J. Phys. Chem. C 2007, 111, 3517-3521
3517
Photoswitching of Conductivity through a Diarylperfluorocyclopentene Nanowire Aleksandar Staykov, Daijiro Nozaki, and Kazunari Yoshizawa* Institute for Materials Chemistry and Engineering, Kyushu UniVersity, Fukuoka 812-8581, Japan ReceiVed: NoVember 16, 2006; In Final Form: December 15, 2006
The optical photoswitching of conductivity of a diarylperfluorocyclopentene nanowire is investigated using Green’s function method combined with density functional theory. A model closer to the real molecular electronic device is considered with relaxation of the molecular geometry under the interaction with external electric field. The ratio of conductance for the closed- and open-ring forms is on the order of magnitude 102. The influence of the HOMO-LUMO gaps and the spatial distributions of frontier molecular orbitals on the quantum transport through the molecular wire is investigated.
1. Introduction During the last decades in the field of molecular electronics, significant experimental results have been reported concerning the first usable molecules as nanosized electronic components.1-3 Although many physical phenomena are not quite understood yet, models based on Laundauer’s theory give results in good agreement with the experiments,4-10 including Aviram-Ratner diodes,6,10 conductance of single atom gold wires,4,7-9 and conductance in nanotubes with point defects.4 Theoretical simulations are used to propose many molecules with useful properties in the field of molecular electronics.6,11-15 Photochromic compounds are potential candidates for active materials in photoswitching devices.16-23 On the basis of the reversible change in molecular and electronic structures of photoresponsive compounds upon irradiation with light, many physical properties can be switched. The design of a switch using molecules that have bistable states is of particular interest in molecular electronics. In his paper,17 Irie investigates the photoswitching of diarylethenes (open- and closed-ring forms) and discusses their properties, in particular, the thermal stability of the closedring form. The photoswitching of diarylperfluorocyclopentenes significantly changes their geometries and especially the π-electron conjugation. Thus, the HOMO-LUMO gap is significantly affected, which leads to a switch in the electronic properties of the molecule. The optical photoswitching of conductivity of diarylperfluorocyclopentenes is investigated and discussed theoretically16 and experimentally.18 Dulic et al. observed a conductance change upon photoirradiation in a diarylperfluorocyclopentene characterized by increased resistance by 3 orders of magnitude.18 In two recent papers,24,25 Yin et al. discuss the influence of the electric field on the geometry, HOMO-LUMO gap, and the spatial distributions of frontier molecular orbitals of a nanowire, which reflects on its conductivity. Our previous study on photoswitching of diarylperfluorocyclopentenes16 is based on non-self-consistent treatment, and the conclusions are derived from the analysis of the transmission spectra for zero applied bias. In this paper we apply accurate full self-consistent treatment of the molecular device and analyze the I-V characteristic of the nanowire. The quantum transport is compared for geometries optimized in external electrical fields of different magnitudes. * Corresponding author.: E-mail:
[email protected]. Tel: +81-92-642-2720. Fax: +81-92-642-2735.
We investigate the open-ring and closed-ring forms of the molecular nanowire shown in Figure 1, which is proposed as an optical photoswitching unit17 (referred to here as PS). PS is a member of a large number of diarylperfluorocyclopentenes.17 It is characterized by the stable closed-ring form and good photochemical reversibility. Our model consists of two bulk gold electrodes with Au(111) surfaces, placed 14.36 Å from each other. The interaction between a S atom and the Au(111) surface is studied in a series of papers26-34 with extended Hu¨ckel, ab initio, and DFT methods with different functionals. Three possible orientations of the S atom on the Au(111) surface are investigated in the literature:26-34 “on-top” interaction of the S atom with a single Au atom, “triangle” interaction with two Au atoms, and “pyramid” interaction with three Au atoms. The conclusions in the theoretical studies26-34 about the most favorable position of a S atom differ significantly. However, most of the studies27-34 predicted that the “triangle” and the “pyramid” interactions are more favorable in energy. Ratner and co-workers31 showed that the interaction between the S-atom and the electrode does not significantly influence the conductance. The main purpose of this work is to determine the switch of conductivity through a photochemical reaction, and therefore the nature of the Au-S interaction is not investigated here. We consider “on-top” Au-S interaction and a distance of 2.341 Å between the sulfur and gold atoms26 because it best simulates the electronic device achieved by a mechanically controllable break junction.18 The distance between the gold electrodes, 14.36 Å, is chosen to fit best the closed-ring form. The open-ring form has more degrees of freedom and can fit well in longer or shorter distances between the electrodes. Its geometry, spatial distribution of frontier orbitals, and energy gap are influenced by this distance. The schematic switch of the electronic properties is shown in Figure 2. It occurs due to the geometrical changes in the molecule, leading to large dihedral angles in the open-ring form, which reduces the conjugation in the π-electron system. Another reason for the switch of the electronic transport properties is the change of type of the π-electron system. The open-ring form of PS represents a sterically hindered 1,2-diarylsubstituted ethylene, and the closed-ring form is an R,ωdisubstituted polyene. The type of the π-electron system can affect the HOMO-LUMO gap and the electronic properties of the nanowire.
10.1021/jp067612b CCC: $37.00 © 2007 American Chemical Society Published on Web 02/03/2007
3518 J. Phys. Chem. C, Vol. 111, No. 8, 2007
Staykov et al.
Figure 1. Model of PS photoswitching system in its open-ring and closed-ring forms.
Figure 2. Switch of electronic properties due to the redused π-electron conjugation in the open-ring form.
Figure 3. Models of PS in its closed-ring and open-ring forms used as a scattering region. A total of 99 atoms from the Au(111) electrods are included.
2. Computational Methods 2.1. Geometry Optimization. We performed geometry optimizations of the closed-ring and open-ring forms of PS. Our model includes one gold atom from the Au(111) surface on each side of the molecule, as shown in Figure 1. The optimization was performed with the Gaussian 03 program36 at the hybrid DFT/B3LYP level of theory with the 6-31G(p,d) basis set for C, H, F, and S atoms and the LANL2DZ basis set for Au atoms. To simulate a more realistic device, we optimized the systems in the presence of electric field.24,25 The geometries were relaxed for external electric fields of 0.0, 4.11 × 108, 6.85 × 108, 10.28 × 108, and 13.93 × 108 V m-1. The electric field was applied through the long Au-Au axis of the molecule. The HOMO-LUMO gap is an important characteristic of the system that determines its conductivity properties. To test the reliability of the results obtained with the hybrid B3LYP functional, we also optimized the geometries with the HartreeFock level of theory and the pure DFT functional-BP86. 2.2. Electron Transport Calculation. To investigate the I-V behavior, the open-ring and closed-ring forms of PS optimized in external electric field are bridged between two Au(111) electrodes, as shown in Figure 3. A bias coresponding to the external electric field, in which the molecules were optimized (0.0, 0.6, 1.0, 1.5, and 2.0 V), was applied between the electrodes and the electric current was calculated using the first principles nonequilibrium Green’s function formalism with the TransSiesta-C program.4,37-39 The method includes full self-consistent treatment of the molecular device.
Figure 4. Geometry and spatial distribution of the frontier orbitals of PS (closed-ring form) for external electric fields of different magnitudes: (A) EF ) 0.0 V m-1; (B) EF ) 4.11 × 108 V m-1; (C) EF ) 13.93 × 108 V m-1.
The models we used for the scattering region4 include 99 atoms from the Au(111) electrods, as shown in Figure 3. 3. Results and Discussion 3.1. Geometry Optimization. The results for the geometry optimizations and the spatial distributions of frontier molecular orbitals (HOMO, LUMO) for the open-ring and closed-ring forms of PS as a function of EF (0.0, 4.11 × 108, 13.93 × 108 V m-1) are summarized in Figure 4, Figure 5, and Table 1. The closed-ring system is characterized by a nearly planar geometry, which means maximal π-overlapping and good conjugation of the π-electron system. The geometry of the molecule and its frontier orbitals, as well as the HOMO-LUMO energy gap, are not significantly affected by the applied external field. The spatial distribution of the HOMO plays a significant role for the conductivity of a nanowire. It was shown that when the HOMO is distributed throughout the molecule and the electrodes are attached to atoms on which the HOMO coefficients have significant values, large conductivity is observed.40 The HOMO and LUMO are slightly asymmetrized only for strong electric field (13.93 × 108 V m-1), but they are symmetrically distributed throughout the molecule for weaker electric fields, as shown in Figure 4. The HOMO-LUMO gap changes slightly, as summarized in Table 1, in the limits of 0.76-0.79 eV, as stronger fields are applied. The geometry of the open-ring form, its frontier orbitals, and energy gap depend significantly on the applied external electric field. As a result, the dihedral angles, which determine the
Photoswitching of Conductivity
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3519 TABLE 2: HOMO-LUMO Gap (EG) of PS for Different Applied External Electric Fields (EF) Obtained with the Hartree-Fock (HF) Level of Theory and the BP86 DFT Functional (DFT/BP86) EF [1 × 108 V m-1] method
EG [eV]
0.0
4.11
6.85
10.28
13.93
HF HF DFT/BP86 DFT/BP86
closed-form open-form closed-form open-form
5.63 7.09 0.10 1.43
5.39 6.75 0.10 1.20
5.23 6.52 0.10 1.02
5.01 6.20 0.11 0.77
4.68 5.75 0.12 0.42
TABLE 3: Calculated Current for Geometries of PS Optimized in an External Field Corresponding to the Applied Bias at the B3LYP Level bias [V] closed-form [µA] open-form [µA]
Figure 5. Geometry and spatial distribution of the frontier orbitals of PS (open-ring form) for external electric fields of different magnitudes: (A) EF ) 0.0 V m-1; (B) EF) 4.11 × 108 V m-1; (C) EF) 13.93 × 108 V m-1.
π-overlapping and the conjugation of the π-electron system, as well as the bond lengths in the molecule are changed. The two dihedral angles, schematically shown in Figure 2, differ in value, which explains the HOMO spatial distribution. Their values were calculated for different external electric fields as follows: 83° and 76° for 0.0 V m-1, 74° and 70° for 4.11 × 108 V m-1, 74° and 68° for 6.85 × 108 V m-1, 73° and 67° for 10.28 × 108 V m-1, 72° and 66° for 13.93 × 108 V m-1. The external field localizes the HOMO toward the negative electrode, whereas the LUMO is more localized near the positive electrode, as seen in Figure 5. Such spatial distribution of the frontier orbitals predicts poor conductivity of a nanowire.40 The HOMO-LUMO gap narrows significantly in the limits of 2.551.52 eV as stronger electric field is applied, as summarized in Table 1. The significant difference in the energy gaps of the open-ring and closed-ring forms of PS shows that both stable states possess different electronic properties. In Table 1 the total energies of the closed-ring and open-ring forms of PS are compared. The open-ring form is more stable and the energy difference with the closed-ring form is 34-38 kcal/mol depending on the strength of the external electric field. This energy difference can be a reason for the nonreversibility of the photochemical reaction reported in the paper of Dulic et al.18 The width of the HOMO-LUMO gaps calculated with the Hartree-Fock method is very large as no correlation energy is taken into account, as listed in Table 2. The applied external electric field affects both the closed-ring and open-ring forms of PS. The values of the HOMO-LUMO gaps are lower when calculated with the DFT/BP86 functional (Table 2) compared
0.0
0.6
1.0
1.5
2.0
0.00 0.00
27.92 0.12
32.10 0.13
33.14 0.22
32.40 0.33
to those calculated with the hybrid DFT/B3LYP functional (Table 1). The HOMO-LUMO gap narrows significantly with increasing external field for the open-ring form of PS and is nearly unchanged as stronger fields are applied for the closedring form of PS. The DFT/B3LYP functional is a reasonable choice for the analysis of the HOMO-LUMO gaps having in mind the limited conductivity calculated for the open-ring form of PS, as listed in Table 3. 3.2. Electron Transport Calculation. In Table 3 are summarized the I-V characteristics of PS (in its open-ring and closed-ring forms) for biases 0.0, 0.6, 1.0, 1.5, and 2.0 V and for geometries optimized in an external electric field that corresponds to the applied bias. The π-electron conjugation and the HOMO-LUMO gap are two important parameters that determine the conductance of the molecular wire. The higher is the delocalization, the faster the electron transfers, and vice versa.24,41 The molecular conductivity is correlated to the width of the HOMO-LUMO gap. In an open system, the Fermi level of the gold electrode aligns between the HOMO and LUMO. In first approximation, the barrier for the electron transport is proportional to the HOMO-LUMO gap, when other factors are kept the same.24,41 As expected from the geometry optimization and spatial distribution of the frontier orbitals, the conductivity of the two stable forms of PS differ significantly. The closed-ring form shows good conductivity even for a small bias (0.6 V), which increases as stronger bias is applied (1.5 V). The conductivity is a result of the π-electron conjugation in the system and the narrow energy gap, as listed in Table 1. The energy gap of the closed-ring form does not decrease as the bias (the external field) is increased. From the graphical analysis of the frontier orbitals in Figure 4, we can conclude that the π-electron delocalization is slightly reduced for strong biases. This explains the decrease of the conductivity for 2.0 V bias.
TABLE 1: HOMO-LUMO Gap (EG) and Total Energy (TE) of PS for Different Applied External Electric Fields (EF) Obtained with the B3LYP Hybrid Functional as Well as the Energy Difference (∆E) between the Two Formsa EF [1 × 108 V m-1] EG closed-form [eV] TE closed-form [au] EG open-form [eV] TE open-form [au] ∆E [kcal/mol] a
0.0
4.11
6.85
10.28
13.93
0.76 -3039.0067 2.55 -3039.0676 38.2
0.76 -3039.0075 2.31 -3039.0678 37.8
0.77 -3039.0087 2.13 -3039.0682 37.3
0.78 -3039.0111 1.88 -3039.0692 36.4
0.79 -3039.0163 1.52 -3039.0713 34.5
The open-ring form is the more stable one.
3520 J. Phys. Chem. C, Vol. 111, No. 8, 2007
Staykov et al. window”. Both spectra describe completely different conductivity properties. The transmission spectra of the closed-ring form (Figure 6A) is characteristic for conductive nanowires, and that of the open-ring form (Figure 6B) is typical for insulators. 4. Concluding Remarks In this paper we have investigated the photoswitching of conductivity through a diarylperfluorocyclopentene nanowire using Green’s function method combined with density functional theory. The geometries of the both stable forms are optimized in external electric field to simulate as good as possible the real electronic device. Analysis of the spatial distribution of frontier orbitals is used to explain the obtained results. The difference of conductivity of both stable forms of PS is on the order of magnitude of several hundred times. The main contribution to this difference is due to the different molecular geometry and π-electron conjugation. On the basis of the obtained results, we can conclude that PS is a good candidate for a photoswitching unit in the modern nanoscaled electronic devices. An open question is the reversibility of the photoswitching reaction in the environment of the gold electrodes.18
Figure 6. Transmission spectra of PS for bias 0.6 V in its (A) closedring and (B) open-ring form. The dash lines show the “bias window”.
On the contrary, the open-ring form shows very low or nearly no conductivity. This is a reasonable result after the analysis of the optimized geometry (poor π-electron conjugation), spatial distribution of frontier orbitals, and energy gap, as shown in Table 1 and Figure 5. The calculated current increases monotonously with an increase in bias, but even for strong biases is very low. The main reason for this is the very poor π-electron conjugation. The increase of current is a result of the significant narrowing of the HOMO-LUMO gap, as listed in Table 1. The difference of conductivity for both stable forms of PS is on the order of magnitude from 0.98 × 102 to 2.46 × 102 times. These values, obtained from the I-V characteristic of PS, are in agreement with the experimental18 results for photoswitching of conductivity through a diarylperfluorocyclopentene nanowire, where an increased resistance from 2 to 3 orders of magnitude is reported. This conclusion is obtained using accurate full selfconsistent treatment4,37-39 of the electronic devise based on the analysis of the I-V characteristic of the nanowire which improves our previous results.16 The transmission spectra are used to interpretate the results in Table 3. The steady-state current I can be explained as a function of the applied bias V :4
I(V) ) G0
∫-∞+∞ n(E) T(E,V) dE
(1)
where G0 ) 2e2/h, n(E) is the distribution function, and T(E,V) is the transmission coefficient for electrons with energy E for bias V. Furthermore, n(E) can be written as
n(E) ) f(E - µL) - f(E - µR)
(2)
where f is the Fermi function, and µL and µR are the electrochemical potentials of each electrode. From the expression of n(E) we can expect that only electrons with energies within a range around the Fermi energy contribute to the total current. A good approximation is the range of the bias window, which is [-V/2, + V/2].4 Thus, only a finite part of the transmission spectrum should be analyzed. In Figure 6A,B are compared the transmission spectra of the open-ring and closed-ring forms of PS for an applied bias of 0.6 V. Dashed lines mark the “bias
Acknowledgment. K.Y. acknowledges Grants-in-Aid (No. 18350088, 18GS02070005, and 18066013) for Scientific Research from Japan Society for the Promotion of Science (JSPS) and the Ministry of Culture, Sports, Science and Technology of Japan (MEXT), the Nanotechnology Support Project of MEXT, the Joint Project of Chemical Synthesis Core Research Institutions of MEXT, and CREST of Japan Science and Technology Cooperation for their support of this work. Supporting Information Available: Atomic Cartesian coordinates for the optimized geometries of the closed-ring and open-ring forms of PS for external fields of 0.0, 4.11 × 108, 6.85 × 108, 10.28 × 108, and 13.93 × 108 V m-1 are available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Metzger, R. M.; Chen, B.; Hopfner, U.; Lakshmikantham, M. V.; Vuillaume, D.; Kawai, T.; Wu, X.; Tachibana, H.; Hughes, T. V.; Sakurai, H.; Baldwin, J. W.; Hosch, C.; Cava, M. P.; Brehmer, L.; Ashwell, G. J. J. Am. Chem. Soc. 1997, 119, 10455. (2) Morales, G. M.; Jiang, P.; Yuan, S.; Lee, Y.; Sanchez, A.; You, W.; Yu, L. J. Am. Chem. Soc. 2005, 127, 10456. (3) Chen, F.; He, J.; Nuckolls, C.; Roberts, T.; Klare, J. E.; Lindsay, S. Nano Lett. 2005, 5, 503. (4) Brandbyge, M.; Mozos, J.-L.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. ReV. B 2002, 65, 165401. (5) Xue, Y.; Datta, S.; Ratner, M. A. Chem. Phys. 2002, 281, 151. (6) Stokbro, K.; Taylor, J.; Brandbyge, M. J. Am. Chem. Soc. 2003, 125, 3674. (7) Agrait, N.; Rodrigo, J. C.; Vieira, S. Phys. ReV. B 1993, 47, 12 345. (8) Pascual, J. I.; Me´ndez, J.; Go´mez-Herrero, J.; Baro´, A. M.; Garcı´a, N. Phys. ReV. Lett. 1993, 71, 1852. (9) Olesen, L.; Lægsgaard, E.; Stensgaard, I.; Besenbacher, F.; Schiøtz, J.; Stoltze, P.; Jacobsen, K. W.; Nørskov, J. K. Phys. ReV. Lett. 1994, 72, 2251. (10) Aviram, A.; Ratner, M. A. Chem. Phys. Lett. 1974, 29, 277. (11) Girard, Y.; Kondo, M.; Yoshizawa, K. Chem. Phys. 2006, 327, 77. (12) Seminario, J. M.; Derosa, P. A.; Bastos, J. L. J. Am. Chem. Soc. 2002, 124, 10266. (13) Kondo, M.; Tada, T.; Yoshizawa, K. J. Phys. Chem. A 2004, 108, 9143. (14) Nozaki, D.; Yoshizawa, K. Chem. Phys. Lett. 2004, 394, 194. (15) Taylor, J.; Brandbyge, M.; Stokbro, K. Phys. ReV. B 2003, 68, 121101. (16) Kondo, M.; Tada, T.; Yoshizawa, K. Chem. Phys. Lett. 2005, 412, 55.
Photoswitching of Conductivity (17) Irie, M. Chem. ReV. 2000, 100, 1685. (18) Dulic, D.; van der Molen, S.; Kudernac, T.; Jonkman, H.; de Jong, J.; Bowden, T.; van Esch, J.; Feringa, B.; van Wees, B. Phys. ReV. Lett. 2003, 91, 207402. (19) Dietz, F.; Tyutyulkov, N. Chem. Phys. 2001, 265, 165. (20) Dietz, F.; Tyutyulkov, N. Phys. Chem. Chem. Phys. 2001, 3, 4600. (21) Kawata, S.; Kawata, Y. Chem. ReV. 2000, 100, 1777. (22) Berkovic, G.; Krongauz, V.; Weiss, V. Chem. ReV. 2000, 100, 1741. (23) Feringa, B. L.; van Delden, R. A.; Koumura, N.; Geertsema, E. M. Chem. ReV. 2000, 100, 1789. (24) Yin, X.; Li, Y.; Zhang, Y.; Li, P.; Zhao, J. Chem. Phys. Lett. 2006, 422, 111. (25) Li, Y.; Zhao, J.; Yin, X.; Yin, G. J. Phys. Chem. A 2006, 110, 11130. (26) Remacle, F.; Levine, R. Chem. Phys. Lett. 2004, 383, 537. (27) Bauschlicher, C. W.; Ricca, A. Chem. Phys. Lett. 2003, 367, 90. (28) Tachibana, M.; Yoshizawa, K.; Ogawa, A.; Fujimoto, H.; Hoffmann, R. J. Phys. Chem. B 2002, 106, 12727. (29) Nara, J.; Higai, S.; Morikawa, Y.; Ohno, T. J. Chem. Phys. 2004, 120, 6705. (30) Nara, J.; Higai, S.; Morikawa, Y.; Ohno, T. Appl. Surf. Sci. 2004, 237, 434. (31) Gronbeck, H.; Curioni, A.; Andreoni, W. J. Am. Chem. Soc. 2000, 122, 3839. (32) Gottschalck, J.; Hammer, B. J. Chem. Phys. 2002, 116, 784. (33) Cao, Y.; Ge, Q.; Dyer, D.; Wang, L. J. Phys. Chem. B 2003, 107, 3803. (34) Cometto, F.; Paredes-Olivera, P.; Macagno, V.; Patrito, E. J. Phys. Chem. B 2005, 109, 21737.
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3521 (35) Yaliraki, S. N.; Kemp, M.; Ratner, M. A. J. Am. Chem. Soc. 1999, 121, 3428. (36) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision b.03; Gaussian, Inc.: Pittsburgh PA, 2003. (37) Atk version 2.0, atomistix a/s (www.atomistix.com), 2004. (38) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys. Condens. Matter 2002, 14, 2745. (39) Taylor, J.; Guo, H.; Wang, J. Phys. ReV. B 2001, 63, 245407. (40) Tada, T.; Yoshizawa, K. ChemPhysChem 2002, 3, 1035. (41) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015.
