (C) phenyl overlapping, respectively, between the two molecules as shown in the inset in Figure 4. The distances between the two sulfur atoms for the bi-OPE-monothiol are respectively b ) 2.18, 2.88, and 3.57 nm. The vertical distance is taken to be 0.28 nm. From Figure 4, it is seen that the onset of the first conductance plateau for the three configurations appears at different bias, 0.7 V for configuration A and 0.9 V for configuration B, but it does not appear in the interested bias regime for configuration C. This is understandable, that is, from configuration A to C, the HOMO-LUMO energy gaps become wider because of the weaker π-π interaction due to the reduced overlap between the molecules as shown in Table 2. Furthermore, the conductance plateau for configuration A takes the largest value, G ) (1.8 × 10-4)G0. Note that this value has the same order of magnitude as that of the OPE-dithiol junction. The largest conductance value is attributed to the strongest coupling between the molecules and the shortest tunneling distance among the three configurations. However, the conductance value is much larger than the experimental observation. From the simulation, one can conclude that configurations A and C are less likely to be formed in experimental circumstances, which is consistent with the predication in ref 15. C. Dependence on Different Tilted Angle β. For the case of a ) 0.838 nm, we study the effect of tilted angles of one molecular backbone relative to the other molecule on the electronic transport properties of the molecular junctions. At β ) 0, the vertical distance d is 0.28 nm. In Figure 5, the conductance of the bimolecular junction at 1.0 V bias is shown as a function of the tilted angle. From Figure 5, one can see that the transport properties of the bimolecular junction are very
Effect of Aromatic Coupling on Electronic Transport
Figure 5. Conductance vs. tilted angle at 1.0 V bias.
J. Phys. Chem. C, Vol. 113, No. 32, 2009 14477 IV. Conclusion The quantum chemical elastic-scattering Green’s function approach is applied for a systematic study of the conductancevoltage characteristics of the bi-OPE-monothiol molecular junctions. The conductances, coupling energy between the molecules, and the charge distribution of the molecular orbits for the bimolecular junctions are analyzed. The theoretical work has supported the experimental findings that the bimolecular junction based on aromatic coupling can be formed. A probable configuration of the bimolecular junction has been obtained. When the vertical distance between the two molecules is increased, the conductance of the bimolecular junction is greatly reduced. The transport properties of the bimolecular junction are very sensitive to the tilted angle of one molecule. The theoretical investigation is helpful in understanding the mechanism of the controlled formation of the molecular bridges between nearby electrodes by the new technique and strategy. Acknowledgment. This work is supported by the National Nature Science Foundation of China under Grant No. 10674084 and Nature Science Foundation of Shandong Province under Grant No. Z2007A02. The authors thank the support of the Swedish International Development Agency (SIDA) (348-20066679). References and Notes
Figure 6. Conductance-voltage curve of the bi-OPE-monothiol molecular junctions with a 13 Au atom cluster at each side.
sensitive to the incline. When the molecular backbone has a tilted angle of just 5°, the conductance is greatly reduced from (1.2 × 10-5)G0 to (3.1 × 10-7)G0. As the tilted angle becomes larger than 15°, the conductance is difficult to observe. The situation is clearly seen because the coupling energy between the molecules is highly decreased from 7.95 to 0.076 eV when β is modified from 0° to 5°. We note that the total energies of the extended molecular system for different tilted angle β show little difference. Therefore, the bimolecular junctions with a tilted angle will probably be formed. Thus, to improve the efficiency for establishing the cofacial bimolecular junctions with β ) 0, one needs to pursue a more delicate technique. In the present study, the three gold cluster in triangle configuration is used as the contact structure to simulate the interaction between the molecule and the electrode. Further work is need to prove the reliability of our results with respect to the size of gold clusters, as even the three gold cluster was found to be adequate for describing sulfur-gold contacts in other molecular junctions.19-21 Thirteen Au atoms are adopted at each side for constructing the extended molecule (see the inset in Figure 6). From Figure 6, one can see that the voltage-conductance curve for the molecular junction with b ) 2.88 nm, d ) 0.28 nm, and a ) 0.838 nm is similar to that in Figure 2. Furthermore, the value of the conductance plateau is (7.9 × 10-6)G0, which is a little smaller than that with three Au clusters, but it is closer to the measured value. The reliability of our results is thus demonstrated.
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