Chapter 0 Hydrogenation of Fullerene C 60 : Material Design of Organic Semiconductors by Computation

Carrier mobility [1] in organic semiconductors is one of the most important properties in the performance of organic light-emitting diodes (OLEDs), organic field-effect transistors (OFETs), and organic solar cells, which are expected to be used in next-generation technologies [2]. Organic semiconductors have the advantages of lightness, flexibility, and low cost. Therefore, research and development of new materials with chemical and thermal stability has recently been very active [3–6]. However, the wide variety of organic materials, which is generally a major advantage of these materials, has hindered the systematic research and development of novel materials. Thus, the establishment of design guidelines for new organic materials is a matter of great urgency.


Motivation
Carrier mobility [1] in organic semiconductors is one of the most important properties in the performance of organic light-emitting diodes (OLEDs), organic field-effect transistors (OFETs), and organic solar cells, which are expected to be used in next-generation technologies [2]. Organic semiconductors have the advantages of lightness, flexibility, and low cost. Therefore, research and development of new materials with chemical and thermal stability has recently been very active [3][4][5][6]. However, the wide variety of organic materials, which is generally a major advantage of these materials, has hindered the systematic research and development of novel materials. Thus, the establishment of design guidelines for new organic materials is a matter of great urgency.
Up till now, much effort has been made to understand theoretically the relationship between the structure and the carrier-transport properties of these materials [7][8][9][10]. Theoretical investigations can give reliable guidelines for the development of such new organic semiconductors. We have also been studying the quantum-chemical design of organic semiconductors based on fullerenes from both scientific and technological viewpoints [11][12][13][14][15][16][17][18][19]. C 60 derivatives (Figure 1) are very interesting from the viewpoint of practical use. Some types of C 60 derivatives are shown in the figure, and C 60 derivatives of types (a) and (b) have already been studied in our research group [11][12][13][14][15][16][17][18][19].
It is well known that C 60 is chemically and thermally stable, and its method of synthesis is also established. Carrier mobility of amorphous silicon is about 1 cm 2 V −1 s −1 , so that a mobility above this value is desirable for organic semiconductors. However, hole mobility in C 60 film is in the order of 10 −5 cm 2 V −1 s −1 [20], so that C 60 has not been used as a hole-transport material (p-channel semiconductor). Thus, the main purpose of our previous studies [11][12][13][14][17][18][19] was to improve the hole mobility of C 60 by chemical methods. There is the possibility that the addition of hydrogen to C 60 would result in a considerable modification of the C 60 materials. This possibility originates from the fact that C 60 has an electronic degeneracy in its cationic state because of its high symmetry I h [21,22], but C 60 hydrides usually do not because of the reduction in symmetry by the addition of hydrogen. Electron mobility in C 60 film is about 1 cm 2 V −1 s −1 [20,23,24] so that C 60 is one of the most useful electron-transport materials. However, to achieve low-cost production and large-area devices, it is necessary for C 60 materials to have a solution-processable form, such as [6,6]-phenyl C 61 -butyric acid methyl ester (PCBM) [25]. Therefore, in organic electronics, the electronic properties of C 60 derivatives rather than those of the original C 60 are of much interest and importance.

Our previous publication: C
In our previous publication [11], the effect on carrier-transport properties of chemical addition of X (X= H ,R ,R -C O O H ,a n dR -S H ,w h e r eRi sa na l k y lc h a i n )t oC 60 was systematically discussed from the viewpoint of reorganization energy (λ) using Marcus theory [28]. We focused on the C 60 derivatives of type (a) in Figure 1, C 60 X n ,w h e r eX is the added group and n is the number of added X. There are many isomers for C 60 X n , so that the position of X was also a subject of investigation. The dependence of carrier-transport properties on the type or chemical nature of X was discussed from the results of C 60 X 2 . The dependence of carrier-transport properties on the number of added groups was discussed from the results of C 60 H n (n = 2, 4, and 6). From these discussions, guidelines for effective design of carrier-transport materials were proposed: • Carrier-transport properties of C 60 X 2 are quite different from those of C 60 [13][14][15]18].
• Chemical addition can improve hole mobility of C 60 for some isomers [13,14,18]. Conversely, electron mobility of C 60 is not influenced or is decreased by the chemical addition [15].
• The values of reorganization energies of both hole transport and electron transport are almost independent of the type (chemical nature) of addition group X,b u ta r e strongly dependent on the position and the number of addition groups [15]. Therefore, reorganization energies of other types of C 60 X 2 will be approximately estimated from the results of C 60 H 2 [15].
• Hole and electron mobilities are closely related to the distribution patterns of the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital), respectively [13][14][15]. Delocalized orbitals give high carrier mobility (small reorganization energy) and localized molecular orbitals produce a low carrier mobility (large reorganization energy).
• There is a clear linear relationship between the reorganization energy and the geometrical relaxation upon carrier injection.
These results will also be applied to other types of X, and give us a guideline for efficient design of novel materials based on C 60 from both experimental and theoretical approaches. For example, in the experimental viewpoint, we can freely select an X that is appropriate for thin-film formation and is easily synthesized without considering the influence of X on the electronic properties. From the theoretical viewpoint, this result enables us to save computation time and resources in the material design because various types of C 60 X 2 can be simplified to C 60 H 2 in the prediction and discussion of these properties.

Our previous publication: C 60 CX 2
In another of our publications [12], the effect of methylene bridging of C 60 by -CX 2 (X =H, halogen, R, R-COOH, and R-SH, where R is an alkyl chain) on carrier-transport properties was systematically discussed. There are two isomers for C 60 CX 2 , I and II ( Figure 2). Systematic 311 Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation analyses of reorganization energies of methylene-bridged fullerenes C 60 CX 2 give us very important knowledge for the efficient design of useful C 60 materials: • Hole mobility of C 60 is strongly influenced by methylene bridging. C 60 CBr 2 (II) has the smallest reorganization energy (93 meV). On the other hand, C 60 CX 2 (I)i s o m e r sw i t hR , R-COOH, and R-SH chains have very large reorganization energies of about 500 meV.
• Electron mobility of C 60 is not influenced or is decreased by methylene bridging [16].
• Values of reorganization energies of both hole transport and electron transport are dependent on the type (chemical nature) of X. Therefore, especially for the case of hole transport, reorganization energies of other types of C 60 CX 2 will not be easily predicted from the results of C 60 CH 2 . This result is quite different from the case of C 60 H 2 and C 60 X 2 .
• There is a clear linear relationship between the reorganization energy and the change in the distance between bridged C···C atoms.
• Hole and electron mobilities are closely related to the distribution patterns of the HOMO and the LUMO between bridged carbon atoms, respectively [16]. Small carrier mobility and large reorganization energy result from strong antibonding character between bridged carbon atoms.
One of the important findings in this work is that the properties of C 60 CX 2 are dependent on the type (chemical nature) of X. T h i si sb e c a u s eC X 2 addition directly changes the carbon network around the addition position. The possibility of a transformation between a closed structure and an open structure upon carrier injection is one of the reasons why the reorganization energy of C 60 CX 2 is strongly dependent on the type of X. Therefore, the molecular design of type (b) molecules is a little more difficult compared with the molecular design of type (a) molecules, C 60 X 2 .
We also found that electron-transport properties are little influenced by the methylene bridging, so that we can freely select an X that is appropriate for thin-film formation and is easily synthesized without considering the effect of X on the electronic properties. On the other hand, when constructing high-mobility hole-transport materials, the use of isomer I of C 60 CX 2 , which includes an alkyl chain with -CH 3 and -COOH terminals, should be avoided.

This chapter
In this chapter, the effect of further hydrogenation of C 60 on hole-transport properties is systematically discussed from the viewpoint of reorganization energy. We again focus on the C 60 derivatives of type (a) in Figure 1. The dependence of hole-transport properties on the number and the position of hydrogen atoms is discussed from the results of C 60 H n (n = 2, 4, 6, 8, 52, 54, 56, 58, and 60). From these discussions, guidelines for the effective design of high-performance carrier-transport materials of type (a) are proposed.
This chapter is organized as follows: In Section 2, the definition of λ and computational details of λ are presented. Synthesis methods of hydrogenated C 60 are reviewed in Section 3. Structures of hydrogenated C 60 molecules studied in this chapter are shown in Section 4. In Section 5, calculated results of λ for hole transport are shown. λ for electron transport is not discussed because it is expected that λ for electron transport is independent of the position and the number of hydrogen atoms. From the systematic discussion of these results, the dependence of λ on the position and the number of hydrogen atoms is shown in Section 6. Summarizing these discussions, simple guidelines for the efficient design of useful C 60 H n semiconductors are proposed in Section 7.

Hopping mechanism
The hole mobility of single-crystal C 60 is around 10 −5 cm 2 V −1 s −1 at a maximum. Materials having a mobility of 0.1−1cm 2 V −1 s −1 are categorized in the boundary region between the hopping and the band-transport mechanisms [29][30][31]. Therefore, in this chapter, only the hopping mechanism is considered because the hole mobility of C 60 is much smaller than 0.1 cm 2 V −1 s −1 .
A schematic picture of hole hopping in an organic solid is shown in Figure 3. C 60 and C 60 H n molecules are represented by spheres in Figure 3. In the treatment of the hopping mechanism, two neighboring molecules are chosen from the solid. Then, a hole hopping between these two molecules, that is, the hole-transfer reaction, is considered. Repeating such a hopping between neighboring molecules, a carrier travels from one edge to the other edge of the organic solid.  Figure 4. Schematic potential energy surfaces of molecules related to the hole-transfer reaction. Q 0 and Q + mean the nuclear coordinates of stable structures in neutral and cationic states, respectively. Subscripts on the right-hand side of E mean the geometrical structure of the molecule and superscripts on the right-hand side of E mean the charge on the molecule.
A localized hole on one molecule (A) jumps to the neighboring molecule (B). From the Marcus theory [28], the hole-transfer rate constant k of a homogeneous carrier-transfer reaction can be estimated from two parameters, the reorganization energy (λ), and the electronic coupling element (H) between adjacent molecules: where k B is the Boltzmann constant, h is the Planck constant, and T is the temperature of the system. We can see that a small λ,l a r g eH, and high temperature T result in a fast hole hopping.

Reorganization energy
From Figure 3, we can see that the reorganization energy is the difference between "the energy in the final state of the system with a stable nuclear configuration in the final state" and "the energy in the final state of the system with a stable nuclear configuration in the initial state". For the calculation of λ, potential energy diagrams of the hole-transfer reaction are shown in Figure 4. The values of λ are obtained by the following procedure: First, the geometries of neutral C 60 and C 60 H n were fully optimized, giving a nuclear coordinate Q 0 and energy E 0 0 .A tQ 0 , single-point energy calculations of cations give E + 0 . Next, the structures were fully optimized in their cationic states, giving Q + and E + + . Single-point energy calculations of the neutral states with geometry Q + give E 0 + . The reorganization energy of the hole-transfer reaction (λ h )isdefinedasthesumofλ + h and λ 0 h : where λ + h and λ 0 h are relaxation energies in the cationic and neutral states, respectively, estimated from

Rate constant
In this chapter, the calculation and analysis of λ h are focused on. The electronic-coupling element for hole transport (H h ) can be approximated by one half of the molecular orbital energy splitting between the HOMO and the next HOMO of the neutral dimer [3,32]. However, the values of H h are dependent on both the distance and the relative orientation between the two molecules. Therefore, H h is assumed to be the same for C 60 and all C 60 H n for ease of discussion in this work [33]. Therefore, we cannot know the numerical values of the rate constants k h . Instead, we define k ′ h as a ratio of the rate constant of C 60 H n to that of C 60 at T = 300 K. The values of k ′ h for hole transport are calculated as in this chapter. All calculations (geometrical optimizations and self-consistent field (SCF) energy calculations) necessary to obtain the values of the energies in Figure 4 were performed by a quantum-chemical method, namely, density functional theory (DFT) using the B3LYP functional. For the calculation of λ h , the 6-311G(d, p) basis set was adopted. All neutral (ionic) systems were calculated in singlet (doublet) states. Calculations were performed using the GAUSSIAN 03 [34] program package.

Hydrogenation of fullerene
Although the main topic of this chapter is a theoretical discussion of hydrogenated fullerenes, synthesis methods of hydrogenated fullerenes are also important for practical use.
Up to now, many types of hydrogenated fullerenes have been synthesized. Hydrogenated fullerenes, C 60 H 2 ,C 60 H 4 ,a n dC 60 H 6 , have been prepared by hydroboration [35,36], hydrozirconation [37], rhodium-catalyzed hydrogenation [38], diimide [39] and hydrazine [40] reduction, dissolving metal reduction [41,42], photoinduced-electron-transfer 315 Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation reduction with 10-methyl-9,10-dihydroacridine [43,44], and ultrasonic irradiation in decahydronaphthalene [45]. In many cases, a mixture of C 60 ,C 60 H 2 ,a n dC 60 H n (n > 2) is obtained [46]. Birch reduction [47] and transfer hydrogenation [48] of C 60 produce C 60 H 18 and C 60 H 36 . In the ruthenium-catalyzed hydrogenation, other types of C 60 H n (n = 10, 12, 34, 36, 38, and 40) were observed using a field-desorption (FD) mass spectrometer [49]. Direct hydrogenation of C 60 was achieved without the use of a catalyst by exposing solid-phase fullerenes to high-pressure hydrogen gas, and many types of C 60 H n (n =2 −18) were identified by laser-desorption Fourier-transform mass spectrometry [50]. Unfortunately, highly hydrogenated fullerenes discussed in this chapter, C 60 [51]. 11 isomers of Figure 5(a) with a small formation energy were selected to consider the possibility of synthesis. The ground state of these isomers is the singlet state. Other isomers that are not considered in this chapter have triplet ground states in semiempirical calculations [51]. The initial hydrogen atom of C 60 H 2 is already shown in the figure. The second hydrogen atom is added to one of the carbon atoms labeled 1-11. T h e s ei s o m e r sa r en a m e d1-11 in boldface. As predicted by Matsuzawa et al. [51] from quantum-chemical calculations, two isomers, 1 from 1,2-addition and 5 from 1,4-addition, have been synthesized [35,39]. Furthermore, isomer 1 has been synthesized by many different methods [52].
Among a total of 418470 isomers of C 60 H 6 [53], we consider only 16 isomers in Figure 5 (c) originating from one H 2 addition to C 60 H 4 -1 at a [6,6]-ring fusion. One hydrogen pair is added to one of the carbon atom pairs labeled 1-16 and these isomers are named 1-16.
We consider only six isomers of C 60 H 8 in Figure 5 (d) originating from H 2 addition to C 60 H 6 -1 at a [6,6]-ring fusion. One hydrogen pair is added to one of the carbon atom pairs labeled 1-6 and these isomers are named 1-6.  Figure 5 are to be considered the nonhydrogenated carbon atoms.

C 60
The electronic structure of C + 60 has been investigated both experimentally and theoretically because of its electronic degeneracy [58,59]. C + 60 has an H u degenerate electronic state so that symmetry lowering because of the Jahn-Teller effect [21] stabilizes C + 60 .T h e m o s t stable structure of C + 60 was calculated as having D 5d symmetry, and its λ + h is 95 meV in our calculation. The result of λ + h is qualitatively consistent with previous works based on the static Jahn-Teller effect [60][61][62] in which the values of λ + h were calculated as 351 [60], 35 [61], and 71 meV [62]. The value of λ 0 h of C + 60 (D 5d ) was calculated as 74 meV. Thus, the reorganization energy of the hole transport, λ h , is 169 meV. It should be noted that the value of λ + h is much larger than that of λ 0 h . This result comes from the fact that geometrical relaxation in the ionic state is very large because of Jahn-Teller distortion [21]. The potential curves of the ionic states are expected to have larger curvature around the minima than that of the neutral state. On average, λ + h of C 60 H 2 is 84 meV, which is smaller than that of C 60 by 11 meV and λ 0 h of C 60 H 2 is 90 meV, which is larger than that of C 60 by 16 meV [12,13]. The average value of λ h of C 60 H 2 (174 meV) is almost as large as that of C 60 (169 meV). However, only the addition of two H atoms leads to the large difference in λ h , 101-257 meV. It is interesting that six isomers of C 60 H 2 (1, 4, 5, 6, 8,and9) have a smaller λ h than C 60 . In particular, isomer 6 has the smallest λ h (101 meV), which is over 40% less than that of C 60 . In addition, the k ′ h of 6 is about 2.5 times as large as that of C 60 . From the viewpoint of practical use, it should be noted that the values of λ h for the two synthesized isomers, 1 and 5, are 133 and 142 meV, respectively, which are about 20% smaller than that of C 60 .T h ev a l u e so fk ′ h for these isomers are about 1.5 times as large as that of C 60 . These results indicate that hydrogenation can be an effective method for modifying the hole-transport properties of C 60 . Two synthesized isomers of C 60 H 2 , 1 and 5, have potential utility as hole-transport materials. For almost all isomers of C 60 H 2 , λ + h is almost equal to λ 0 h . This means that the potential curves of the ionic and neutral states have almost the same curvature around the minima because the hydrogenation removes the electronic degeneracy in ionic states of C 60 .
On average, λ + h of C 60 H 4 is 65 meV, which is smaller than that of C 60 by 30 meV and λ 0 h of C 60 H 4 is 68 meV, which is smaller than that of C 60 by 6 meV [12,14]. The average value of λ h of C 60 H 4 (134 meV) is much smaller than that of C 60 (169 meV) and is almost as large as that of C 60 H 2 -1 (133 meV). The addition of two H atoms to C 60 H 2 -1 results in the large difference in λ h , 83-183 meV. Seven isomers of C 60 H 4 (1, 3, 4, 5, 6, 7,a n d8) have smaller λ h than C 60 . Remarkably, the major product 1 has the smallest λ h (83 meV), which is over 50% less than that of C 60 . In addition, k ′ h of 1 is 3.28 times as large as that of C 60 , and more than twice as large as that of the synthesized C 60 H 2 -1 [13]. Isomer 7 with the second smallest λ h has a value for k ′ h that is 2.83 times as large as that of C 60 . Other identified isomers 4, 6,a n d8 also have small λ h (138, 150, and 126 meV, respectively), and k ′ h of these isomers are respectively 1.49, 1.26, and 1.74 times larger than that of C 60 . Synthesized isomers of C 60 H 4 , especially the major product 1, have potential utility as useful hole-transport materials.
On average, λ + h of C 60 H 6 is 61 meV, which is much smaller than that of C 60 by 34 meV and λ 0 h of C 60 H 6 is 66 meV, which is smaller than that of C 60 by 8 meV [12]. The average value of λ h for C 60 H 6 (127 meV) is much smaller than that for C 60 (169 meV); however, it is much larger than that for C 60 H 4 -1 (83 meV). Further addition of two H atoms to C 60 H 4 -1 leads to a large difference in λ h , 71-182 meV. 14 of the 16 isomers have smaller λ h than C 60 .I s o m e r1 has the smallest λ h (71 meV), which is about 60% less than that of C 60 . In addition, k ′ h of 1 is 3.94 times as large as that of C 60 .I s o m e r4 with the second smallest λ h has a value of k ′ h that is 3.22 times as large as that of C 60 .
λ h and k ′ h of C 60 H 8 are shown in Table 1. On average, λ + h of C 60 H 8 is 51 meV, which is much smaller than that of C 60 by 44 meV, and λ 0 h of C 60 H 8 is 62 meV, which is smaller than that of C 60 by 12 meV. The average value of λ h for C 60 H 8 (113 meV) is much smaller than that for C 60 (169 meV); however, it is much larger than that for C 60 H 6 -1 (71 meV). Further addition of two H atoms to C 60 H 6 -1 leads to a large difference in λ h , 81-175 meV. Five of the six isomers have smaller λ h than C 60 .I s o m e r5 has the smallest λ h (81 meV), and k ′ h of 5 is 3.39 times as large as that of C 60 .I s o m e r6 with the second smallest λ h has a value of k ′ h that is 3.23 times as large as that of C 60 .

C 60 H 52 -C 60 H 58
λ h and k ′ h of C 60 H 52 are shown in Table 2. On average, λ + h of C 60 H 52 is 122 meV, which is much larger than that of C 60 by 27 meV, and λ 0 h of C 60 H 52 is 132 meV, which is much larger than that of C 60 by 58 meV. The average value of λ h of C 60 H 52 (254 meV) is much larger than that of C 60 (169 meV). Hydrogenation leads to a large difference in λ h , 175-441 meV. Isomer 6 has λ h as large as C 60 .  Values of λ h and k ′ h for C 60 H 54 isomers are shown in Table 3. On average, λ + h of C 60 H 54 is 176 meV, which is much larger than that of C 60 by 81 meV, and λ 0 h of C 60 H 54 is 181 meV, which is much larger than that of C 60 by 107 meV. The average value of λ h of C 60 H 54 (357 meV) is much larger than that of C 60 . It is interesting that the values of λ h are in the range 254-397 meV and there is not so large a difference.
Values of λ h and k ′ h for C 60 H 56 isomers are shown in Table 4. On average, λ + h of C 60 H 56 is 140 meV, which is much larger than that of C 60 by 45 meV, and λ 0 h of C 60 H 56 is 154 meV, which is much larger than that of C 60 by 80 meV. The average value of λ h for C 60  much larger than that for C 60 .T h ev a l u e so fλ h are in the range 230-501 meV. Isomer 2 has the largest λ h of more than 500 meV.   Table 5. On average, λ + h of C 60 H 58 is 606 meV, which is much larger than that of C 60 by 511 meV and λ 0 h of C 60 H 58 is 468 meV, which is much larger than that of C 60 by 394 meV. The average value of λ h of C 60 H 58 (1074 meV) is much larger than that of C 60 . It is interesting that the values of λ h are in the range 392-2411 meV. Isomers 1, 2,and4 have smaller λ h . These results mean that highly hydrogenated C 60 H 52 − C 60 H 58 are generally not suited for hole-transport materials.

C 60 H 60
C 60 H + 60 has nine electrons in fivefold degenerate h u orbitals. Thus, C 60 H + 60 has an H u degenerate electronic state, and symmetry lowering because of the Jahn-Teller effect [21] stabilizes C 60 H + 60 . The most stable structure of C + 60 was calculated as having D 3d symmetry, and its λ + h is 101 meV in our calculation. The value of λ 0 h for C + 60 (D 3d ) was calculated as 40 meV. Thus, the reorganization energy for hole transport, λ h , is 140 meV. Similar to C 60 , λ + h is much larger than λ 0 h because of the Jahn-Teller effect. k ′ h of C 60 H + 60 is 1.44 times as large as that of C 60 . Figure 6 shows minimum and average values of λ h for C 60 H n .C 60 and C 60 H 60 have only one isomer so that the minimum values are equal to the average values. From the systematic discussion through C 60 H n (n = 2, 4, 6, and 8), it was found that hydrogenation has a large effect on the improvement of hole-transport properties (λ h ). The minimum values of λ h decrease as the number of hydrogen atoms increases: C 60 (169 meV) → C 60 H 2 -6 (101 meV) → C 60 H 4 -1 (83 meV) → C 60 H 6 -1 (71 meV). However, λ h increases for C 60 H 8 -5 (81 meV). The average values of λ h change as C 60 (169 meV) → C 60 H 2 (174 meV) → C 60 H 4 (134 meV) → C 60 H 6 (127 meV) → C 60 H 8 (113 meV). The average λ h of C 60 H 4 (134 meV) is almost as large as that of C 60 H 2 -1 (133 meV), but the average λ h of C 60 H 6 (127 meV) is much larger than that of C 60 H 4 -1 (83 meV), and the average λ h of C 60 H 8 (113 meV) is much larger than that of C 60 H 6 -1 (71 meV). Highly hydrogenated C 60 H n generally has large λ h . The average λ h is C 60 H 52 (254 meV), C 60 H 54 (357 meV), C 60 H 56 (294 meV), C 60 H 58 (1074 meV), and C 60 H 60 (140 meV). Only C 60 H 60 has a smaller λ h than C 60 . 6. Analysis for molecular design 6

.1. Geometrical relaxation
The reorganization energy is a stabilization energy by geometrical relaxation originating from the change in electronic structure [64][65][66]. The strong forces on the nuclei generally result in large λ and geometrical relaxation. In our previous publications, we defined parameters ∆r that characterize the geometrical relaxation as ∆r = ∑ i |∆r i |, ( 7 ) where ∆r i is the difference in the ith bond length between neutral and cationic states. The summation is taken over all bonds. It has already been shown that there is an almost linear relationship between ∆r and λ h for C 60 H n (n = 2, 4, and 6) [11]. Figure 7 shows the relationship between λ and ∆r for hole transport in C 60 H 8 ,C 60 H 52 ,C 60 H 54 ,C 60 H 56 ,C 60 H 58 , and C 60 H 60 . A linear relationship between ∆r and λ h is observed for C 60 H 8 and C 60 H 58 .A clear linear relationship is not found for C 60 H 52 ,C 60 H 54 ,a n dC 60 H 56 because the values of the reorganization energy for these species are almost the same. When the values of ∆r are the same, C 60 H 8 has a smaller reorganization energy but C 60 H 58 has a larger reorganization energy.

Molecular orbital pattern
It is well known that the electronic properties of the HOMO have a close relation to hole-transport properties. Therefore, we focus on the distribution of the HOMOs of C 60 H n . The HOMO of C 60 , which is originally fivefold degenerate, splits because of the interaction between C 60 and the H atoms. The distribution of the HOMO easily changes depending on the interaction between C 60 and the H atoms. The HOMOs of isomer-1 of C 60 H n are shown in Figure 8. The HOMOs of C 60 H 8 -1 and other lowly hydrogenated fullerenes [11,13,14]   contrast, the HOMOs of C 60 H 52 -1,C 60 H 54 -1,C 60 H 56 -1,andC 60 H 58 -1 are localized around the nonhydrogenated C atoms. Therefore, highly hydrogenated C 60 has a large reorganization energy. In particular, the HOMO of C 60 H 58 -1 is localized on two carbon atoms, therefore the reorganization energy is very large. The HOMO of C 60 H 60 is delocalized over the whole molecule because C 60 H 60 has high symmetry, so that the value of λ h is smaller than that for other highly hydrogenated fullerenes.
Further hydrogenation does not reduce the reorganization energy.
• Highly hydrogenated fullerenes, especially C 60 H 58 , have very large reorganization energies because the HOMOs are localized around nonhydrogenated carbon atoms. Therefore, these C 60 derivatives are not suited for hole-transport materials.
• However, C 60 H 60 has a smaller reorganization energy than other highly hydrogenated fullerenes and C 60 because the HOMO of C 60 H 60 is distributed over the whole molecule.
• There is a linear relationship between the reorganization energy and the geometrical relaxation. When the values of ∆r are the same, lowly hydrogenated fullerenes have smaller reorganization energies than highly hydrogenated fullerenes.