A Direct Molecular Orbital−Molecular Dynamics Study on the Diffusion

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A Direct Molecular Orbital-Molecular Dynamics Study on the Diffusion of the Li Ion on a Fluorinated Graphene Surface Hiroto Tachikawa* DiVision of Materials Chemistry, Graduate School of Engineering, Hokkaido UniVersity, Sapporo 060-8628, Japan ReceiVed: January 16, 2008; ReVised Manuscript ReceiVed: April 10, 2008

A direct molecular orbital-molecular dynamics (MO-MD) method has been applied to diffusion processes of the Li+ ion on a fluorinated graphene surface. A graphene sheet composed of C96F24 (denoted by F-graphene) was used as a model of the fluorinated graphene surface. The total energy and energy gradient on the full dimensional potential energy surface of the Li+C96F24 system were calculated at each time step in the trajectory calculation. The calculations were carried out at the AM1 level. Simulation temperatures were chosen in the range 200-1000 K. At low temperatures, below 200 K, the diffusion of lithium ion did not occur, and the ion vibrates around an equilibrium point. At around room temperature (∼300 K), the lithium ion diffused freely on the surface, but the ion did not approach to the edge region of the surface. This is due to the repulsive interaction with positively charged carbon atom connecting to the fluorine atom where the C-F bond is polarized as Cδ+-Fδ-. The repulsive interaction strongly dominates the diffusion path of the Li+ ion on the F-graphene. However, the order of magnitude of diffusion coefficient for the Li+ ion moving on the F-graphene surface was close to that of the normal graphene surface (H-graphene). At higher temperatures, the Li+ ion moves freely on the F-graphene, and it fell in the edge region. On the basis of theoretical results, we designed a molecular device composed of F-graphite sheets. 1. Introduction Graphite is capable of accommodating several species between carbon layers. Hence, this character has been applied to the anode material of a lithium secondary battery with high electromotive force and high energy density.1–7 As well as the graphite materials, amorphous carbon materials, which are composed of small carbon sheets, have higher performance than that of the crystalline graphite having a layer structure. This particular feature is comparable to that of amorphous carbon in that it can involve a large amount of lithium ions. Actually, the theoretical maximum capacity of graphite material (LiC6) is 372 mAh/g (capacity per unit mass),8 whereas amorphous carbon materials have remarkably high capacities (500-1100 mAh/ g).9 This characteristic originates from the nonlayer structure where Li atoms and ions are stored in the edge region of the carbon layer. Recently, halogen substitution and doping of graphene sheet have been examined to develop higher performance graphite materials.10–12 Delabarre et al. used fluorinated graphite as the cathode in primary lithium batteries. The higher capacity values were achieved for low temperature fluorinated graphite.11 The halogenation of carbon materials may open new materials chemistry. However, the effects of halogen substitution on the electronic structure of the carbon materials are not clearly understood. In the present paper, diffusion of lithium ion on a fluorinated graphene surface has been investigated by means of a direct molecular orbital-molecular dynamics (MO-MD) method in order to shed light on the mechanism of diffusion of lithium on fluorinated graphene from a theoretical point of view. In particular, we focus our attention on the effect of F-substitution of graphene on the dynamics behavior of a lithium ion. * E-mail: [email protected]; fax +81-11-706-7897.

Figure 1. Structure of F-graphene and lithium ion adsorbed F-graphene in site A (Li+C96F24) used in the present calculation. Notations of A-F and a-b mean the trapping sites of the lithium ion on the on the ringover sites and edge sites of C96F24 surface, respectively. The carbon atoms in the edge region are terminated by fluorine atoms

In previous papers,13–15 we investigated the diffusion dynamics of a lithium ion and atom (Li+ and Li, respectively) on the

10.1021/jp800398y CCC: $40.75  2008 American Chemical Society Published on Web 06/12/2008

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Figure 3. Potential energy curve for the diffusion of Li+ along a diffusion path (A f B f C f D and z ) 2.45 Å) and the energy levels calculated at the AM1, B3LYP/6-31G(d), and MP2/LANL2MB// B3LYP/LANL2MB levels of theory (given as horizon bars). Notations of A-D indicate the stable positions of Li+ ion on the ring-over sites.

TABLE 1: Relative Energies of Li+ Ion Located on the Sites A-F and a of F-graphene (in kcal/mol) site AM1 B3LYP/LANL2MBa MP2/LANL2MBa B3LYP/6-31G(d)a

Figure 2. (Top panel) PES relevant for the movement of Li+ on a F-graphene surface calculated at the AM1 level. Contour is drawn at each 0.5 kcal/mol. (Bottom panel) The height of Li+ is fixed to z ) 2.45 Å from the planar F-graphene surface. A total of 2601 points are calculated (51 × 51 points). PECs along the path A-B-C-D are calculated at the AM1 level.

graphite sheet using a direct MO-MD method developed by us. In this method, the potential energy surface and the energy gradient of all atoms of the system are explicitly calculated quantum chemically. Therefore, the different characteristics from usual classical MD calculation are obtained. It was found that the Li+ ion preferentially diffuses along the node of the highest occupied molecular orbital (HOMO) of the graphite sheet. This implies that modification of the HOMO leads to control of the diffusion route of the lithium ion. Also, it was found that diffusion of a lithium atom is much different from that of a Li+ ion. The Li atom moves together with spin density distribution generated on the graphite surface. Hence, the diffusion rate for a Li atom is slower than that of the Li+ ion. The diffusion coefficients calculated were in good agreement with the experiments. In this work, the similar technique has been applied to the diffusion of Li+ on Li+C96F24. The interactions between Li/Li+ and a graphite surface have been theoretically investigated by several groups using lithium carbon cluster models.16–24 Using density functional theory (DFT), Marquez et al. investigated the interaction between Li+ and a hydrogen-

A 0.0 B 0.7 C 1.6 D 1.8 E 0.9 F 3.1 a -49.0

0.0 0.4 1.8 4.8 1.6 2.9 -19.6

0.0 0.0 1.3 3.6 1.5 2.0 -50.2

0.0 0.7 1.9 3.6 (1.7)b 1.7 2.0 -36.8

a Structures are obtained at the B3LYP/LANL2MB level. Energy after relaxing in the z-direction (See the Supporting Information). b

terminated cluster model (C32H18). They suggested that the Li+ ion is preferentially bound outside the cluster model (i.e, the edge site).16 On the basis of semiempirical MO calculations using a C96 planer carbon cluster and Li+, Nakadaira et al. suggested that the edge site is more stable than that of the ring-over site.18 Ab initio calculations for the interaction of a lithium atom with graphite model clusters indicated that charge transfer from the Li atom to a graphite cluster is important in the large cluster size.20,21 Thus, the static feature about the interaction between Li+/Li and graphite cluster models has been extensively studied. However, the information about the dynamics feature of Li+ on the graphene surface is still unclear. In this work, we mainly investigate the diffusion dynamics of a lithium ion on the fluorinated graphene and compare with that of normal graphene. 2. Method of Calculation First, the model cluster (C96F24) was fully optimized at the AM1 level. The structure of F-graphene including one lithium ion is illustrated in Figure 1. The carbon atoms in the edge region are terminated by fluorine atoms in the F-graphene. For the interaction

Diffusion of the Li Ion

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Figure 5. Trajectory of Li+ superimposed on a F-graphene surface at 500 K. The Li+ is started from site A.

We chose temperatures in the ranges 200-1000 K. The velocities of atoms at the starting point were adjusted to the selected temperature. To keep a constant temperature of the system, bath relaxation time (τ) was introduced in the calculation.30 We have chosen τ ) 0.01 ps in all trajectory calculations. The equations of motion for n atoms in the system are given by eq 2,

Figure 4. (Color) Trajectories of Li+ superimposed on (top panel) F-graphene surface and (bottom panel) H-graphene surfaces at 350 K. The Li+ is started from site A at time zero. The values in ovals indicate elapsed time (in ps) after starting the trajectory.

system (Li+C96F24), one Li+ ion was put above the center-of-mass of the model cluster (denoted by site A), and then the structures of the Li+C96F24 cluster was fully optimized. Diffusion processes of a Li+ ion on the graphene surface were investigated by means of a direct MO-MD method.25–28 The total energy and energy gradient on the multidimensional potential energy surface of the LiC96H24 system were calculated at each time step at the AM1 level of theory, and then the classical equation of motion is full-dimensionally solved. Therefore, charges and electronic states of the Li+ ion and all carbon and hydrogen atoms are exactly treated within the level of theory. This point is much different from usual classical molecular dynamics (MD) calculation where the charges of all atoms and ion are constant during the diffusion. We carried out the direct MO-MD calculations under constant temperature condition. Mean temperature of the system is defined by eq 1,

T)

1 3kN

〈∑ m V 〉 2 i i

(1)

i

where N is number of atoms; Vi and mi are velocity and mass of the ith atom, respectively; and k is Boltzmann’s constant.

dQi ∂H ) dt ∂Pj

(2)

dPj ∂U ∂H ))dt ∂Qj ∂Qj

(3)

where j ) 1 - 3N, and H is the classical Hamiltonian. The parameters Qj, Pj, and U are Cartesian coordinate of the jth mode, the conjugated momentum, and the potential energy of the system, respectively. These equations were numerically solved by the Runge-Kutta method. No symmetry restriction was applied to the calculation of the gradients. The time step size was chosen as 0.2 fs, and a total of 10 000 steps was calculated for each dynamics calculation. The drift of the total energy is confirmed to be less than 1 × 10-3% throughout at all steps in the trajectory. The momentum of the center of mass and the angular momentum are set to zero. Static ab initio, DFT, and semiempirical calculations—MP2/ LANL2MB, B3LYP/6-31G(d), B3LYP/LANL2MB—and AM1 calculations for the electronic states and structures and potential energy curves (PECs) along a diffusion path on the surface were carried out using the Gaussian 03 program package.30 3. Results A. Structures of the Model Cluster of Amorphous Carbon. First, the structure of the F-graphene is fully optimized at the AM1 level of theory. Next, the Li+ ion is put in site A with a height of z ) 2.45 Å from the surface (this distance shows the lowest energy as shown later). Then, a two-dimensional (2D) potential energy surface (PES) is calculated in the range x ) 0-10 Å and y ) 0-10 Å. The X- and Y-axes are located on the F-graphene surface, and the Z-axis is perpendicular to the surface. A total of 2601 points (51 × 51 points) are calculated at the AM1 level. The PES obtained is illustrated as a contour

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TABLE 2: Optimized Geometriesa and Charges on Li+ Ion AM1 site A B C D E F a a

B3LYP/LANL2MB

B3LYP/6-31G(d)b

MP2/LANL2MB

b

h

charge

h

Mulliken

NPA

Mulliken

NPA

2.277 2.294 2.310 2.341 2.296 2.355

0.75 0.75 0.76 0.77 0.76 0.77 0.65

1.650 1.652 1.652 1.675 1.652 1.656

0.41 0.41 0.41 0.37 0.41 0.38 0.66

0.96 0.96 0.96 0.95 0.96 0.96 0.95

0.39 0.37 0.37 0.39 0.40 0.36 0.52

0.69 0.67 0.67 0.68 0.69 0.66 0.76

Height of Li+ from the surface is reported in Ångstro¨ms. b Structures are obtained at the B3LYP/LANL2MB level.

Figure 6. Arrhenuis plots of the diffusion coefficients of the Li+ ion on F-graphene in the temperature range 300-500K. For comparison, the diffusion coefficients for the Li+ ion on the H-graphite surface and C60 are plotted. The data for H-graphene surface and for C60 are cited from previous papers.13,15

plot in Figure 2 (top panel). The plot region is also illustrated as a square in Figure 1. The energy minima are found in sites A-F in the surface region and in site b in the edge region. Site c is not bound, but the position of site c corresponds to a saddle point between edge regions. PECs along the X-axis (X ) 0.0-10.0 Å) are plotted in Figure 2 (bottom panel). The height of the Li+ ion from the surface is fixed to z ) 2.00-2.60 Å (interval is 0.15 Å and y ) 0.0 Å) in each PEC. The PEC and height of activation barrier are drastically changed by the height of the Li+ ion (z). However, the potential minima are located in sites A-D in all PECs. The PEC with z ) 2.45 shows the lowest energy in the surface region. The minima and maxima PECs are found in the hexagonal sites (A-D) and the C-C bond center sites of the F-graphene, respectively. This result indicates that the barrier height is located in the C-C bond center between hexagonal sites, whereas the Li+ ion can be stabilized in these trapping sites. Next, the geometries of system (Li+C96F24) at sites A-F are fully optimized at the AM1 and B3LYP/LANL2MB levels of theory. The relative energies of sites A-D are given in Figure 3 together with the PEC for z ) 2.45 Å. The energy levels calculated by AM1, MP2/LANL2MB//B3LYP/LANL2MB, and B3LYP/6-31G(d)//B3LYP/LANL2MB levels are shown as horizon bars. The values of the relative energies are given in Table 1. The relative energies of sites A-F are calculated to be 0.0, 0.7, 1.6, 1.8, 0.9, and 3.1 kcal/mol, respectively, at the AM1 level. The B3LYP/6-31G(d)//B3LYP/LANL2MB calculation gives simi-

Figure 7. Atomic charges of carbon atoms constructing the F-graphene plotted as a function of Rcm. The atomic charges are calculated by natural population analysis (NPA) at the B3LYP/LANL2MB level. Notations of regions a-c indicate the classification of carbon atoms of the F-graphene.

lar energetics; the relative energies are 0.0, 0.7, 1.9, 3.6, 1.7, and 2.0 kcal/mol, respectively. Also, the MP2/6-31G(d)// B3LYP/LANL2MB calculation gives similar energies. Note that the geometry optimization of the B3LYP/LANL2MB method underestimates the height of the Li+ ion from the surface (See the Supporting Information). To estimate the structural relaxation effect on the relative energy, the PEC relevant for movement of Li+ in site D is calculated at the B3LYP/6-31G(d) level. The height of Li+ at the energy minimum is changed from 1.675 to 2.00 Å, and the energy decreases -1.9 kcal/mol. The relaxed relative energy is given as a horizon bar of asterisks (*). The difference between AM1 and B3LYP calculations becomes smaller after the structural relaxation. These results indicate that the AM1 calculation gives the reasonable relative energies for the diffusion of the lithium ion on the F-graphene. At the very least, one can obtain a qualitative feature for diffusion dynamics of Li+ on the F-graphene using the AM1 calculation.

Diffusion of the Li Ion

Figure 8. Potential energy curves for the diffusion of Li+ along a diffusion path (A f B f C f D). Solid and dashed curves indicate that PEC for Li+ on F-graphene and H-graphene, respectively. Both graphenes are optimized at the AM1 level, and the heights of the lithium ions are fixed to z ) 2.45 Å (F-graphene) and z ) 2.40 Å (H-graphene).

Figure 9. Trajectory of Li+ superimposed on F-graphene with a hydrogen gate at 350 K. The Li+ is started from site A. One of fluorine atoms of edge region of F-graphene is substituted by hydrogen atoms.

B. Diffusion Dynamics of the Li+ Ion on F-graphene. The dynamics calculation indicates that the Li+ ion does not diffuse below 250 K and that it vibrates around the equilibrium point in site A. The diffusion of the Li+ ion is observed at 300 K. A trajectory of the Li+ ion superimposed on the F-graphene at 350 K is illustrated in Figure 4 (top panel). The Li+ ion is located in site A at time zero. After thermal activation, the Li+ ion moves toward the edge region. At 0.4 ps, the ion reaches near the second carbon atom from the edge. However, the ion can not approach the edge region and it rebounds to the bulk region. Thus, it can be concluded that the Li+ moves around the central region and it can not approaches the edge region at 300 K. For comparison, the trajectory of lithium ion on the Hgraphene is illustrated in Figure 4 (bottom panel). After thermal

J. Phys. Chem. C, Vol. 112, No. 27, 2008 10197 activation, the lithium ion moves toward the edge region, and it falls directly down into the edge at a time of 0.8 ps. After that, the ion vibrates strongly in the edge region. The attractive interaction between the Li+ ion and the C-H bond takes place in this region. Thus, the dynamics featured by the lithium ion on the F- and H-graphenes at 350 K is much different for each case. The movement of Li+ is strongly restricted on the F-graphene due to the repulsive interaction with positive charged carbon atoms (Cδ+-Fδ-), as shown later. On the other hand, the Li+ ion can move freely on the H-graphene because no repulsive interaction is present. A trajectory of Li+ at 500 K superimposed on the F-graphene surface is given in Figure 5. The Li+ ion transfers from site A to E via the C-C axis between sites B and B′. This path is the same as that of 350 K. Although the trajectory at 350 K rebounds to the starting point from the region E, the trajectory at 500 K moves parallel to the edge and proceeds to a bay area of the edge region (site b).Table 2. C. Diffusion Coefficients and Arrhenius Plots. The diffusion coefficients (D) of the Li+ ion on the F-graphene are calculated in the temperature ranges 250-500 K. The values increase with increasing temperature. The diffusion coefficients for 250, 300, and 500 K are calculated to be 0.51 × 10-10, 0.88 × 10-10 and 1.80 × 10-10 m2/s, respectively. An Arrhenius plot of the diffusion coefficient of the Li+ ion is given in Figure 6 together with those of the Li+ ion on H-graphene and C60. The diffusion coefficient for the Li+ ion on the F-graphene is significantly close to that of H-graphene. The activation energy of Li+ on F-graphene is calculated to be 0.6 kcal/mol, which is slightly similar to that of H-graphene (0.8 kcal/mol). The experimental value for diffusion of Li+ is 1.22 kcal/mol in graphite (H-graphene),30 which is in good agreement with the calculated value. This agreement implies that the present calculation would be valid to simulate the diffusion processes of Li/Li+-graphene systems. D. Electronic States of the F-graphene. The charges of carbon atoms constructing the F-graphene are calculated by means of natural population analysis (NPA) at the B3LYP/ LANL2MB level. Figure 7 shows the NPA charges of carbon atoms plotted as a function of distance of the carbon atom (Rcm), where Rcm is defined by a distance of the carbon atom from the center of mass of the graphene. To elucidate the effect of fluorination of graphene on the electronic states, the NPA charges of normal graphene (H-graphene) are plotted for comparison. The carbon atoms on the surface can be classified to three groups: carbon atoms in the bulk region (region a), the inner edge region (region b), and the outer edge region (region c). In normal graphene (H-graphene), the charges of carbon atoms in region a are close to zero (-0.04), whereas they are slightly changed to negative in regions b and c (-0.20). In the case of F-graphene, the charge distribution is much different from that of H-graphene. Although, the charges of carbon atoms in the outer edge region c are close to zero in the case of H-graphene, the charges of carbon atoms in the outer edge region of F-graphene are largely positive (+0.4 to +0.5). This large enhancement in the positive charge is caused by the large electron affinity of the F-atom, and the C-F bond is largely polarized as Cδ+-Fδ-. This polarization strongly affects the movement of the Li+ ion on the surface. The charge distribution indicates that the Li+ ion is able to freely move on both the bulk surface and the edge regions in the case of H-graphene. In contrast, movement of the Li+ ion on F-graphene will be restricted by the repulsive interaction.

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Figure 10. Ion-switching cell material theoretically designed on the basis of the direct MO-MD calculation. The arrows indicates a typical trajectory of Li+ superimposed on the material. At low temperature (around room tempeararure), the Li+ ion moves pseudo-one-dimensionally (path a) on the surface due to the repulsive interaction with the C-F bond in the edge region. On the other hand, the Li+ ion moves freely on F-graphite sheets at higher temperatures. The diffusion path of the Li+ ion is selectively changed by thermal activation of the system.

PECs relevant for the movement of the Li+ along the path A f B f C f D are calculated on both F- and H-graphenes. First, the graphene surfaces without the the Li+ ion (i.e., free F-graphene) are optimized at the AM1 level. Next, the heights of Li+ from the surface are fixed to z ) 2.45 Å (F-graphene) and 2.40 Å (H-graphene), and then PEC is calculated along the path. The PECs obtained are given in Figure S2 of the Supporting Information. The PEC shows that the height of x ) 2.40 Å gives the lowest energy curve for H-graphene. The results for z ) 2.40 Å is plotted in Figure 8 together with that of F-graphene. Around sites A and B, the energy level and shape of the PECs for H- and F-graphenes are close to each other. However, the shape of PECs in sites C and D are much different. The energy level of site C in H-graphene is close to zero (0.4 kcal/mol), whereas that of F-graphene is 1.4 kcal/mol higher in energy than zero level. Furthermore, the energy levels of site D are significantly different from each other (-4.9 kcal/mol for H-graphene and 2.0 kcal/mol for F-graphene). These differences cause the difference of diffusion dynamics in F-graphene. The specific feature is caused by the electronic states of the edge region (i.e., polarization of edge carbon such as Cδ+-Fδ-). F. Dynamics of Li+ Ion in F-graphene with a Hydrogen Gate. As shown in previous sections, it is found that the Li+ ion preferentially moves on the central region of F-graphene, and it can not approach the edge region at near room temperature. On the other hand, in H-graphene, the Li+ ion can move freely on the surface and easily falls in the edge region, even at room temperature. To confirm these situations, the diffusion dynamics on an actual system composed of F- and H-terminated graphene is examined. Figure 9 shows the F-graphene with a hydrogen gate, that is, a part of fluorine atoms of F-graphene are substituted by hydrogen atoms. The result of trajectory calculations at 300 K is given as a trajectory in Figure 9. The trajectory is started from site A at time zero. The Li+ ion moves to site B′ at 0.3 ps and site E at 0.6 ps. After that, the ion rebounds at site E and then return to near the starting point. At 1.2-1.6 ps, the ion gradually approaches the H-edge region. Finally, the ion falls in the hydrogen edge region. These results strongly indicate that the Li+ ion moves freely on the H-graphene and easily escapes to the edge region. On the other hand, the movement of the Li+ ion is restricted by the F-edge in the F-graphene. This restriction is caused by the polarization of the C-F bond in F-graphene.

MD method at the AM1 level of theory. From the results, it was found that diffusion coefficient of Li+ on the F-graphene surface is close to that of normal H-graphene, but the thermal behavior on the F-graphene surface is much different from that on the H-graphene surface. Namely, the Li+ ion on the F-graphene surface can not approach the edge region because of the repulsive interaction with a positive charge of the C-F carbon atoms. In the case of the diffusion of the Li+ ion on F-graphene with a hydrogen gate, the Li+ ion preferentially escaped via the hydrogen gate Figure 10 On the basis of these theoretical results, we designed a high performance molecular device composed of F-graphene sheets. The designed molecular device is illustrated in Figure 10. This device is composed of F-graphene sheets where both sides of the graphene sheets are terminated by F atoms, whereas the entrance and exit regions are composed of H-terminated graphene. The present study suggested that the Li+ ion can not approach the edge region due to the repulsive interaction around room temperature. Therefore, the Li+ ion diffuses preferentially near the center of the graphene sheet at low temperature around room temperature (path a). The Li+ ion moves one-dimensionally on the sheet, suggesting that the random walking of Li+ is efficiently restricted in the case of the designed F-graphene sheet. The direction of diffusion can be controlled by F-substitution on the graphene sheet. Thus, the direction of diffusion can be controlled by F-substitution of the graphene sheet. This performance is important in the development of a lithium secondary battery. At higher temperatures, on the other hand, the Li+ ion diffuses freely on surface and edge regions of F-graphene (path b). The diffusion moves preferentially on the F-graphite surface. Thus, the diffusion path of the Li+ ion on the designed molecular device is drastically changed by the control of temperature. This point is also important as the ion-switching device. Acknowledgment. The authors are indebted to the Computer Center at the Institute for Molecular Science (IMS) for the use of the computing facilities. H.T. also acknowledge a partial support from a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan. This work is partially supported by the Kurata foundation. Supporting Information Available: Additonal materials referenced within are provided. This material is available free of charge via the Internet at http://pubs.acs.org.

4. Discussion In the present study, the diffusion of the lithium ion on the F-graphene has been investigated by means of a direct MO-

References and Notes (1) Inagaki, M. J. Mater. Res. 1989, 4, 1560.

Diffusion of the Li Ion (2) Koksbang, R.; Barker, J.; Shi, H.; Saidi, M. Y. Solid State Ionics 1996, 84, 1. (3) Inagaki, M., In Chemical Physics of Intercalation, NATO ASI Ser. B, 172; Legrand, A. P., Flandrois, S., Eds.; Plenum: New York, 1987; p 105. (4) Inagaki, M.; Tachikawa, H.; Nakahashi, T.; Konno, H.; Hishiyama, Y. Carbon 1998, 36, 1021. (5) Konno, H.; Oka, H.; Shiba, K.; Tachikawa, H.; Inagaki, M. Carbon 1999, 37, 887. (6) Shimizu, A.; Inagaki, M.; Tachikawa, H. J. Phys. Chem. Sold 1999, 60, 1811. (7) Konno, H.; Shiba, K.; Tachikawa, H.; Nakahashi, T.; Oka, H.; Inagaki, M. Synth. Metal. 2001, 125, 189. (8) Guerard, D.; Herold, A. Carbon 1975, 13, 337. (9) Yata, S.; Hato, Y.; Kinoshita, H.; Ando, N.; Anekawa, A.; Hashimoto, T.; Yamaguchi, M.; Tanaka, K.; Yamabe, T. Synth. Met. 1995, 73, 273. (10) Liu, Y.; Vander, R. L.; Khabashesku, V. N. Chem. Mater. 2007, 19, 778. (11) Delabarre, C.; Dubois, M.; Giraudet, J.; Guerin, K.; Hamwi, A. Carbon 2006, 44, 2543. (12) Achiha, T.; Nakajima, T.; Ohzawa; Y., J. Electrochem. Soc. 2007, 154, A827–833. (13) Tachikawa, H.; Shimizu, A. J. Phys. Chem. B 2005, 109, 13255. (14) Tachikawa, H.; Shimizu, A. J. Phys. Chem. B 2006, 110, 20445. (15) Tachikawa, H. J. Phys. Chem. C 2007, 111, 13087. (16) Marquez, A.; Vargas, A.; Balbuena, P. B. J. Electrochem. Soc. 1998, 145, 3328. (17) Khantha, N.; Cordero, N. A.; Molina, L. M.; Alonso, J. A.; Girifalco, L. A. Phys. ReV. B 2004, 70, 125422. (18) Nakadaira, M.; Saito, R.; Kimura, T.; Dresselhaus, G.; Dresselhaus, M. S. J. Mater. Res. 1997, 12, 1367. (19) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. J. Phys. Soc. Jpn. 1996, 65, 1920.

J. Phys. Chem. C, Vol. 112, No. 27, 2008 10199 (20) Boehm, R. C.; Banerjee, A. J. Chem. Phys. 1992, 96, 1150. (21) Hankinson, D. J.; Almlo¨f, J. J. Mol. Struct. (THEOCHEM) 1996, 388, 245. (22) Ishikawa, S.; Madjarova, G.; Yamabe, T. J. Phys. Chem. B 2001, 105, 11986. (23) Suzuki, T.; Hasegawa, T.; Mukai, S. R.; Tamon, H. Carbon 2003, 41, 1933. (24) Lunell, S.; Stashans, A.; Ojamae, L.; Lindstrom, H.; Hagfeldt, A. J. Am. Chem. Soc. 1997, 119, 7374. (25) Tachikawa, H.; Abe, S. J. Chem. Phys. 2007, 126, 194310. (26) Tachikawa, H. J. Chem. Phys. 2006, 125, 144307. (27) Tachikawa, H. J. Chem. Phys. 2006, 125, 133119. (28) Tachikawa, H. J. Phys. Chem. A 2006, 110, 153–159. (29) Ab-initio MO calculation program: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, Jr., T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar,S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; MCossi, G.; Scalmani, N.; Rega, G.; Petersson, 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, Rev. B.04; Gaussian, Inc.: Pittsburgh PA, 2003. (30) Yu, P.; Popov, B. N.; Ritter, J. A.; White, R. E. J. Electrochem. Soc. 1999, 146, 8.

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