ARTICLE pubs.acs.org/JPCC
Single Electron Tunneling through a Tailored Arylthio-coronene Peter Kowalzik,† Nicolae Atodiresei,‡ Marc Gingras,§ Vasile Caciuc,‡ Stefan Bl€ugel,‡ Rainer Waser,† and Silvia Karth€auser†,* †
Peter Gr€unberg Institut (PGI-7), ‡Peter Gr€unberg Institut (PGI-1) and Institute for Advanced Simulation (IAS-1), Forschungszentrum J€ulich GmbH and JARA, 52428 J€ulich, Germany § CNRS, Aix-Marseille University, UPR 3118 CINAM, 13288 Marseille Cedex 09, France
bS Supporting Information ABSTRACT: The possibility to control the charge transport properties in molecular scale devices strongly depends upon the nature of the moleculemetal interfaces, causing an intense request to engineer at molecular level the interface properties. Here, we report on single electron tunneling effects observed in a STM-tip/single molecule/substrate device at room temperature using a molecule with a three-dimensional aromatic system. The molecule consists of a coronene core per-substituted with arylthio groups which are tailored in such a way that the aromatic system is efficiently decoupled from the metal substrate, and thus a double-barrier tunnel junction is created by means of a built-in insulating spacer. Comparing ab initio calculations with the experimental observations allows us to identify the specific arrangement of the substituents in the most stable conformer of this molecule. The tailored molecular structure in combination with the identified adsorption geometry controls the electron transport behavior and results in single electron transport features.
’ INTRODUCTION Implementing specific electrical functions in single molecules by tailored synthetic molecular design represents one of the main visions of the molecular electronics approach for constructing future nanodevices usable at room temperature.1,2 Besides the intrinsic properties of molecules, the nature of the electrode molecule interface plays a significant role for the transport characteristics of molecular junctions.3 A powerful experimental tool for investigating the electronic properties of single molecules is the scanning tunneling microscope (STM), due to the possibility to perform simultaneously nanoscale topographic imaging and electrical transport measurements.4,5 An important factor when working with single molecule junctions is the strength of the coupling between the electrodes and the molecule. A rather strong coupling leads to a significant broadening of the molecular energy levels due to a mixing of molecular and metallic electronic states. In contrast, specific properties characteristic for the isolated single molecule can be preserved by a weak coupling of the functional molecular unit to the substrate. A common approach to adjust the coupling strength is the attachment of alkanethiol groups with varying length to the functional backbone. In this way, the molecule gets chemically anchored to a metallic surface by forming for example a goldsulfur bond. This method has already been successfully applied for instance to fabricate single molecule single electron transistors6 or to retain magnetic hysteresis of single molecule magnets chemically wired to a metallic substrate.7 However, other attempts to decouple functional molecular units, especially those with aromatic systems, from a metallic surface by attaching bulky spacer groups failed. Here, significant geometrical distortions tend to bring the r 2011 American Chemical Society
aromatic backbone closer to the surface.8,9 A more effective decoupling could be achieved by depositing first a thin insulating layer and afterward the molecules of interest. By this means, a doublebarrier tunnel junction (DBTJ)1013 can be realized within a scanning tunneling spectroscopy (STS) experiment. The DBTJ configuration is a promising setup for applications in future nanoelectronic devices exploiting single electron transport properties.14 Earlier spectroelectrochemical studies performed on coronene derivatives revealed a charge stabilization effect in the arylthio-substituted species when compared to the nonsubstituted coronenes.1517 For instance, two consecutive single electron reduction waves with redox potentials being ∼1 V lower than for coronene itself were observed for the related compound dodecakis(p-methylphenylthio)-coronene.15 These findings suggest that DMPTC molecules can be seen as nanosized systems with a three-dimensional delocalized electronic network. In our combined experimental and theoretical study, we demonstrate that DMPTC adsorbs on Au(111) without a remarkable distortion as compared to its most stable gas phase conformer. We also prove that the methoxy groups act as ideal spacers and enable a decoupling of the aromatic molecular system from substrate states, which in turn results in single electron tunneling effects. Thus, we will present a unique way for both to decouple the aromatic backbone from the metallic surface and to stabilize the molecular conformation by intermolecular interactions so that a molecular unit with the intrinsic property to form a DBTJ is Received: February 23, 2011 Revised: March 30, 2011 Published: April 14, 2011 9204
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Figure 1. (a) Chemical structure of dodecakis(p-methoxyphenylthio)coronene (DMPTC). The core of the molecules, namely, the coronene unit, has a diameter of 0.9 nm. (b) STM image (40 nm 40 nm, sample voltage Vs = 1.2 V, tunneling current It = 0.12 nA) of less than one monolayer DMPTC on Au(111). Inset: magnified STM image (Vs = 1.3 V, It = 0.12 nA) revealing the hexagonal ordering on a short-range. (c) Submolecular resolution image of the occupied states of three neighboring DMPTC molecules (Vs = 1.3 V, It = 0.13 nA).
created. Moreover, we will show that these characteristics will be available at room temperature, so that a potential application in the field of molecular electronics can be envisioned.
’ EXPERIMENTAL SECTION Chemical Synthesis. The synthesis of dodecakis(p-methoxyphenylthio)coronene (DMPTC) was based on the sulfuration of perchlorocoronene as a precursor. The synthetic preparation of perchlorocoronene was previously described from the chlorination of coronene.18 Dodecakis(p-methoxyphenylthio)coronene was prepared similarly to a previously published procedure for dodecakis(p-methylphenylthio)coronene.15 See the Supporting Information for details of the synthesis. Scanning Tunneling Methods. The scanning tunneling microscopy (STM) and spectroscopy (STS) experiments were carried out with a commercial JEOL 4500S STM head operated in ultrahigh vacuum at room temperature. Probe tips were electrochemically etched from tungsten wires. The (111)-oriented gold thin films were fabricated by electron beam evaporation of gold on mica in a two-step deposition process.19 DMPTC molecules were deposited by applying a diluted solution (concentration c ≈ 106 mol/L) of the molecules in toluene onto the freshly prepared substrates, resulting in a submonolayer coverage. After complete solvent evaporation, the samples were immediately transferred into the UHV-STM measurement chamber. STM images were obtained in constant current mode. The sample voltage and the tunneling current used during image acquisition are denoted as Vs and It, respectively. Positive voltages mean that electrons tunnel from the tip into unoccupied states of the sample. Raw STM image data (except Figure 1b) were low-pass filtered to enhance the visibility of relevant features. dI/dV spectra were obtained by differentiating an average of 20 single I(V) curves, measured after the tipsample distance had been adjusted according to the values of the voltage Vs and the tunneling current It and after switching off the feedback loop. The quality of the STM-tip was checked by recording STS spectra next to the molecules on the clean Au(111) surface. The occurrence of the characteristic Shockley-type surface state and no other pronounced peaks ensured that additional STS features recorded on DMPTC molecules are indeed related to molecular states and not to tip-states. Computational Methods. By means of ab initio calculations, we investigated the geometry and electronic structure of several conformers of the isolated DMPTC molecule. In our study, the
first-principles total-energy calculations have been performed in the framework of the density-functional theory (DFT) as implemented in the pseudopotential plane wave VASP code.20,21 The electronion interactions are described by pseudopotentials obtained with the projector-augmented wave (PAW) method.22,23 As the DFT exchange-correlation energy functional we used the generalized gradient approximation (GGA) as parametrized by Perdew, Burke, and Ernzerhof (PBE).24 To account for the effect of the longrange van der Waals interactions on the geometry and total energy of the DMPTC conformers, we employed the semiempirical approach proposed by Grimme.25 In this method, the semiempirical energy and forces corrections derived from a damped atom-pairwise potential V(R) = C6 3 R6 (C6 represents the dispersion coefficient for a given atom pair, and R is the distance between the atoms) are added during the self-consistent cycle of the DFT-GGA calculations. Previously, this semiempirical method was successfully used to describe the flat adsorption of molecules onto surfaces.26,27
’ RESULTS/DISCUSSION The investigated molecule dodecakis(p-methoxyphenylthio)coronene (DMPTC) consists of a conjugated coronene core substituted by 12 arylthio ligands (Figure 1(a)). The aryl groups are forced to adopt a position above or below the plane of the core due to the tetrahedral angle of the sp3-hybridized sulfur atoms and the space requirements of the aryl rings themselves resulting in an overall nonplanar geometrical structure. In Figure 1(b) the morphology of DMPTC molecules adsorbed on Au(111) at submonolayer coverage is shown in a 60 nm 60 nm STM scan. It is observed that DMPTCs self-assemble into structures having a short-range order with hexagonal symmetry and a lattice constant of (1.75 ( 0.20) nm, corresponding to the intermolecular distance. The higher-resolution image of the occupied states of the DMPTC molecules (Figure 1(c)) shows that each molecule appears with a characteristic pattern of three bright features. Since the STM images represent a combination of electronic and topographic information, the measurements can be explained by an adsorption configuration of DMPTC where the coronene plane is parallel to the surface (face-on adsorption) and the bright STM features correspond to three groups of protruding aryl groups above this plane. To figure out the stability of possible DMPTC conformers with different sequences of the aryl groups above and below the coronene plane, we performed density functional theory (DFT) calculations including long-range van der Waals interactions to investigate the 9205
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Figure 2. Top and side views of the optimized geometries of the DMPTC conformers: (a) updown, (b) 2up2down, and (c) upup conformer. Plots of the aryl groups above the plane of the coronene core are illustrated for the sake of clarity in the case of the updown and the 2up2down conformer.
geometrical and electronic structure for several conformations of the isolated molecule. In this study, we present the three relevant molecular geometries: (i) in the updown conformer the aryl groups alternate between the position above and below the plane of the coronene unit, (ii) in the 2up2down conformer alternately two adjacent aryl groups are located above and below the plane, and (iii) in the upup conformer all 12 aryl groups are located above the plane. We optimized the geometry of each DMPTC conformer in the gas phase by relaxing all atoms using an orthorhombic supercell with dimensions of 2.7 2.7 2.7 nm3. The relaxed molecular geometries were achieved when the sum of the calculated HellmannFeynman and van der Waals forces was smaller than a threshold of 0.01 eV/nm. To evaluate such accurate forces, the plane wave basis set consists of all plane waves up to a cutoff energy Ecut of 500.0 eV. Due to the large size of the supercells used in our ab initio simulation, the Brillouin zone was sampled at the Γ point only. Figure 2 shows the top and side views of the optimized geometries of the isolated DMPTC conformers. Comparing the dimensions of the optimized conformers with the respective distances from STM images, the upup conformation can be excluded as a possible adsorption geometry since the diameter of this conformer (∼2 nm) is too large and no 3-fold symmetry is observed. Also, an interdigitation of the aryl groups of adjacent molecules is not possible for this conformer because the substituents occupy the whole space around the coronene core. On the other hand, in principle the diameters of both the 2up2down conformer and the updown conformer are in accordance with the intermolecular distance obtained from STM. However, the STM topographic contrast (Figure 1(c)) points rather to a loose packing than to interdigitation favoring the updown conformer. Furthermore, from Figure 2 (middle panel) it can be seen easily that in both updown and 2up2down conformers the aryl groups are arranged in pairs of two. This pairing is caused by intermolecular interactions resembling weak directional hydrogen bonds between methoxy groups and yields a 3-fold symmetry. In the case of the updown conformer the distance between the centers of these aryl pairs (0.7 nm) is practically identical with the distance between the
bright features of the occupied states depicted by the STM image (Figure 1(c)). The corresponding comparison with the geometry of the 2up2down conformer is significantly worse since here the distance between the centers of aryl pairs is ∼1.1 nm. This clearly points to the updown conformer as the favorite adsorption geometry. Besides this, the updown conformer is energetically more stable than the other two. More specifically, the updown conformer is 1.15 eV lower in energy than the 2up2down conformer and 1.18 eV lower in energy than the upup conformer. Finally, this significantly higher stability of the updown conformer as revealed by our first-principles calculations advises us to assume that this configuration should also be observed when the molecules are physisorbed on the Au(111) substrate. Figure 3 shows a comparison between experimental STM images recorded for Vs = 1.3 V and Vs = 1.1 V, respectively, and the simulated charge density distribution of the occupied and unoccupied states of the isolated DMPTC updown conformer from the Fermi level to Vs. The simulations confirm that the occupied states show the characteristic pattern of three bright features. The same symmetry is also observed in the case of the unoccupied states but appears with a “triangle-like” shape similar to the experimental finding. Normally aryl substituents above the plane of the coronene core, which give a dominant contribution to the STM images, are supposed to be not absolutely immobile at RT. Therefore, the second interesting information of these UHV-STM images is that the theoretically predicted pairing of the aryl groups even prevents thermal motions at RT; i.e., intramolecular interaction stabilizes the updown configuration. The STM topographical findings correlate well with the DFT calculations of most stable gas phase conformers and indicate that DMPTC molecules adsorb on Au(111) in updown conformation without significant geometrical distortion. The methoxy groups pointing toward the substrate surface act as distance defining (insulating) spacers giving rise to a tunneling barrier between the substrate and the three-dimensional aromatic system of the molec9206
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The Journal of Physical Chemistry C ules (Figure 4(c)). For this reason, the STM-tip/DMPTC/Au(111) system represents a double-barrier tunnel junction (DBTJ). Figure 4(a) and (b) shows the tunneling spectroscopy data measured after stabilizing the tip above a single DMPTC molecule. Note that the spectra are an average of 20 single curves obtained in an area of 0.5 nm2 around the molecule center. No spatial dependence could be resolved within this area. Averaging spectra recorded on different molecules also resulted in the same characteristic features. The observed peaks in the differential conductance spectra can be ascribed to specific fingerprints of a double-barrier tunnel junction. More precisely, the experimentally measured spectra exhibit a multiple peak structure with the following features: (i) the energetic gap ΔESTS between the peaks labeled N and N þ 1 depends on the tipsample separation and is larger when the tip is close to the sample, (ii) subsequent to the first peaks at positive and negative voltages, respectively, additional peaks are observed (denoted as N 1 for V < 0 and N þ 2, N þ 3 for V > 0), and (iii) all energy differences EC,STS (between the peaks N þ 1 f N þ 2, N þ 2 f N
Figure 3. Simulated charge density distribution of the occupied and unoccupied states of the isolated DMPTC updown conformer (upper part) agrees well with the experimental STM constant current images (lower part). The experimental and simulated images of the occupied states (left) exhibit three bright features corresponding to the pairs of aryl groups above the coronene plane, while the unoccupied states (right) have rather a “triangle-like” shape.
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þ 3, and N f N 1) are approximately equal for a fixed tipsample separation but get larger when the tip is brought closer to the sample. We interpret these findings using the results of DFT calculations of the electronic structure of single DMPTC molecules and by modeling the measurement configuration as a DBTJ. First, we calculated the ground state total energies of the anion (Etot(N þ 1)), neutral (Etot(N)), and cation (Etot(N 1)) species and then deduced the corresponding ionization potential (IP = Etot(N 1) Etot(N)) and electron affinity (EA = Etot(N) Etot(N þ 1)) of the DMPTC updown conformer, from which the fundamental energetic gap28 ΔEtheo = IP EA = 2.16 eV is obtained (Figure 5). Next the peaks N and N þ 1 in the STS spectra were assigned to a sequential tunneling via the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively. The energetic difference between subsequent charge states of the molecule has been approximated within a constantinteraction description2931 as ΔEtheo = IP EA = μNþ1 μN = EC þ ΔHL, where μN = Etot(N) Etot(N 1) is the energy required to add the N-th electron to the molecule, ΔHL is the HOMO LUMO gap of the neutral molecule in the ground state, and EC is the charging energy due to Coulomb interactions of the tunneling electron with all other electrons. ΔHL is estimated from the optical HOMOLUMO gap (onset of optical absorption of DMPTC) to be (2.00 ( 0.05) eV (Supporting Information, Figure S1). Thus, the charging energy amounts to ΔEtheo ΔHL = EC = (0.16 ( 0.05) eV. Remarkably, these quantities agree nicely with the STS measurements, considering that every pronounced STS peak corresponds to the opening of a new tunneling channel when an additional charge state passes into the transport window. Due to the asymmetric insulating barriers, it can be expected that a given fraction η of the total bias voltage will drop between the molecule and the substrate and (1 η) between the STM-tip and the molecule. Taking the molecular energy levels as a fixed reference, the electrochemical potentials of the tip (μt) and the substrate (μs) float up or down by applying a voltage V by an amount μt = EF þ (1 η) eV and μs = EF η eV, where EF denotes the common electrochemical potential of the tip and the substrate for V = 0 (Figure 4(d)). Therefore, the experimentally measured transport gap between μNþ1 and μN and is given by ΔESTS ¼ eðVN þ 1 VN Þ ¼ ðΔHL þ EC Þ=ð1 ηÞ
ð1Þ
The energetic distances between the charge states N þ 1 f N þ 2 and N f N 1 provide an experimental estimation of EC
Figure 4. Current and differential conductance versus voltage curves measured on DMPTC with spectroscopy set point values of (a) Vs = 1.3 V and It = 0.08 nA and (b) Vs = 1.3 V and It = 0.65 nA. (c) Schematic drawing of the STS measurement configuration. (d) Energy diagram of the double-barrier tunnel junction for V > 0, illustrating the relevant quantities and notations. 9207
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subsequent LUMOþ2 is situated at much higher energy than the first two unoccupied states. Furthermore, the DFT calculations show that the LUMO and LUMOþ1 are three-dimensional π orbitals delocalized over the whole molecule. During the measurement process, the charging of the DMPTC molecule occurs by occupying these LUMO and LUMOþ1 orbitals. Since the additional electrons filling these three-dimensional delocalized π orbitals will be screened by the 1020 electrons of the DMPTC molecule, the charging energy EC is expected to be approximately the same for all of them. This explains why the N þ 1, N þ 2, and N þ 3 peaks are energetically equally spaced and appear as single electron tunneling features in our measured dI/dV spectra.
Figure 5. Schematic energy diagram of the frontier molecular orbitals of the DMPTC conformers. The ground state total energies of the anion (Etot(N þ 1)), neutral (Etot(N)), and cation (Etot(N 1)) species have been used to calculate the ionization potentials (IP = Etot(N 1) Etot(N)) and electron affinities (EA = Etot(N) Etot(N þ 1)) of the three different DMPTC conformers, from which the fundamental energetic gap ΔEtheo = IP EA is obtained.
since the (N þ 2)-th electron can occupy the same orbital (LUMO) as the (N þ 1)-th electron and the (N 1)-th electron the same orbital (HOMO) as the N-th electron. Therefore, EC is approximated by EC, STS ¼ eðVN þ 2 VN þ 1 Þ ¼ eðVN VN 1 Þ ¼ EC =ð1 ηÞ
ð2Þ
Using the measured quantities ΔESTS and EC,STS, the charging energy EC and the parameter η for a given tipsample distance can be derived from eqs 1 and 2. EC = (0.19 ( 0.06) eV and η = (0.20 ( 0.02) are obtained for It = 0.08 nA and EC = (0.20 ( 0.06) eV and η = (0.26 ( 0.02) in the case of It = 0.65 nA. Both measurements yield the same value for the charging energy and agree very well with the value EC = (0.16 ( 0.05) eV within the limit of error, estimated above by using the findings of DFT calculations and optical absorption measurements. The reason for this relatively low charging energy can be found in the large three-dimensional π orbitals involving almost the whole molecule, except the methoxy groups, which allow for a thorough charge delocalization. It is also important to note that only the fundamental gap ΔEtheo = 2.16 eV of the updown conformer (Figure 5) is consistent with the value ΔESTS ≈ 2.2 eV, deduced from experimental data in the limit of η = 0, i.e., for a very large STMtip substrate distance. The fundamental gaps of the 2up2down and upup conformer amount to 1.05 and 1.40 eV, respectively. This gives a further confirmation for the suggested updown conformation of the physisorbed DMPTCs besides the STM topographical findings. The experimental tunneling spectra suggest that the tunneling process involves different charge states of the molecule due to a weak coupling to both electrodes. Another striking characteristic displayed by measured dI/dV curves is the same charging energy EC that connects the N þ 1, N þ 2, and N þ 3 peaks. To understand this feature in a qualitative picture we note that the DMPTC updown conformer has two degenerate lowest unoccupied molecular orbitals (LUMO and LUMOþ1), but the
’ CONCLUSIONS To summarize, we performed an experimental STM/STS and theoretical ab initio study of the unique structural and electron transport properties of DMPTC molecules physisorbed on Au(111). The structural characteristics revealed a face-on adsorption of the molecules in their most stable updown conformation. The paramount advantage of our DMPTC moleculeAu(111) system is that a double-barrier tunnel junction is constructed without the need of an additional insulating layer. The experimental tunneling spectra show that the electron transport through DMPTCs involves a stepwise charging of the molecules. Thus, we demonstrate that the methoxy groups efficiently decouple the three-dimensional aromatic system of DMPTC from the Au(111) surface in this adsorption configuration and facilitate the observation of single electron tunneling effects through the physisorbed molecules. Such molecularsurface systems presenting single electron tunneling effects are promising as active elements in future nanoelectronic devices. ’ ASSOCIATED CONTENT
bS
Supporting Information. Movie clips of the geometry and the degenerate HOMOs/LUMOs of the DMPTC updown conformer. UV/vis absorption spectrum of DMPTC. Details of the synthetic preparation of DMPTC. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The computations were performed on JUROPA and JUGENE supercomputers at the J€ulich Supercomputing Centre, Forschungszentrum J€ulich (Germany). M.G. acknowledges the French National Center for Scientific Research (CNRS) and the Universite de la Mediterranee (Aix-Marseille 2). We would also like to thank N. Schnaebele and the Spectropole of Marseille. ’ REFERENCES (1) Maruccio, G.; Cingolani, R.; Rinaldi, R. J. Mater. Chem. 2004, 14, 542–554. (2) Tao, N. J. Nature Nanotechnol. 2006, 1, 173–181. (3) Xue, Y. Q.; Ratner, M. A. Int. J. Quantum Chem. 2005, 102, 911–924. (4) Binnig, G.; Rohrer, H. Rev. Mod. Phys. 1987, 59, 615–625. 9208
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(5) Datta, S.; Weidong, T.; Seunghun, H.; Reifenberger, R.; Henderson, J. I.; Kubiak, C. P. Phys. Rev. Lett. 1997, 79, 2530–2533. (6) Park, J.; Pasupathy, A. N.; Goldsmith, J. I.; Chang, C.; Yaish, Y.; Petta, J. R.; Rinkoski, M.; Sethna, J. P.; Abruna, H. D.; McEuen, P. L.; Ralph, D. C. Nature 2002, 417, 722–725. (7) Mannini, M.; Pineider, F.; Danieli, C.; Totti, F.; Sorace, L.; Sainctavit, Ph.; Arrio, M.-A.; Otero, E.; Joly, L.; Cezar, J. C.; Cornia, A.; Sessoli, R. Nature 2010, 468, 417–421. (8) Moresco, F.; Gourdon, A. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 8809–8814. (9) McNellis, E. R.; Bronner, C.; Meyer, J.; Weinelt, M.; Tegeder, P.; Reuter, K. Phys. Chem. Chem. Phys. 2010, 12, 6404–6412. (10) Porath, D.; Levi, Y.; Tarabiah, M.; Millo, O. Phys. Rev. B 1997, 56, 9829–9833. (11) Mikaelian, G.; Ogawa, N.; Tu, X. W.; Ho, W. J. Chem. Phys. 2006, 124, 131101. (12) Tu, X. W.; Mikaelian, G.; Ho, W. Phys. Rev. Lett. 2008, 100, 126807. (13) van der Molen, S. J.; Liljeroth, P. J. Phys.: Condens. Matter 2010, 22, 133001. (14) Li, B.; Zeng, C. G.; Zhao, J.; Yang, J. L.; Hou, J. G.; Zhu, Q. S. J. Chem. Phys. 2006, 124, 064709. (15) Tucker, J. H. R.; Gingras, M.; Brand, H.; Lehn, J. M. J. Chem. Soc., Perkin Trans., II 1997, 2, 1303–1307. (16) Gingras, M.; Pinchart, A.; Dallaire, C.; Mallah, T.; Levillain, E. Chem.—Eur. J. 2004, 10, 2895–2904. (17) Gingras, M.; Raimundo, J. M.; Chabre, Y. M. Angew. Chem., Int. Ed. 2006, 45, 1686–1712. (18) Braid, T.; Gall, J. H.; MacNicol, D. D.; Mallinson, P. R.; Michie, C. R. J. Chem. Soc., Chem. Commun. 1988, 1471–1473. (19) L€ussem, B.; Karth€auser, S.; Haselier, H.; Waser, R. Appl. Surf. Sci. 2005, 249, 197–202. (20) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558–561. (21) Kresse, G.; Furthm€uller Phys. Rev. B 1996, 54, 11169–11186. (22) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953–17979. (23) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (25) Grimme, S. J. Comput. Chem. 2006, 27, 1787–1799. (26) Atodiresei, N.; Caciuc, V.; Lazic, P.; Bl€ugel, S. Phys. Rev. Lett. 2009, 102, 136809. (27) Tonigold, K.; Gross, A. J. Chem. Phys. 2010, 132, 224701. (28) Kummel, S.; Kronik, L. Rev. Mod. Phys. 2008, 80, 3–60. (29) Kouwenhoven, L. P.; Austing, D. G.; Tarucha, S. Rep. Prog. Phys. 2001, 64, 701–736. (30) Allara, Y.; Selzer und, D. L. Annu. Rev. Phys. Chem. 2006, 57, 593–623. (31) Thijssen, J. M.; Van der Zant, H. S. J. Phys. Status Solidi B 2008, 245, 1455–1470.
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