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Electronic Structures and Properties of Pdn-C60-Pdn Nanocontacts: A Theoretical Investigation Manoj K. Shukla,† Madan Dubey,‡ Eugene Zakar,‡ and Jerzy Leszczynski*,† NSF CREST Interdisplinary Nanotoxicity Center, Department of Chemistry and Biochemistry, Jackson State UniVersity, Jackson, Mississippi 39217, and U.S. Army Research Laboratory, Sensors and Electron DeVices Directorate, AMSRD-ARL-SE-RL, Adelphi, Maryland 20783 ReceiVed: January 14, 2009; ReVised Manuscript ReceiVed: April 30, 2009
Theoretical study at the B3LYP/6-31G(d)∪LANL2DZ level was carried out to explore the structures and properties of nanocontacts in Pdn-C60-Pdn systems. Predicted interaction energies between the palladium clusters and the C60 were corrected for the basis set superposition error. It is revealed that palladium clusters interact more strongly with C60 than the analogous gold clusters. Further, generally in the case of C60-Pd complexes, electronic charges are transferred from metal clusters to C60 which is contrary to the direction of a charge transfer in C60-Au complexes. HOMO-LUMO energy gaps in Pdn-C60-Pdn system are found to be lower than C60 as well as the corresponding Aun-C60-Aun complexes. Charge transport properties in the Pdn-C60-Pdn system are discussed in terms of molecular orbitals and the Fermi energy level. Molecular electrostatic potential (MEP) mappings were performed for the qualitative visualization of the Schottky barrier at the C60-Pd interface. Similarity and differences between the Pdn-C60-Pdn and Aun-C60-Aun systems are also explored. Introduction The understanding of mechanisms of electron transport in nanomaterials including fullerene (C60), carbon nanotubes (CNTs), and nanocrystals for the development of new nano and molecular devices are forefront in the area related to material science.1-3 A significant amount of research work has been carried out to understand the performance of C60 and CNTs in nanoelectronics.4-11 The C60 as a single molecular transistor with gold electrodes was fabricated by Park et al.4 Seideman and co-workers9-11 have used theoretical methods to study the charge transport in C60 placed between gold electrodes. Seminario and co-workers12-14 have performed series of investigations to understand the structures and transport properties of various nanomaterials and molecular systems. In an investigation of transport characteristics of metals involving groups 10 and 11 with thio and isonitrile alligator clip at the density functional theory level (B3PW91/LANL2DZ level) and the Green function approach, the performance of former group metals was found to be better than those belonging to the latter group metals.14 In particular, the performance of Pd was found to be the best compared to other metals. Also in an experimental study the Pd is reported to form better contact than Au.15 In another experiment, the Pd-CN type contact barrier was found smaller than that of Au-CN junction.16 Materials obtained as the result of formation of complexes between C60 and palladium can be used for the gas sensor and gas filter17,18 and hydrogenation catalyst.19 Hayashi et al.17 have studied the reaction of toluene on C60Pdn polymer like materials and found that such adsorption is largest in C60Pd2 type system for even smaller concentration (1000 ppb) of the organic molecule, which is comparable to concentrations that are present in the environment. It was suggested that a partial positive charge on Pd that * Corresponding author. E-mail:
[email protected]. † Jackson State University. ‡ U.S. Army Research Laboratory.
appears due to the electronic charge transfer to C60 is responsible for the binding of toluene with the metal. It has been argued that the metallic site in the C60-metal polymeric materials is important for the toluene adsorption. A thorough and reliable understanding of nanocontacts between materials and electrode in nanodevices is very important to explore the charge transport. Different experimental and theoretical investigations have been performed to comprehend the transport properties of nanodevices.1-14 In the computational modeling of electron transport through nanomaterials (e.g., fullerene, carbon nanotubes, and organic molecules), the electrode surfaces are generally idealized. Nature of contact has significant influence on the performance of electronics devices. Although, at the point of contact the atomic structure of electrode is not well understood, it is expected that surface would be rough and structure would vary between samples even those made under the same conditions.20,21 Further, it is also not possible to have perfectly pure and defect free electrode materials. In quest for nanodevices with best performance and minimum cost, it is imperative to explore the electronic structures and properties of nanocontacts involving different metals. Therefore, we have undertaken theoretical investigation of Pdn-C60-Pdn system and compared the computed results with the corresponding Aun-C60-Aun system studied by us earlier.22 It has been revealed that palladium and gold behave differently when interacting with C60. For example, palladium clusters form stronger bond with C60 than that of the corresponding gold clusters. In the case of Aun-C60-Aun system there is charge transfer from the C60 to the gold clusters, while reverse was revealed for the Pdn-C60-Pdn system. Computational Details Molecular geometries of complexes were optimized at the density functional theory (DFT) level using the Becke’s23 threeparameter nonlocal hybrid exchange potential with the nonlocal
10.1021/jp900370h CCC: $40.75 2009 American Chemical Society Published on Web 06/10/2009
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Figure 1. Optimized structure of Pdn-C60-Pdn complexes. Geometrical parameters are in Å.
TABLE 1: Computed Pd-C and Interacting C-C Distances (Å), Mulliken Charges (in au) on Each Side of Pd Cluster, BSSE Corrected Binding Energies (∆EBE, kcal/mol), HOMO-LUMO Energy Gap (H-L, eV), and Fermi Energy (EFL, eV) of Pdn-C60-Pdn Complexesa Pdn-C60-Pdn
Aun-C60-Aun
n
Pd-C
C-C
Charge
∆EBE
H-L
EFL
Au-C
C-C
Charge
∆EBE
EFL
H-Lb
2 3 4 6 7 8
2.132 2.140 2.162 2.192 2.167 2.155
1.461 1.455 1.450 1.449 1.453 1.455
0.116 -0.003 -0.004 0.049 0.043 0.032
63.5 60.1 45.4 43.7 51.5 55.6
1.53 1.61 1.59 1.20 1.28 1.34
-4.53 -4.62 -4.65 -4.75 -4.53 -4.54
2.322 2.355 2.372 2.302 2.285 2.306
1.433 1.434 1.434 1.444 1.450 1.442
-0.139 -0.200 -0.197 -0.143 -0.088 -0.181
27.9 14.5 32.8 35.2 38.7 36.4
-5.06 -5.03 -4.91 -4.86 -4.96 -5.07
2.37 0.23 (1.60) 1.80 2.12 0.31 (1.35) 2.01
a For comparison, corresponding Aun-C60-Aun data are also given. Interaction energy calculation as a three body term; Mulliken charges are on the each side of Pd cluster of the complex. The corresponding C-C distance in isolated C60 is 1.395 Å. b Values in parentheses corresponds to that obtained from the single point energy calculation of triplet state using the reference singlet ground state optimized geometry [ref 22].
correlation functional of Lee, Yang, Parr (B3LYP).24 The standard 6-31G(d) basis set was used for carbon atoms while the LANL2DZ effective core potential (ECP) was used for palladium atoms. The combined basis set, hereafter, will be called as 6-31G(d)∪LANL2DZ basis set. Geometries of complexes were optimized under the C2h symmetry. It is well-known that the computation of interaction energy with finite basis sets introduces error known as basis set superposition error (BSSE). Since interaction energy is defined as the energy difference between the complex and that of the energies of constituent monomers, the BSSE error arises due to the fact that different number of basis functions is used to describe the complex and that of monomers for the same basis set. Due to the larger number of basis function the complex has comparatively lower energy than the sum of its components. The BSSE corrected interaction energy was computed using the Boys-Bernardi counterpoise correction scheme.25 Interaction energies of complexes were computed from the three body terms given by eq 1
Eint)EABC-EA(ABC)-EB(ABC)-EC(ABC)
(1)
where Eint represents the interaction energy, EABC is the total energy of the complex, EB(ABC) represents the total energy of the C60 with ghost atoms in place of rest of the system, EA(ABC) or EC(ABC) represent the total energy of either side of palladium clusters of the complex with ghost atoms for the rest of the system. The BSSE correction is important to determine the stability of complexes correctly. All calculations were performed using the Gaussian 03 suite of programs.26 Molecular orbitals were visualized using the Molekel program27a and molecular electrostatic potential maps were generated using the gOpenMol program.27b,c Results and Discussion The optimized geometries of Pdn-C60-Pdn complexes are displayed in the Figure 1 while the Pd-C and C-C distances between carbons involved in direct interactions with Pd are shown in the Table 1. For comparison the corresponding distances in the Aun-C60-Aun complexes are also shown in the same table. Palladium atoms can bind at different centers of C60. Lichtenberger et al.28,29 have shown that η2(6)-coordination (interaction at the top of the center of the fused six-membered
Structures and Properties of Pdn-C60-Pdn rings of C60) is the most favored among all bonding sites. We have found that for Aun-C60-Aun system the η2(6)-coordination of gold clusters yields more stable complexes than for those involved in bonding at the top of the center of the fused fiveand six-membered rings (η2(5)-coordination) of C60.22 In the present investigation the η2(6)-coordination for interaction of palladium with C60 has been considered. Earlier, we have found that the Au5-C60-Au5 complex has C2 symmetry while for other complexes geometries were optimized at the C2h symmetry. Therefore, in the present investigation the number of Pd atoms on each side of C60 was varied in the range of 2-8, excluding 5. Contrary to the Aun-C60-Aun systems, where complexes involving odd number of gold atoms on each side of C60 are characterized by triplet while those with even numbers of gold atoms with singlet as the ground state,22 all the considered Pdn-C60-Pdn systems have been found to have singlet as the ground state. The Pd-C coordination distance is found to increase parallel with the size of the cluster up to twelve-palladium atoms. However, for larger clusters this distance is found to be decreased. Thus, it appears that the size of the palladium cluster has significant influence on binding with fullerene. The Pd-C coordination distance for Pd2-C60-Pd2 is the smallest among all complexes (Table 1). From Table 1, it is clear that the Pd-C distance in the C60-palladium complexes are significantly smaller that the Au-C distance in the corresponding C60-gold species. The difference between the coordination distances in these complexes is due to the different chemical and electronic properties of palladium and gold complexes. The C-C bond length between the carbons from the fusing six-membered rings in C60 is computed to be 1.395 Å at the B3LYP/6-31G(d) level. This is in good agreement with the experimental value of 1.401 Å obtained from the electron diffraction of C60.30 The complexation of palladium clusters causes the elongation of the C-C bond involved in direct interaction with metal from 1.395 Å in C60 to 1.449 - 1.461 Å in the C60-Pd complexes. Although, the maximum elongation was predicted for the Pd2-C60-Pd2 cluster, but substantial change in C-C bond length with the size of the Pd cluster is not revealed (Table 1). For comparison, the C-C distances for the corresponding C60-Au complexes are also shown in the Table 1. The C-C bond length elongation consequent to the gold binding with C60 is also revealed, but such increase is generally smaller than that in the corresponding C60-Pd complexes. The binding energies of the complexes computed as the negative of the respective BSSE corrected interaction energies are presented in the Table 1. For comparison, the binding energies of the corresponding Aun-C60-Aun complexes are also presented in the Table 1. It is clear that C60 forms stable complexes with Pd clusters. The binding energies of the studied systems are found to be in the range of 44-64 kcal/mol, where Pd2-C60-Pd2 has the largest and Pd6-C60-Pd6 has the lowest binding energy. Interestingly, initially with increasing the Pd cluster size the binding energy was found to be decreased for up to six atoms in each cluster. Thus, it appears that generally the size of cluster also has significant influence on binding with C60. The stronger binding energy in the Pd2-C60-Pd2 system may be related to the reactivity of smaller palladium cluster where an experimental investigation has suggested that C60Pd2 complex has the best adsorptivity toward the toluene.17 The tracer diffusion of the C60 adsorbed on the Pd(110) surface was found to proceed through a barrier of about 1.4 ( 0.2 eV (32.3 ( 4.6 kcal/mol).31 This tracer diffusion barrier height can be compared with our computed binding energy of studied system
J. Phys. Chem. C, Vol. 113, No. 26, 2009 11353 shown in the Table 1. It is evident that tracer diffusion barrier height is in the lower range of the computed binding energy.31 In comparison to the C60-gold complexes, it is clear that Pd clusters form stronger complexes than the gold clusters. But the fundamental difference between these two metal complexes is that, in general, the smaller gold clusters have smaller binding energies toward C60 than the larger clusters while opposite is found for the C60-Pd complexes. Computed Mulliken charges on each side of Pd cluster in the studied C60-Pd complexes are shown in the Table 1, while for comparison the corresponding C60-Au data are also displayed in the same table. Generally, a substantial amount of electronic charge transfer from the Pd clusters to the C60 is predicted, except for Pd3-C60-Pd3 and Pd4-C60-Pd4 complexes where each Pd cluster possesses about -0.003e to -0.004e of electronic charge. Further, for other complexes (Pdn-C60-Pdn; n ) 2, 6-8) the amount of electronic charge transferred to the C60 is significantly decreased with the increase in the size of the Pd cluster. Thus, each Pd cluster in Pd2-C60-Pd2 complex has comparatively significantly larger amount of positive charge than the other complexes. The migration of electronic charge from Pd to C60 was also suggested in the other experimental investigation where C60Pdn complexes were used as an absorbent of toluene gas.17 The largest amount of electronic charge transfer to C60 from metal cluster in the Pd2-C60-Pd2 complex compared to the other complexes might also be related to the fact and explained by the higher adsorptivity of C60Pd2 complex toward the toluene than the other complexes.17 In this adsorption reaction, it has been suggested that the π-charge cloud of toluene interacts with the partially positive charged palladium. The Mulliken atomic charge distributions in the form of varying color of atoms in the complexes (red color is the most negative and green color being the most positive charged atoms) are shown in the Figure 2. The amount of Mulliken charge at selected atomic sites is also indicated in the same figure. It is clear that the C-C pair of carbon atoms of C60 involved in direct interaction with Pd has negative and other carbon atoms directly connected to the C-C carbon atoms have positive electronic charge. Other carbon atoms of C60 have electronic charges generally close to zero. However, a clear trend regarding the charge distribution on Pd atom directly coordinated to C60 is not revealed. On the other hand, in the Aun-C60-Aun complexes the Au atom directly coordinated to C60 has positive and the interacting C-C atoms have negative Mulliken charges.22 The terminal Pd atoms of the Pd2-C60-Pd2 complex have significantly large amount of positive charge (0.168 au on each atom) compared to that in other complexes. The computed large amount of positive charge on terminal Pd atoms in the Pd2-C60-Pd2 complex explains the largest selectivity of C60-Pd2 toward binding with toluene compared to the other C60-Pdn complexes.17 Theoretical calculations have been found to be very useful for the exploration of charge transport properties in molecular systems. It has been pointed out that orbitals delocalized through the molecules and located near the Fermi energy level are crucial for forming a good conduction pathway through the molecular junction.12-14,32,33 Seminario and co-workers13 have performed detailed investigation of transport properties of polyynes and alkanes and predicted that former has significantly larger conduction than the latter one. It was found that although densities of states near Fermi level are similar for both system, but for polyynes the molecular orbitals near Fermi energy level were more delocalized than those of alkanes. Yoshizawa et al.34
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Figure 2. Mulliken charge (in au) distribution in the Pdn-C60-Pdn complexes. The range of charge distribution for each complex is also given where red being the most negative and green being the most positive charge.
have recently analyzed frontier orbitals of extended π-conjugated molecules in predicting charge transport in molecular devices and found that the nature of these orbitals including the orbital amplitudes are generally able to account for the direction and relative amount of transport, especially in system where electrodes have weak contact with molecular systems. The π-charge cloud associated with the C-C bond provides a route for transport of electron currents and the same is true for C60.35 Computed energy difference between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of studied complexes are shown in the Table 1. On the basis of B3LYP/6-31G(d) level of calculation on C60 where the HOMO-LUMO energy gap was revealed to be 2.77 eV22,36 and the experimental investigation where the band gap of solid C60 was found to be 2.3 ( 0.1 eV,37 it was suggested that such computed energy difference can be approximated as the band gap of C60 in the solid phase.22 From the data shown in the Table 1, it is evident that the computed HOMO-LUMO energy gap of the C60-Pd complexes are significantly lower than that of the isolated C60. For smaller complexes (2-4 Pd atoms on each side of C60) the computed band gap is in the range of 1.5-1.6 eV while for larger complexes (6-8 Pd atoms on each side) the energy difference is further reduced and is in the range of 1.2-1.3 eV. The HOMO-LUMO energy gaps of the corresponding Aun-C60-Aun complexes, on the other hand, are considerably larger. This is due to the fact that Pd clusters form more stable complexes with C60 than the gold clusters. Consequently, the orbitals of C60 are comparatively more influenced by the binding with Pd clusters than the Au clusters. Fermi level energy (EFL) of some carbon nanostrutures namely C28, C60, and C70 was determined by Witek et al.38 where authors have taken an average of the HOMO and LUMO orbital energies. We have earlier found that the computed EFL value
for C60 at -4.6 eV at the B3LYP/6-31G(d) level is in good agreement with the corresponding parameter obtained at the BLYP/cc-pVTZ level.38 We have also computed the Fermi level energy of the Pdn-C60-Pdn complexes by taking the average of HOMO and LUMO orbital energies and they are presented in the Table 1. Computed EFL values of studied C60-Pd complexes are found to be in the range of -4.53 to -4.75 eV. Selected occupied and unoccupied molecular orbitals of the studied C60-Pd complexes which are significantly delocalized and are located near the respective Fermi energy level are shown in the Figure 3, while several occupied and unoccupied molecular orbitals of complexes are shown in the Supporting Information. For comparison, the HOMO and LUMO orbitals of C60 obtained at the B3LYP/6-31G(d) level are also presented in the Supporting Information. Clearly, for C60 the HOMOs are 5-fold degenerate with hu symmetry, whereas LUMOs are triply degenerate with t1u symmetry.1 The analysis of several occupied and unoccupied molecular orbitals of C60-Pd complexes and their comparison with HOMOs and LUMOs of C60 suggested that although the predicted 5-fold degeneracy in HOMOs of C60 is usually not revealed, but the 3-fold degeneracy in LUMOs of C60 is somewhat maintained in all C60-Pd complexes. For all complexes, the HOMO and LUMO orbitals are localized at the Pd-clusters. Further, it is evident that in each complex, there are occupied and unoccupied orbitals which are largely delocalized and are located near to the respective Fermi energy level. These orbitals are expected to contribute to electron conduction in the respective system under the sufficient external biasing. For example, in the Pd2-C60-Pd2 complex the HOMO-1 and LUMO+4 orbitals are largely delocalized and are located about 0.86 eV below and 1.72 eV above, respectively, of the Fermi energy level. Further, the HOMO orbital is also slightly delocalized, especially in the contact region of C60
Structures and Properties of Pdn-C60-Pdn
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Figure 3. Selected molecular orbitals and their energies (eV) of Pdn-C60-Pdn complexes.
and therefore its role in the charge transport can not be ignored. In the Pd3-C60-Pd3 complex, the HOMO-6 and LUMO+4 are significantly delocalized and therefore are most important for the charge transport. It appears that in the Pd4-C60-Pd4 system, HOMO-8, HOMO-13, and LUMO+4 are vital for this process, due to their delocalization. Similarly, for Pd6-C60-Pd6, the HOMO-2, HOMO-7, and LUMO+2 are
essential. The HOMO-6 and LUMO+4 are expected to participate in the charge transport in the Pd7-C60-Pd7 while orbital delocalization is revealed for HOMO-8 and LUMO+4 for Pd8-C60-Pd8 system and therefore they appear important for the charge transport. Thus, it has been found that the occupied molecular orbitals, which are largely delocalized, are generally 0.8-1.4 eV below, while the unoccupied orbitals
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Figure 4. Molecular electrostatic potentials of Pdn-C60-Pdn complexes mapped onto electronic density of 0.006 au isosurface. The range of MEP plot (in eV) is provided next to each complex where the maximum negative potential corresponds to blue and largest positive potential corresponds to red color. The location and value (in eV) of MEP minima in each complex is indicated by arrow. From the symmetry the corresponding location on the other side of C60 in each complex can be located.
showing delocalization are generally about 1.4-1.7 eV above the Fermi energy level. These orbitals are expected to be involved in the charge transport in the respective system under the sufficient external biasing. It appears that the higher conductance of the Pd electrode compared to the gold electrode is due to the fact that Pd clusters form stronger complex with C60 than the gold clusters. Due to the stronger complexation the molecular orbitals of C60 are significantly rearranged and become more favorable to charge conduction. Molecular electrostatic potential (MEP) maps39 of PdnC60-Pdn complexes are shown in the Figure 4. These MEPs were mapped on the 0.006 au value electron density isosurface. It is well-known that metal-semiconductor interface gives rise to Schottky barrier.40 Since MEP is defined as the attractive potential to positive probe of unit charge due to electrons in
the system under investigation and thus, MEP minima along the contact region should provide a barrier for electron transport. Therefore, the Schottky barriers at the metal-semiconductor interface can be qualitatively visualize by the analysis of MEP maps in the interface region. The results of such analysis presented in the Figure 4 indicate that all studied complexes possess MEP minima which are located at Pd clusters near the interface region. However, the location and amount of MEP values depend upon the structure of the metal cluster (Pd cluster) at the interface. The MEP values are computed to be in the -0.4 to -1.02 eV range for studied complexes. The Pd4-C60-Pd4 has the highest and Pd6-C60-Pd6 has the smallest MEP value (in magnitude), and therefore, the former will have the larger and the latter will have the smaller Schottky barrier.
Structures and Properties of Pdn-C60-Pdn Thus, Schhottky barrier will depend upon the nature of metallic cluster at the semiconductor-metal interface. Conclusions Based upon the computational study of nanocontacts involving Pdn-C60-Pdn system and the comparison of results with the corresponding Aun-C60-Aun system, it was revealed that Pd clusters form stronger complexes with C60 than the gold clusters. However, smaller gold clusters have smaller binding energies than the larger clusters while opposite is found to be true for C60-Pd complexes. The Pd2-C60-Pd2 complex has the largest binding energy among the studied C60-Pd complexes. All studied Pdn-C60-Pdn complexes have been found to be characterized by singlet ground state. On the other hand for the Aun-C60-Aun systems, the complexes involving odd numbers of gold atoms on each side of C60 are characterized by triplet while those with even numbers of gold atoms by singlet as the ground state. Generally, in the C60-Pd complexes, electronic charge transfer is found from metal clusters to C60 which is opposite to the features revealed for the C60-Au complexes. The maximum charge transfer is predicted for the Pd2-C60-Pd2 complex. A clear trend regarding the charge distribution on Pd directly coordinated to C60 is not revealed. Depending upon the complexes, the Pd atom can be positively (Pd3-C60-Pd3 and Pd4-C60-Pd4) or negatively charged. On the other hand in C60-Au complexes, the Au atom involved in direct interaction with fullerene was found to have positive and the C-C atoms involved in direct interaction with gold clusters were found to have negative Mulliken charges. The MEP maps can be used for qualitative description of the Schottky barrier phenomena at the semiconductor-metal interface. Acknowledgment. M.K.S. and J.L. are thankful to financial support from Army Research Laboratory BAA# DAAD19-03R-0017, section # 2.41, Contract No. W911QX-07-C-0100, NSF-CREST Grant No. HRD-0833178, ONR Grant No. N0001408-1-0324, and the Mississippi Center for Supercomputing Research (MCSR) for the generous computational facility. Supporting Information Available: HOMO, LUMO, and some other closed laying occupied and unoccupied molecular orbitals. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Balch, A. L.; Olmstead, M. M. Chem. ReV. 1998, 98, 2123. (2) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. ReV. 2008, 108, 845. (3) Tao, N. J. Nat. Nanotechnol. 2006, 1, 173. (4) Park, H.; Park, J.; Lim, A. K. L.; Anderson, E. H.; Alivisatos, A. P.; McEuen, P. L. Nature 2000, 407, 57–60. (5) Frank, S.; Poncharal, P.; Wang, Z. L.; de Heer, W. A. Science 1998, 280, 1744–1746. (6) Bachtold, A.; Fuhrer, M. S.; Plyasunov, S.; Forero, M.; Anderson, E. H.; Zettl, A.; McEuen, P. L. Phys. ReV. Lett. 2000, 84, 6082–6085. (7) Nygard, J.; Cobden, D. H.; Lindelof, P. E. Nature 2000, 408, 342– 346. (8) Palacios, J. J.; Perez-Jimenez, A. J.; Louis, E.; SanFabian, E.; Verges, J. A. Phys. ReV. Lett. 2003, 90, 106801-1-4. (9) Jorn, R.; Seideman, T. J. Chem. Phys. 2006, 124, 84703-1-11.
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