J. Phys. Chem. C 2009, 113, 20967–20973
20967
Conductance of Conjugated Molecular Wires: Length Dependence, Anchoring Groups, and Band Alignment Guowen Peng,† Mikkel Strange,‡ Kristian S. Thygesen,*,‡ and Manos Mavrikakis*,† Department of Chemical and Biological Engineering, UniVersity of Wisconsin-Madison, Madison, Wisconsin 53706, and Center for Atomic-scale Materials Design, Department of Physics, Technical UniVersity of Denmark, DK-2800 Kgs. Lyngby, Denmark ReceiVed: September 2, 2009; ReVised Manuscript ReceiVed: October 19, 2009
The conductance of π-conjugated molecular wires bonded to gold electrodes at zero bias is studied using density functional theory combined with nonequilibrium Green’s function method. For all systems considered, we find that the conductance length dependence follows the simple exponential law characteristic of tunneling through a barrier, G ) Gc exp(-βL). For thiophene, pyrrole, and phenyl wires with thiol end-groups, we calculate decay constants (β) of 0.211, 0.257, and 0.264 Å-1, respectively, and contact conductances (Gc) of 1.25, 2.90, and 1.22G0, where G0 ) 2e2/h is the conductance quantum. In comparison, the corresponding values for amine-terminated thiophene are calculated to be β ) 0.160 Å-1 and Gc ) 0.038G0. These results show that (1) the contact resistance is mainly determined by the anchoring group and (2) the decay constant, which determines the conductance in the long wire limit, is not solely determined by the intrinsic band gap of the molecular wire but also depends on the anchoring group. This is because the alignment of the metal Fermi level with respect to the molecular levels is controlled by charge transfer and interface dipoles which in turn are determined by the local chemistry at the interface. Analysis of the charge transfer at the interface shows that the thiol-bonded molecules receive electrons from the Au electrodes while the amine-bonded molecules donate electrons to the Au electrodes. Introduction Bottom-up molecular electronics based on the idea of using single molecules as circuitry building blocks have attracted considerable attention in the past decade.1–4 Understanding the electrical properties and transport mechanism of molecules bonded to two electrodes is an essential prerequisite for modeling and eventually for the design of more complex devices and is therefore a key challenge to molecular electronics.5–7 It is well established that the transport properties of a molecule connecting two electrodes depend on the intrinsic properties of the molecule,8 such as the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO),9–12 the molecular conformation,6,13,14 and the molecular bond characteristics (e.g., saturated versus unsaturated).2,15 In addition, the chemical groups anchoring the molecule to the electrodes,16–18 the work function of the electrodes,17,19 and the contact geometry of the molecule-electrode interface1,2,20,21 also affect the transport properties of molecular junctions. The electron transport typically occurs via a nonresonant tunneling process. In this regime, the conductance of a molecular wire decays exponentially with increasing length:8
G ) Gc exp(-βL)
(1)
where Gc is the contact conductance, β is the decay constant, and L is the length of the wire. The contact conductance Gc is expected to depend strongly on the chemical identity of the * To whom correspondence should be addressed. E-mail: thygesen@ fysik.dtu.dk (K. S. T.) and
[email protected] (M. M.). † University of Wisconsin-Madison. ‡ Technical University of Denmark.
groups anchoring the molecule to the electrodes. On the other hand, it is reasonable to expect that the decay constant β, which determines the conductance in the limit of long wires, is less sensitive to the anchoring group and is mainly determined by the intrinsic properties of the molecule such as the HOMOLUMO gap. Indeed, experiments show that saturated σ-bonded alkanes with larger HOMO-LUMO gaps have larger decay constants (∼1.0 Å-1),2,18,19,22 while unsaturated π-conjugated molecules have lower decay constants (0.2-0.6 Å-1).2,8,15,23 In the case of alkanes, the decay constant has also been found to be weakly dependent on the anchoring groups16 and the work function of the electrodes.19 Over the past few years, much experimental and theoretical work has been done on transport properties of saturated molecules, in particular, alkane chains.5,6,11,16,18–20,24,25 Compared to saturated molecules, few systematic studies have been done on the transport properties of the more conducting unsaturated π-conjugated molecules, though the simplest unsaturated π-conjugated molecule benzene probably is the most extensively studied model system.12,26–30 Recently, the conductance of oligothiophene, the unit making up polythiophene, has been measured.31,32 The measurement of length dependence of the conductance of oligothiophene molecules terminated with a thiocyanate group showed that oligothiophene has an estimated decay constant of 0.1 Å-1 which makes it a good candidate molecular wire for long-range conduction.32 Theoretical work on the length dependence of conductance and the transport mechanism of oligothiophenes, however, is still lacking. Here, we report a systematic first-principles study on the transport properties of π-conjugated molecules bonded to gold electrodes with dithiol and diamine anchoring groups. We calculate the conductance of thiol-terminated thiophene (T), pyrrole (P), and phenyl (Ph) oligomers as well as amine-
10.1021/jp9084603 CCC: $40.75 2009 American Chemical Society Published on Web 11/09/2009
20968
J. Phys. Chem. C, Vol. 113, No. 49, 2009
Figure 1. Geometries of (a) hexathiophene-dithiol and (b) hexathiophene-diamine junctions. Different thiophene units are denoted by u1, u2, and u3 according to their distances from the anchoring S atoms.
terminated oligothiophene containing one to eight units, and we extract the decay constants and prefactors. The effect of the intrinsic properties of the molecules, in particular, their HOMO-LUMO gaps, versus the effect of the anchoring groups is discussed. To understand the transport mechanism through these conjugated molecules, we perform a detailed analysis of the band alignment of the molecular orbitals with the metal Fermi level, the charge transfer between molecule and electrodes, the dipoles at the contacts, and the electrostatic potential change at the interface. Methods Molecular junctions with a dithiol (deprotonated) anchoring group are modeled in a supercell containing the molecule sandwiched between two Au(111)-(3 × 3) slabs with the S atoms placed in face-centered cubic (fcc) hollow sites of the Au(111) surfaces (see Figure 1a). Both the molecule and its two nearest neighboring Au layers on either side have been fully relaxed. For molecular junctions with a diamine anchoring group, we include two four-atom Au pyramids attached to Au(111)-(3 × 3) surfaces as shown in Figure 1b considering the fact that diamine prefers to bond with Au at a top site.33 Both the Au4 pyramids and the molecule are fully relaxed. The geometry optimizations of all structures are performed using the VASP code34,35 on the basis of density functional theory (DFT). Ultrasoft pseudopotentials36 are used for electron-ion interactions, and the generalized gradient approximation (GGAPW91)37 is used for exchange and correlation. The electron wave function is expanded using plane-waves with a cutoff energy of 300 eV (for systems without nitrogen atoms) or 400 eV (for systems with nitrogen atoms). The Brillouin zone is sampled using a (1 × 6 × 6) k-point mesh using the Monkhorst-Pack scheme.38 The conductance is computed within the Landauer-Bu¨ttiker formalism where the conductance is given by G ) G0T(εF), where G0 ) 2e2/h is the conductance quantum and T(εF) is the transmission function at the Fermi level.39 The transmission function is calculated using the nonequilibrium Green’s function method which has been described elsewhere.26,27 The Kohn-Sham Hamiltonian of the optimized molecular junctions is obtained using the SIESTA code40 with a single-ζ-polarized (SZP) basis. In the Green’s function method, the system is divided into the left electrode, the right electrode, and the scattering region. The left and right electrodes are modeled by a periodic nine-layer Au(111)-(3 × 3) slab. The geometry of the scattering region is schematically illustrated in Figure 1. Eight irreducible k-points are used to sample the transmission function over the transverse Brillouin zone. Results and Discussion We first focus on the transport properties of the dithiolterminated conjugated molecules. To obtain a realistic contact
Peng et al. geometry between the molecules and the Au electrodes, we first performed adsorption calculations, where the molecule was adsorbed on a Au(111) slab with one terminal sulfur atom (S), whereas the other terminal S-atom was passivated by an additional hydrogen atom (H). After getting the preconverged geometry, the passivation-H was removed and a second Au(111) slab was used to sandwich the dithiol-terminated molecule. Then, the whole system was optimized until the residual forces were smaller than 0.05 eV/Å. Figure 1a shows the optimized contact geometry of hexathiophene-dithiol junction, Au(S-6T-S)-Au. The Au-S bond lengths in the optimized thiophene-dithiol Au junctions range from 2.47 to 2.56 Å. Figure 2a-c shows the calculated transmission functions for thiol-terminated thiophene, pyrrole, and phenyl oligomers containing one, two, four, and eight units. For all three molecules, the transmission functions of the short wires show a broad peak around -1 eV. Interestingly, for oligophenyldithiol, this broad peak disappears as the wire becomes longer. It has previously been found that a transmission peak around -1 eV is characteristic of Au-S-Au junctions,41 and we therefore ascribe this common feature in the transmission functions to tunneling via the sulfur p-orbitals. For the long wires, one clearly sees the beginning of the formation of continuous valence and conduction bands with the Au Fermi level (EF) positioned inside the band gap. The position of the Fermi level with respect to the HOMO and LUMO levels, that is, the level alignment, as well as the size of the HOMO-LUMO gap is, however, different for the three molecules. For both oligothiophenes and oligopyrroles, the Au Fermi level is positioned just above the HOMO level (in the long wire limit), and the distance to the LUMO is 0.9 and 1.5 eV, respectively. The relatively close proximity of the HOMO with EF indicates that oligothiophenes and oligopyrroles should have good (and similar) conducting properties. That this is indeed the case follows from Figure 3 which shows the conductances on a logscale as a function of the molecular length. The best-fit lines yield a decay constant of 0.211 and 0.257 Å-1 for oligothiophene and oligopyrrole, respectively. Returning to Figure 2c, we see that for oligophenyl, the EF is closer to the LUMO in the long wire limit rather than to the HOMO as was the case for oligothiophene and oligopyrrole. The energy separation between the EF and the LUMO in oligophenyl is larger than the energy separation between the EF and the HOMO in oligothiophene and oligopyrrole suggesting that oligophenyl (in the long wire limit) is less conductive. This is confirmed by Figure 3 which shows that the decay constant of oligophenyl is 0.264 Å-1. Our calculated decay constants for oligothiophene (0.211) and oligophenyl (0.264) should be compared to the experimental values of 0.132 and 0.42,15 respectively. While the relative sizes of our decay constants, that is, the fact that βT < βPh, agree with experiments, the absolute values differ significantly. There could be several reasons for the disagreement. One reason could result from uncertainties in the level alignment predicted by our DFT calculations. Indeed, this is a rather sensitive quantity and we did observe differences between the SIESTA (SZP) and VASP results, whereby SIESTA (SZP) systematically predicts a slightly higher position of the Fermi level relative to the HOMO and LUMO energies. Another possible reason could result from the uncertainties of the nature of contact geometries20 and of the molecular conformation6 in experiments. It is interesting that a recent experimental study observed an unusual length dependence of the conductance of thiophene molecules: the longer thiophene molecule (4T-CH2) has larger conductance than the
Conductance of Conjugated Molecular Wires
J. Phys. Chem. C, Vol. 113, No. 49, 2009 20969
Figure 2. Transmission functions for thiophenedithiol (a), pyrroledithiol (b), phenyldithiol (c), and thiophenediamine (d) oligomers with one, two, four, and eight units.
shorter one (3T-CH2),31 contrary to the exponential decay shown in Figure 3. One possible reason for this discrepancy could be the different contact geometry or molecular conformation in experiments compared to our model. Indeed, our calculated transmission function of oligothiophene is different from that obtained in a previous theoretical work42 using a cluster model. From the best-fit lines in Figure 3, we extract contact conductances of 1.25, 2.90, and 1.22G0 for dithiol-terminated oligothiophene, oligopyrrole, and oligophenyl molecules, respectively. These contact conductances are in the same order, which is expected because the same dithiol anchoring group is used to connect to the Au electrodes. To gain insight into the mechanism determining the band alignment and thus the conductance of the thiol-terminated wires, we performed an analysis of the electronic structures of the contact region illustrated in Figure 1a. We first analyzed the band alignment of the molecular energy levels to the electrode Fermi level of the molecular junctions Au-(Soligomer-S)-Au. To this end, we projected the density of states (DOS) on different thiophene, pyrrole, or phenyl units which are schematically illustrated as u1, u2, and u3 in Figure 1a. The projected density of states (PDOS) of each unit of molecules is calculated by summing the projected density of states on each atom. The total DOS and PDOS on different units for dithiol-
Figure 3. Semilog plot of conductance as a function of molecular length for thiophenedithiol, pyrroledithiol, phenyldithiol, and thiophenediamine molecules. Points show calculated data. Lines shown are best fits yielding a decay constant of 0.211, 0.257, 0.264, and 0.160 Å-1 for thiophenedithiol, pyrroledithiol, phenyldithiol, and thiophenediamine molecules, respectively. The y-intercepts give a contact conductance of 1.25, 2.90, 1.22, and 0.038G0 for thiophenedithiol, pyrroledithiol, phenyldithiol, and thiophenediamine molecules, respectively.
20970
J. Phys. Chem. C, Vol. 113, No. 49, 2009
Peng et al. pyrrole. This indicates that the conduction through these conjugated molecules is via a hole-tunneling mechanism. As clearly seen in Figure 4, the states in the HOMO-LUMO gap decay rapidly as we move away from the interface, which allows us to assign the band edges from the PDOS of the deepest oligomer units.10 The calculated energy difference between the Fermi level and the nearest band (valence or conduction) edges, ΦB, are 0.3, 0.2, and 0.7 eV for Au-(S-6T-S)-Au, Au-(S-6P-S)-Au, and Au-(S-6Ph-S)-Au, respectively. The difference in ΦB can qualitatively explain why oligothiophenes and oligopyrroles have comparable conductances, whereas the conductance of oligophenyls is smaller. We also calculated the energy difference between the electrode Fermi level and the isolated 6T, 6P, and 6Ph molecular levels in which the geometries of the electrodes and the molecules are fixed as in the optimized contact structures. Similarly, as done in Figure 4, we calculated the PDOS of each molecular unit of the isolated molecules. The calculated energy separation between the electrode Fermi level and the band edge of the deepest molecular unit,ΦB, is 1.7, 1.7, and 0.1 eV for 6T, 6P, and 6Ph, respectively. This implies that after bonding to Au electrodes, the HOMO or LUMO upshifts by 1.4, 1.5, and 0.6 eV for 6T, 6P, and 6Ph, respectively. The molecular level upshift suggests that electron transfer from the Au electrodes to the molecules. To investigate how the charge redistribution occurs at the interface between the molecule and the Au electrodes, we calculated the charge density difference between a junction and the corresponding isolated molecule and the Au electrodes. We then averaged the charge density difference on the (x, y) plane. The (x, y)-plane averaged charge density difference, ∆F(z), for the Au-(S-6T-S)-Au junction is plotted in Figure 5a. The charge transfer between the molecule and the electrodes is estimated by integrating ∆F(z) over the molecule from the left to the right interfaces as indicated by the vertical dashed lines in Figure 5a. The calculated charge transfer is 0.06e, 0.06e, and 0.07e for Au-(S-6T-S)-Au, Au-(S-6P-S)-Au, and Au-(S-6Ph-S)-Au, respectively. Nearly the same amount of charge transfer is found in other Au-(S-oligomer-S)-Au junctions. The charge transfer is from the Au electrodes to the molecule. In other words, the dithiol-terminated molecules gain electrons. This result is consistent with the observed upshift of the molecular orbitals relative to the electrode Fermi level upon binding. The charge transfer between the Au electrodes and the molecule will induce local dipole moments at the interfaces.43 The local dipole moment at the left interface can be estimated from
µL )
Figure 4. Total density of states and projected densities of states on each molecular unit for (a) Au-S-hexathiophene-S-Au, (b) Au-S-hexapyrrole-S-Au, and (c) Au-S-hexaphenyl-S-Au. The energy separation between the metal Fermi level and the nearest band edge of the deepest molecular unit is 0.3, 0.2, and 0.7 eV for Au-S-hexathiophene-S-Au, Au-S-hexapyrrole-S-Au, and Au-S-hexaphenyl-S-Au, respectively.
terminated hexathiophene, hexapyrrole, and hexaphenyl oligomers are shown in Figure 4a-c. Notice that the HOMO state is near to the Fermi level for dithiol-terminated thiophene and
∫0c/2 z∆F(z)dz
(2)
where the integration is over half of the unit cell along the wire axis. The local dipole moment at the right half unit cell has the same magnitude as that at the left half but has an opposite direction. The calculated local dipole moments are 1.6, 1.4, and 1.3 D for Au-(S-6T-S)-Au, Au-(S-6P-S)-Au, and Au-(S-6Ph-S)-Au, respectively. Because of the local dipole effect, the electrostatic potential of a junction will change. We investigated this effect by calculating the electrostatic potential difference between a junction and the corresponding isolated molecule and the electrodes. The vacuum levels of the isolated molecule and the electrode are aligned during the calculations of the electrostatic potential difference. Figure 5b shows the
Conductance of Conjugated Molecular Wires
Figure 5. Plane-averaged charge density difference (a) and electrostatic potential difference (b) for Au-S-hexathiophene-S-Au. About 0.06e charge transfers from the Au electrode to the molecule resulting in a local dipole moment of 1.59 D developing at the interface. Vertical dashed lines indicate the interface positions.
(x, y) plane-averaged electrostatic potential difference, ∆ESP, for the Au-(S-6T-S)-Au junction. ∆ESP increases while going away from the interface and becomes nearly flat in the middle of the molecular wire. The electrostatic potential increases by 0.9 eV at the center of the S-6T-S molecule. The increase of the electrostatic potential in the molecule is in accord with the fact that a charge transfer occurs from the metal to the molecule. We now examine the effect of anchoring groups on the conductance of the conjugated oligomers. For this purpose, we study the transport properties of diamine-terminated oligothiophenes and compare with those of dithiol-terminated oligothiophenes. In Figure 1b, we show the optimized contact geometry of hexathiophene-diamine junction, Au-(NH2-6T-NH2)-Au. In the optimized structures of all thiophene-diamine junctions considered in this study, the Au-N bond lengths are in the range of 2.40-2.45 Å, and the Au-N-C angles are in the range of 120 - 126°. Figure 2d shows the transmission functions of diamineterminated oligothiophene molecules having one, two, four, and eight thiophene units (denoted as 1T-NH2, 2T-NH2, 4T-NH2, and 8T-NH2). Compared to the transmission functions of dithiol-terminated oligothiophenes shown in Figure 2a, no broad transmission peak around -1 eV is found. With the same number of thiophene units, the sharp transmission peak contributed by the LUMO of diamime-terminated
J. Phys. Chem. C, Vol. 113, No. 49, 2009 20971 oligothiophene is closer to the Fermi level than that of dithiolterminated oligothiophene. The transmission at the Fermi level, T(εF), of diamine-terminated oligothiophenes is 1 order of magnitude smaller than that of dithiol-terminated oligothiophenes. The semilog plot of the conductances of diamine-terminated oligothiophenes versus their molecular lengths is also shown in Figure 3. We note that the calculated conductance for oligothiophene-diamine deviates slightly from the ideal exponential decay. Interestingly, the deviations look like so-called even-odd oscillations superimposed on an exponentially decreasing background. Even-odd oscillations have been observed in atomically thin metal wires where electron waves resonating back and forth within the wire cause the conductance to oscillate between high and low values depending on the number of atoms in the wire.44 A best-fit line of the conductances of all diamine-terminated oligothiophenes yields a decay constant of 0.16 Å-1 and a contact conductance of 0.038G0. The decay constant of diamine-terminated oligothiophenes is 0.05 Å-1 smaller than that of dithiol-terminated oligothiophenes. The weak dependence of the decay constant on the chemical identity of the anchoring groups was observed experimentally for alkanes, where β(dithiol) > β(diamine) was reported.16 The effect of anchoring groups on the contact conductance is significant; the contact conductance of diamine-terminated oligothiophenes is 33 times smaller than that of dithiol-terminated oligothiophenes. The difference in contact conductances is related to the larger strength of the Au-S bond as compared to the Au-N bond. This suggests that a stronger (weaker) binding gives a larger (smaller) contact conductance, which is in line with previous experiment results.16 To compare the effect of different anchoring groups on the band alignment, we calculated the total DOS and PDOS on each thiophene unit for Au-(NH2-6T-NH2)-Au. The results are shown in Figure 6a. In contrast to the thiol-bonded molecules where the band alignment is determined by the HOMO, the Fermi level is closer to the LUMO of amine-terminated molecules. The distance from the Fermi level to the conduction band edge, ΦB, is only 0.15 eV for Au-(NH2-6T-NH2)-Au. This number is smaller than the ΦB found for all the thiol-terminated junctions which explains the relation β(dithiol) > β(diamine). We also calculated the band alignment for isolated NH26T-NH2 and Au electrodes. Our calculations show that the LUMO state is 1.4 eV above the electrode Fermi level before the two systems are brought into contact. The downshift of the LUMO upon bonding indicates that electron transfer from the molecule to the electrode. The (x, y) plane-averaged charge density difference plotted in Figure 6b confirms this: about 0.3 electrons are transferred from the NH2-6T-NH2 to the Au electrodes. The local dipole moment induced by this charge transfer is 3.6 D for the Au-(NH2-6T-NH2)-Au junction. The dipole moment at the interface of junctions with a diamine anchoring group is larger than that with a dithiol group. This correlates well with the larger charge transfers in the diamineterminated oligomers. The electron-donor characteristics of the diamine anchoring group can also be clearly shown by the (x, y) plane-averaged electrostatic potential difference ∆ESP in Figure 6c, where ∆ESP drops rapidly at the interface and becomes nearly flat inside the molecule. This is in sharp contrast to the shape of ∆ESP of S-6T-S shown in Figure 5b. The electrostatic potential drops as much as 1.9 eV in the center of NH2-6T-NH2 molecule as compared with the electrostatic potential increase of 0.9 eV in the center of S-6T-S molecule.
20972
J. Phys. Chem. C, Vol. 113, No. 49, 2009
Peng et al. Conclusions In summary, we presented a systematic first-principles study of the transport properties of π-conjugated molecules bonded to gold electrodes with dithiol and diamine anchoring groups. We showed that the conductance of thiophenedithiol, pyrroledithiol, and phenyldithiol molecules decreases exponentially with molecular length with a decay constant of 0.211, 0.257, and 0.264 Å-1, respectively. Analysis of the alignment of the metal Fermi level to molecular orbitals demonstrated that the transport through thiophenedithiol and pyrroledithiol molecules is mediated by a nonresonant hole-tunneling mechanism. Comparison of the conductance of thiophene-diamine to that of thiophene-dithiol molecules showed that the contact conductance strongly depends on the chemical identity of the anchoring groups. The contact conductance of molecules with a diamine anchoring group is 33 times smaller than that of molecules with a dithiol anchoring group. The decay constant, on the other hand, was found to be mainly determined by the intrinsic properties of the molecule wire and also to be dependent on the chemical identity of the anchoring groups. We showed that in molecular junctions terminated with a dithiol anchoring group, charge transfers from the electrode to the molecule. In contrast, in molecular junctions terminated with a diamine anchoring group, charge transfers from the molecule to the electrode. This charge transfer induces local dipole moments at the interface of the contacts, which results in a change of the electrostatic potential and a shift of the HOMO and LUMO. Acknowledgment. This work was supported by NSF through the University of Wisconsin-Madison Materials Research Science and Engineering Center (NSF Grant No. DMR-0520527). Computational resources were provided by the Department of Defense Supercomputing Resources Centers (NAVY, ARSC, MHPCC, ERDC). M. S. and K. S. T. were supported by The Lundbeck Foundation’s Center for Atomic-scale Materials Design (CAMD). References and Notes
Figure 6. (a) Total density of states and projected densities of states on each molecular unit, (b) plane-averaged charge density difference, and (c) plane-averaged electrostatic potential difference for Au-NH2hexathiophene-NH2-Au. The conduction band edge is at 0.15 eV above the Fermi level as shown in a. Charge transfer (∼0.31e) occurs from the molecule to the Au electrode resulting in a local dipole moment of 3.60 D. Vertical dashed lines in b and c indicate the interface positions.
The variation of electrostatic potential in the molecule with different anchoring groups is in good accord with the electronacceptor or electron-donor characteristics of dithiol and diamine groups, respectively.
(1) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384–1389. (2) Salomon, A.; Cahen, D.; Lindsay, S.; Tomfohr, J.; Engelkes, V. B.; Frisbie, C. D. AdV. Mater. 2003, 15, 1881–1890. (3) Tao, N. J. Nat. Nanotechnol. 2006, 1, 173–181. (4) Joachim, C.; Ratner, M. A. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 8801–8808. (5) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571–574. (6) Venkataraman, L.; Klare, J. E.; Nuckolls, C.; Hybertsen, M. S.; Steigerwald, M. L. Nature 2006, 442, 904–907. (7) Choi, S. H.; Kim, B.; Frisbie, C. D. Science 2008, 320, 1482– 1486. (8) Magoga, M.; Joachim, C. Phys. ReV. B 1997, 56, 4722–4729. (9) Tomfohr, J. K.; Sankey, O. F. Phys. ReV. B 2002, 65, 245105. (10) Wang, J. G.; Prodan, E.; Car, R.; Selloni, A. Phys. ReV. B 2008, 77, 245443. (11) McDermott, S.; George, C. B.; Fagas, G.; Greer, J. C.; Ratner, M. A. J. Phys. Chem. C 2009, 113, 744–750. (12) Xue, Y. Q.; Datta, S.; Ratner, M. A. J. Chem. Phys. 2001, 115, 4292–4299. (13) Ke, S. H.; Baranger, H. U.; Yang, W. T. Phys. ReV. Lett. 2007, 99, 146802. (14) Pauly, F.; Viljas, J. K.; Cuevas, J. C.; Schon, G. Phys. ReV. B 2008, 77, 155312. (15) Wold, D. J.; Haag, R.; Rampi, M. A.; Frisbie, C. D. J. Phys. Chem. B 2002, 106, 2813–2816. (16) Chen, F.; Li, X. L.; Hihath, J.; Huang, Z. F.; Tao, N. J. J. Am. Chem. Soc. 2006, 128, 15874–15881. (17) Beebe, J. M.; Engelkes, V. B.; Miller, L. L.; Frisbie, C. D. J. Am. Chem. Soc. 2002, 124, 11268–11269.
Conductance of Conjugated Molecular Wires (18) Park, Y. S.; Whalley, A. C.; Kamenetska, M.; Steigerwald, M. L.; Hybertsen, M. S.; Nuckolls, C.; Venkataraman, L. J. Am. Chem. Soc. 2007, 129, 15768–15769. (19) Engelkes, V. B.; Beebe, J. M.; Frisbie, C. D. J. Am. Chem. Soc. 2004, 126, 14287–14296. (20) Li, X. L.; He, J.; Hihath, J.; Xu, B. Q.; Lindsay, S. M.; Tao, N. J. J. Am. Chem. Soc. 2006, 128, 2135–2141. (21) Stadler, R.; Thygesen, K. S.; Jacobsen, K. W. Phys. ReV. B 2005, 72, 241401(R). (22) Venkataraman, L.; Klare, J. E.; Tam, I. W.; Nuckolls, C.; Hybertsen, M. S.; Steigerwald, M. L. Nano Lett. 2006, 6, 458–462. (23) Holmlin, R. E.; Haag, R.; Chabinyc, M. L.; Ismagilov, R. F.; Cohen, A. E.; Terfort, A.; Rampi, M. A.; Whitesides, G. M. J. Am. Chem. Soc. 2001, 123, 5075–5085. (24) Paulsson, M.; Krag, C.; Frederiksen, T.; Brandbyge, M. Nano Lett. 2009, 9, 117–121. (25) Xu, B. Q.; Tao, N. J. Science 2003, 301, 1221–1223. (26) Thygesen, K. S.; Jacobsen, K. W. Chem. Phys. 2005, 319, 111– 125. (27) Strange, M.; Kristensen, I. S.; Thygesen, K. S.; Jacobsen, K. W. J. Chem. Phys. 2008, 128, 114714. (28) Xiao, X. Y.; Xu, B. Q.; Tao, N. J. Nano Lett. 2004, 4, 267–271. (29) Venkataraman, L.; Park, Y. S.; Whalley, A. C.; Nuckolls, C.; Hybertsen, M. S.; Steigerwald, M. L. Nano Lett. 2007, 7, 502–506. (30) Xue, Y. Q.; Ratner, M. A. Phys. ReV. B 2004, 69, 085403.
J. Phys. Chem. C, Vol. 113, No. 49, 2009 20973 (31) Xu, B. Q.; Li, X. L.; Xiao, X. Y.; Sakaguchi, H.; Tao, N. J. Nano Lett. 2005, 5, 1491–1495. (32) Yamada, R.; Kumazawa, H.; Noutoshi, T.; Tanaka, S.; Tada, H. Nano Lett. 2008, 8, 1237–1240. (33) Quek, S. Y.; Venkataraman, L.; Choi, H. J.; Louie, S. G.; Hybertsen, M. S.; Neaton, J. B. Nano Lett. 2007, 7, 3477–3482. (34) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15–50. (35) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169–11186. (36) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892–7895. (37) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244–13249. (38) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188–5192. (39) Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, U.K., 1995. (40) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745– 2779. (41) Kristensen, I. S.; Mowbray, D. J.; Thygesen, K. S.; Jacobsen, K. W. J. Phys.: Condens. Matter 2008, 20, 374101. (42) Zhou, Y. X.; Jiang, F.; Chen, H.; Note, R.; Mizuseki, H.; Kawazoe, Y. Phys. ReV. B 2007, 75, 245407. (43) Risko, C.; Zangmeister, C. D.; Yao, Y.; Marks, T. J.; Tour, J. M.; Ratner, M. A.; van Zee, R. D. J. Phys. Chem. C 2008, 112, 13215–13225. (44) Smit, R. H. M.; Untiedt, C.; Rubio-Bollinger, G.; Segers, R. C.; van Ruitenbeek, J. M. Phys. ReV. Lett. 2003, 91, 076805.
JP9084603
