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

Ken Tokunaga

to

308 Hydrogenation

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[63] Ranjit K.T, Krishnamoorthy R, Viswanathan B (1994) Photocatalytic Reduction of

[64] Kudo A, Sekizawa M (2000) Photocatalytic H2 Evolution under Visible Light Irradiation

[65] Kudo A, Hamanoi O (2002) Reduction of Nitrate and Nitrite Ions over Ni-ZnS Photocatalyst under Visible Light Irradiation in the Presence of a Sacrificial Reagent.

[66] Yamauchi M, Abe R, Tsukuda T, Kato K, Tanaka M (2011) Highly Selective Ammonia Synthesis from Nitrate with Photocatalytically Generated Hydrogen on CuPd/TiO2. J.

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Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48534

### **1. Introduction**

### **1.1. 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 [3–6]. 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 [7–10]. 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 [11–19]. C60 derivatives (Figure 1) are very interesting from the viewpoint of practical use. Some types of C60 derivatives are shown in the figure, and C60 derivatives of types (a) and (b) have already been studied in our research group [11–19].

It is well known that C60 is chemically and thermally stable, and its method of synthesis is also established. Carrier mobility of amorphous silicon is about 1 cm2V−1s−1, so that a mobility above this value is desirable for organic semiconductors. However, hole mobility in C60 film is in the order of 10−<sup>5</sup> cm2V−1s−<sup>1</sup> [20], so that C60 has not been used as a hole-transport material (p-channel semiconductor). Thus, the main purpose of our previous studies [11–14, 17–19] was to improve the hole mobility of C60 by chemical methods. There is the possibility

©2012 Tokunaga, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ©2012 Tokunaga, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

C60

C C

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 311

*open closed*

C60

CX2 C C

CX2

(a) (b)

**Figure 2.** (a) Two addition patterns of C*X*2. (b) Open and closed structures of C60C*X*2.

of C60H*<sup>n</sup>* (*n* = 2, 4, and 6). From these discussions, guidelines for effective design of

• The values of reorganization energies of both hole transport and electron transport are almost independent of the type (chemical nature) of addition group *X*, but are strongly dependent on the position and the number of addition groups [15]. Therefore, reorganization energies of other types of C60*X*<sup>2</sup> will be approximately estimated from the

• 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 [13–15]. Delocalized orbitals give high carrier mobility (small reorganization energy) and localized molecular orbitals produce a low carrier mobility

• There is a clear linear relationship between the reorganization energy and the geometrical

These results will also be applied to other types of *X*, and give us a guideline for efficient design of novel materials based on C60 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 C60*X*<sup>2</sup> can be

In another of our publications [12], the effect of methylene bridging of C60 by –C*X*<sup>2</sup> (*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 C60C*X*2, **I** and **II** (Figure 2). Systematic

simplified to C60H2 in the prediction and discussion of these properties.

• Carrier-transport properties of C60*X*<sup>2</sup> are quite different from those of C60 [13–15, 18]. • Chemical addition can improve hole mobility of C60 for some isomers [13, 14, 18]. Conversely, electron mobility of C60 is not influenced or is decreased by the chemical

X2C X2C

carrier-transport materials were proposed:

addition [15].

results of C60H2 [15].

(large reorganization energy).

relaxation upon carrier injection.

**1.3. Our previous publication: C**60**C***X*<sup>2</sup>

**I II**

**Figure 1.** Fullerene C60 and some examples of C60 derivatives.

that the addition of hydrogen to C60 would result in a considerable modification of the C60 materials. This possibility originates from the fact that C60 has an electronic degeneracy in its cationic state because of its high symmetry *Ih* [21, 22], but C60 hydrides usually do not because of the reduction in symmetry by the addition of hydrogen. Electron mobility in C60 film is about 1 cm2V−1s−<sup>1</sup> [20, 23, 24] so that C60 is one of the most useful electron-transport materials. However, to achieve low-cost production and large-area devices, it is necessary for C60 materials to have a solution-processable form, such as [6,6]-phenyl C61-butyric acid methyl ester (PCBM) [25]. Therefore, in organic electronics, the electronic properties of C60 derivatives rather than those of the original C60 are of much interest and importance.

Although ambipolar transport in [6,6]-phenyl-C71-butyric acid methyl ester ([70]PCBM) was reported recently, its hole mobility (2×10−<sup>5</sup> cm2V−1s−1) is much smaller than its electron mobility (2×10−<sup>3</sup> cm2V−1s−1) [26]. Therefore, the enhancement of hole mobility is necessary for the practical use of fullerene derivatives as ambipolar transistor materials. Very recently, conduction-type control of fullerene C60 films from *n*- to *p*-type by doping with molybdenum(VI) oxide (MoO3) was demonstrated [27]. Thus, analysis of the hole-transport properties of C60 derivatives is very important for the practical use of C60 materials.

### **1.2. Our previous publication: C**60*Xn* **(***n* **= 2, 4, and 6)**

In our previous publication [11], the effect on carrier-transport properties of chemical addition of *X* (*X*=H, R, R-COOH, and R-SH, where R is an alkyl chain) to C60 was systematically discussed from the viewpoint of reorganization energy (*λ*) using Marcus theory [28]. We focused on the C60 derivatives of type (a) in Figure 1, C60*Xn*, where *X* is the added group and *n* is the number of added *X*. There are many isomers for C60*Xn*, 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 C60*X*2. The dependence of carrier-transport properties on the number of added groups was discussed from the results

**Figure 2.** (a) Two addition patterns of C*X*2. (b) Open and closed structures of C60C*X*2.

(a)

(b)

Addition

**Figure 1.** Fullerene C60 and some examples of C60 derivatives.

X X

C60

Addition

C60X<sup>n</sup>

X X X X

X X

C60 derivatives

that the addition of hydrogen to C60 would result in a considerable modification of the C60 materials. This possibility originates from the fact that C60 has an electronic degeneracy in its cationic state because of its high symmetry *Ih* [21, 22], but C60 hydrides usually do not because of the reduction in symmetry by the addition of hydrogen. Electron mobility in C60 film is about 1 cm2V−1s−<sup>1</sup> [20, 23, 24] so that C60 is one of the most useful electron-transport materials. However, to achieve low-cost production and large-area devices, it is necessary for C60 materials to have a solution-processable form, such as [6,6]-phenyl C61-butyric acid methyl ester (PCBM) [25]. Therefore, in organic electronics, the electronic properties of C60

derivatives rather than those of the original C60 are of much interest and importance.

properties of C60 derivatives is very important for the practical use of C60 materials.

**1.2. Our previous publication: C**60*Xn* **(***n* **= 2, 4, and 6)**

Although ambipolar transport in [6,6]-phenyl-C71-butyric acid methyl ester ([70]PCBM) was reported recently, its hole mobility (2×10−<sup>5</sup> cm2V−1s−1) is much smaller than its electron mobility (2×10−<sup>3</sup> cm2V−1s−1) [26]. Therefore, the enhancement of hole mobility is necessary for the practical use of fullerene derivatives as ambipolar transistor materials. Very recently, conduction-type control of fullerene C60 films from *n*- to *p*-type by doping with molybdenum(VI) oxide (MoO3) was demonstrated [27]. Thus, analysis of the hole-transport

In our previous publication [11], the effect on carrier-transport properties of chemical addition of *X* (*X*=H, R, R-COOH, and R-SH, where R is an alkyl chain) to C60 was systematically discussed from the viewpoint of reorganization energy (*λ*) using Marcus theory [28]. We focused on the C60 derivatives of type (a) in Figure 1, C60*Xn*, where *X* is the added group and *n* is the number of added *X*. There are many isomers for C60*Xn*, 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 C60*X*2. The dependence of carrier-transport properties on the number of added groups was discussed from the results

C60

of C60H*<sup>n</sup>* (*n* = 2, 4, and 6). From these discussions, guidelines for effective design of carrier-transport materials were proposed:


These results will also be applied to other types of *X*, and give us a guideline for efficient design of novel materials based on C60 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 C60*X*<sup>2</sup> can be simplified to C60H2 in the prediction and discussion of these properties.

### **1.3. Our previous publication: C**60**C***X*<sup>2</sup>

In another of our publications [12], the effect of methylene bridging of C60 by –C*X*<sup>2</sup> (*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 C60C*X*2, **I** and **II** (Figure 2). Systematic

#### 4 Hydrogenation 312 Hydrogenation Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation <sup>5</sup>

analyses of reorganization energies of methylene-bridged fullerenes C60C*X*<sup>2</sup> give us very important knowledge for the efficient design of useful C60 materials:

• Hole mobility of C60 is strongly influenced by methylene bridging. C60CBr2 (**II**) has the smallest reorganization energy (93 meV). On the other hand, C60C*X*<sup>2</sup> (**I**) isomers with R, R-COOH, and R-SH chains have very large reorganization energies of about 500 meV.

λ

+

Reaction Coordinate

−→ <sup>M</sup>(A)··· <sup>M</sup>+(B). (1)

Initial Final

M+(A) … M(B) M(A) … M+(B)

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 313

C60 or C60H<sup>n</sup>

C60 (C60Hn) solid

=

semiconductors are proposed in Section 7.

**2. Hole-transport mechanism**

**2.1. Hopping mechanism**

0.1 cm2V−1s−1.

+

**Figure 3.** Schematic reaction diagram of a hole-transfer reaction M+(A) ··· M(B) <sup>→</sup> M(A) ··· <sup>M</sup>+(B).

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 C60H*<sup>n</sup>*

The hole mobility of single-crystal C60 is around 10−<sup>5</sup> cm2V−1s−<sup>1</sup> at a maximum. Materials having a mobility of 0.1−1 cm2V−1s−<sup>1</sup> are categorized in the boundary region between the hopping and the band-transport mechanisms [29–31]. Therefore, in this chapter, only the hopping mechanism is considered because the hole mobility of C60 is much smaller than

A schematic picture of hole hopping in an organic solid is shown in Figure 3. C60 and C60H*<sup>n</sup>* 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. The initial and final states of a hole-transfer reaction are represented as M+(A)··· <sup>M</sup>(B) and <sup>M</sup>(A)··· <sup>M</sup>+(B). The system is fluctuating around the bottom of the potential curve as a result of molecular vibrations in its initial state. When the system occasionally reaches the transition state at which energies of the initial state and the final state are the same, the system jumps from the initial state to the final state with a rate constant *k*. This reaction is written as

<sup>M</sup>+(A)··· <sup>M</sup>(B) *<sup>k</sup>*

Energy

k


One of the important findings in this work is that the properties of C60C*X*<sup>2</sup> are dependent on the type (chemical nature) of *X*. This is because C*X*<sup>2</sup> 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 C60C*X*<sup>2</sup> 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, C60*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 C60C*X*2, which includes an alkyl chain with -CH3 and -COOH terminals, should be avoided.

### **1.4. This chapter**

In this chapter, the effect of further hydrogenation of C60 on hole-transport properties is systematically discussed from the viewpoint of reorganization energy. We again focus on the C60 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 C60H*<sup>n</sup>* (*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 C60 are reviewed in Section 3. Structures of hydrogenated C60 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

**Figure 3.** Schematic reaction diagram of a hole-transfer reaction M+(A) ··· M(B) <sup>→</sup> M(A) ··· <sup>M</sup>+(B).

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 C60H*<sup>n</sup>* semiconductors are proposed in Section 7.

### **2. Hole-transport mechanism**

#### **2.1. Hopping mechanism**

4 Hydrogenation

analyses of reorganization energies of methylene-bridged fullerenes C60C*X*<sup>2</sup> give us very

• Hole mobility of C60 is strongly influenced by methylene bridging. C60CBr2 (**II**) has the smallest reorganization energy (93 meV). On the other hand, C60C*X*<sup>2</sup> (**I**) isomers with R, R-COOH, and R-SH chains have very large reorganization energies of about 500 meV. • Electron mobility of C60 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 C60C*X*<sup>2</sup> will not be easily predicted from the results of C60CH2. This result is quite different from the case of C60H2 and C60*X*2. • There is a clear linear relationship between the reorganization energy and the change in

• 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

One of the important findings in this work is that the properties of C60C*X*<sup>2</sup> are dependent on the type (chemical nature) of *X*. This is because C*X*<sup>2</sup> 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 C60C*X*<sup>2</sup> 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

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 C60C*X*2, which includes an alkyl chain with -CH3 and -COOH terminals, should be avoided.

In this chapter, the effect of further hydrogenation of C60 on hole-transport properties is systematically discussed from the viewpoint of reorganization energy. We again focus on the C60 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 C60H*<sup>n</sup>* (*n* = 2, 4, 6, 8, 52, 54, 56, 58, and 60). From these discussions, guidelines for the effective design of

This chapter is organized as follows: In Section 2, the definition of *λ* and computational details of *λ* are presented. Synthesis methods of hydrogenated C60 are reviewed in Section 3. Structures of hydrogenated C60 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

high-performance carrier-transport materials of type (a) are proposed.

important knowledge for the efficient design of useful C60 materials:

the distance between bridged C··· C atoms.

carbon atoms.

**1.4. This chapter**

design of type (a) molecules, C60*X*2.

The hole mobility of single-crystal C60 is around 10−<sup>5</sup> cm2V−1s−<sup>1</sup> at a maximum. Materials having a mobility of 0.1−1 cm2V−1s−<sup>1</sup> are categorized in the boundary region between the hopping and the band-transport mechanisms [29–31]. Therefore, in this chapter, only the hopping mechanism is considered because the hole mobility of C60 is much smaller than 0.1 cm2V−1s−1.

A schematic picture of hole hopping in an organic solid is shown in Figure 3. C60 and C60H*<sup>n</sup>* 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. The initial and final states of a hole-transfer reaction are represented as M+(A)··· <sup>M</sup>(B) and <sup>M</sup>(A)··· <sup>M</sup>+(B). The system is fluctuating around the bottom of the potential curve as a result of molecular vibrations in its initial state. When the system occasionally reaches the transition state at which energies of the initial state and the final state are the same, the system jumps from the initial state to the final state with a rate constant *k*. This reaction is written as

$$\mathbf{M}^+(\mathbf{A})\cdot\cdots\mathbf{M}(\mathbf{B}) \stackrel{k}{\longrightarrow} \mathbf{M}(\mathbf{A})\cdot\cdots\mathbf{M}^+(\mathbf{B}).\tag{1}$$

**Figure 4.** Schematic potential energy surfaces of molecules related to the hole-transfer reaction. *Q*<sup>0</sup> and *Q*<sup>+</sup> 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:

$$k = \frac{4\pi^2}{h} \frac{H^2}{\sqrt{4\pi\lambda k\_\text{B}T}} \exp\left(-\frac{\lambda}{4k\_\text{B}T}\right),\tag{2}$$

where *λ*<sup>+</sup>

estimated from

**2.3. Rate constant**

the rate constants *k*h. Instead, we define *k*�

C60H*<sup>n</sup>* h *k* C60 h

 *H*C60H*<sup>n</sup>* h *H*C60 h

<sup>2</sup> · *λ*C60 h *λ*C60H*<sup>n</sup>* h

<sup>h</sup> <sup>≈</sup> *<sup>H</sup>*C60

· exp

<sup>h</sup> are usually calculated using Equation 6 in this chapter.

<sup>−</sup> *<sup>λ</sup>*C60H*<sup>n</sup>*

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

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, C60H2, C60H4, and C60H6, 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

*k*� <sup>h</sup> <sup>=</sup> *<sup>k</sup>*

=

≈ *λ*C60 h *λ*C60H*<sup>n</sup>* h

C60 at *T* = 300 K. The values of *k*�

on the supposition that *H*C60H*<sup>n</sup>*

the GAUSSIAN 03 [34] program package.

**3. Hydrogenation of fullerene**

values of *k*�

<sup>h</sup> and *<sup>λ</sup>*<sup>0</sup>

<sup>h</sup> are relaxation energies in the cationic and neutral states, respectively,

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 315

<sup>+</sup>, (4)

<sup>0</sup>. (5)

<sup>h</sup> as a ratio of the rate constant of C60H*<sup>n</sup>* to that of

<sup>0</sup> <sup>−</sup> *<sup>E</sup>*<sup>+</sup>

<sup>+</sup> <sup>−</sup> *<sup>E</sup>*<sup>0</sup>

<sup>h</sup> for hole transport are calculated as

· exp

<sup>h</sup> <sup>−</sup> *<sup>λ</sup>*C60 h

4*k*B*T*

<sup>h</sup> . Hereafter, we regard *k*�

<sup>−</sup> *<sup>λ</sup>*C60H*<sup>n</sup>*

<sup>h</sup> <sup>−</sup> *<sup>λ</sup>*C60 h

<sup>h</sup> as the hole mobility. The

(6)

4*k*B*T*

In this chapter, the calculation and analysis of *λ*<sup>h</sup> 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*<sup>h</sup> are dependent on both the distance and the relative orientation between the two molecules. Therefore, *H*<sup>h</sup> is assumed to be the same for C60 and all C60H*<sup>n</sup>* for ease of discussion in this work [33]. Therefore, we cannot know the numerical values of

*λ*+ <sup>h</sup> <sup>=</sup> *<sup>E</sup>*<sup>+</sup>

*λ*0 <sup>h</sup> <sup>=</sup> *<sup>E</sup>*<sup>0</sup>

where *k*<sup>B</sup> is the Boltzmann constant, *h* is the Planck constant, and *T* is the temperature of the system. We can see that a small *λ*, large *H*, and high temperature *T* result in a fast hole hopping.

#### **2.2. 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 C60 and C60H*<sup>n</sup>* were fully optimized, giving a nuclear coordinate *Q*<sup>0</sup> and energy *E*0 <sup>0</sup>. At *<sup>Q</sup>*0, single-point energy calculations of cations give *<sup>E</sup>*<sup>+</sup> <sup>0</sup> . Next, the structures were fully optimized in their cationic states, giving *Q*<sup>+</sup> and *E*<sup>+</sup> <sup>+</sup>. Single-point energy calculations of the neutral states with geometry *Q*<sup>+</sup> give *E*<sup>0</sup> <sup>+</sup>. The reorganization energy of the hole-transfer reaction (*λ*h) is defined as the sum of *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> and *<sup>λ</sup>*<sup>0</sup> h:

$$
\lambda\_{\mathbf{h}} = \lambda\_{\mathbf{h}}^{+} + \lambda\_{\mathbf{h}'}^{0} \tag{3}
$$

where *λ*<sup>+</sup> <sup>h</sup> and *<sup>λ</sup>*<sup>0</sup> <sup>h</sup> are relaxation energies in the cationic and neutral states, respectively, estimated from

$$
\lambda\_{\mathbf{h}}^{+} = E\_{\mathbf{0}}^{+} - E\_{+\prime}^{+} \tag{4}
$$

$$
\lambda\_\mathbf{h}^0 = E\_+^0 - E\_0^0. \tag{5}
$$

#### **2.3. Rate constant**

6 Hydrogenation

Energy

on the right-hand side of *E* mean the charge on the molecule.

*<sup>k</sup>* <sup>=</sup> <sup>4</sup>*π*<sup>2</sup> *h*

<sup>0</sup>. At *<sup>Q</sup>*0, single-point energy calculations of cations give *<sup>E</sup>*<sup>+</sup>

fully optimized in their cationic states, giving *Q*<sup>+</sup> and *E*<sup>+</sup>

the neutral states with geometry *Q*<sup>+</sup> give *E*<sup>0</sup>

reaction (*λ*h) is defined as the sum of *<sup>λ</sup>*<sup>+</sup>

element (*H*) between adjacent molecules:

**2.2. Reorganization energy**

hopping.

*E*0

Nuclear Coordinate (Q)

 <sup>−</sup> *<sup>λ</sup>* 4*k*B*T* , (2)

<sup>0</sup> . Next, the structures were

<sup>+</sup>. Single-point energy calculations of

<sup>h</sup>, (3)

<sup>+</sup>. The reorganization energy of the hole-transfer

**Figure 4.** Schematic potential energy surfaces of molecules related to the hole-transfer reaction. *Q*<sup>0</sup> and *Q*<sup>+</sup> 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

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

where *k*<sup>B</sup> is the Boltzmann constant, *h* is the Planck constant, and *T* is the temperature of the system. We can see that a small *λ*, large *H*, and high temperature *T* result in a fast hole

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 C60 and C60H*<sup>n</sup>* were fully optimized, giving a nuclear coordinate *Q*<sup>0</sup> and energy

> <sup>h</sup> and *<sup>λ</sup>*<sup>0</sup> h:

*<sup>λ</sup>*<sup>h</sup> = *<sup>λ</sup>*<sup>+</sup>

<sup>h</sup> <sup>+</sup> *<sup>λ</sup>*<sup>0</sup>

*H*<sup>2</sup> <sup>√</sup>4*πλk*B*<sup>T</sup>* exp

Q<sup>0</sup> Q<sup>+</sup>

M(A)

M(B) <sup>E</sup><sup>0</sup>

M+(A)

M <sup>+</sup> +(B)

+h -h

λh

λ h 0

0

E+ 0

E0 +

E+ +

> In this chapter, the calculation and analysis of *λ*<sup>h</sup> 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*<sup>h</sup> are dependent on both the distance and the relative orientation between the two molecules. Therefore, *H*<sup>h</sup> is assumed to be the same for C60 and all C60H*<sup>n</sup>* 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*� <sup>h</sup> as a ratio of the rate constant of C60H*<sup>n</sup>* to that of C60 at *T* = 300 K. The values of *k*� <sup>h</sup> for hole transport are calculated as

$$\begin{split} \mathbf{k}'\_{\mathbf{h}} &= \frac{\mathbf{k}^{\mathbf{C\_{60}} \mathbf{H}\_{\mathbf{h}}}}{k\_{\mathbf{h}}^{\mathbf{C\_{60}}}} \\ &= \left(\frac{H\_{\mathbf{h}}^{\mathbf{C\_{60}} \mathbf{H}\_{\mathbf{h}}}}{H\_{\mathbf{h}}^{\mathbf{C\_{60}}}}\right)^{2} \cdot \sqrt{\frac{\lambda\_{\mathbf{h}}^{\mathbf{C\_{60}}}}{\lambda\_{\mathbf{h}}^{\mathbf{C\_{60}} \mathbf{H}\_{\mathbf{h}}}}} \cdot \exp\left(-\frac{\lambda\_{\mathbf{h}}^{\mathbf{C\_{60}} \mathbf{H}\_{\mathbf{h}}} - \lambda\_{\mathbf{h}}^{\mathbf{C\_{60}}}}{4k\_{\mathbf{B}}T}\right) \\ &\approx \sqrt{\frac{\lambda\_{\mathbf{h}}^{\mathbf{C\_{60}}}}{\lambda\_{\mathbf{h}}^{\mathbf{C\_{60}} \mathbf{H}\_{\mathbf{h}}}}} \cdot \exp\left(-\frac{\lambda\_{\mathbf{h}}^{\mathbf{C\_{60}} \mathbf{H}\_{\mathbf{h}}} - \lambda\_{\mathbf{h}}^{\mathbf{C\_{60}}}}{4k\_{\mathbf{B}}T}\right) \end{split} \tag{6}$$

on the supposition that *H*C60H*<sup>n</sup>* <sup>h</sup> <sup>≈</sup> *<sup>H</sup>*C60 <sup>h</sup> . Hereafter, we regard *k*� <sup>h</sup> as the hole mobility. The values of *k*� <sup>h</sup> are usually calculated using Equation 6 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.

#### **3. 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, C60H2, C60H4, and C60H6, 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 reduction with 10-methyl-9,10-dihydroacridine [43, 44], and ultrasonic irradiation in decahydronaphthalene [45]. In many cases, a mixture of C60, C60H2, and C60H*<sup>n</sup>* (*n >* 2) is obtained [46]. Birch reduction [47] and transfer hydrogenation [48] of C60 produce C60H18 and C60H36. In the ruthenium-catalyzed hydrogenation, other types of C60H*<sup>n</sup>* (*n* = 10, 12, 34, 36, 38, and 40) were observed using a field-desorption (FD) mass spectrometer [49]. Direct hydrogenation of C60 was achieved without the use of a catalyst by exposing solid-phase fullerenes to high-pressure hydrogen gas, and many types of C60H*<sup>n</sup>* (*n* = 2−18) were identified by laser-desorption Fourier-transform mass spectrometry [50]. Unfortunately, highly hydrogenated fullerenes discussed in this chapter, C60H52 − C60H60, have not been synthesized.

(a) C60H2 (b) C60H4

 

H

 

   

> 

> > (d) C60H8

H

H

H H H H

> 

 

 

<sup>60</sup>. The most

<sup>h</sup> is much

<sup>h</sup> is 95 meV in our

 

 

 

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 317

H H

H H H H

> 

<sup>60</sup> was calculated as having *<sup>D</sup>*5*<sup>d</sup>* symmetry, and its *<sup>λ</sup>*<sup>+</sup>

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.

**Figure 5.** Isomers of (a) C60H2, (b) C60H4, (c) C60H6 (2 figures), and (d) C60H8. Hydrogen atoms are bonded to the labeled carbon atoms. Figures (a), (b), (c), and (d) also correspond to isomers of C60H58,

so that symmetry lowering because of the Jahn–Teller effect [21] stabilizes C<sup>+</sup>

energy of the hole transport, *<sup>λ</sup>*h, is 169 meV. It should be noted that the value of *<sup>λ</sup>*<sup>+</sup>

 

<sup>60</sup> has been investigated both experimentally and theoretically

<sup>h</sup> is qualitatively consistent with previous works based on the static

<sup>h</sup>. This result comes from the fact that geometrical relaxation in the ionic

<sup>60</sup>(*D*5*d*) was calculated as 74 meV. Thus, the reorganization

<sup>60</sup> has an *Hu* degenerate electronic state

<sup>h</sup> were calculated as 351 [60], 35 [61], and

(c) C60H6

 

**5.1. C**<sup>60</sup>

 

 

C60H56, C60H54, and C60H52, respectively.

The electronic structure of C<sup>+</sup>

stable structure of C<sup>+</sup>

larger than that of *λ*<sup>0</sup>

calculation. The result of *λ*<sup>+</sup>

71 meV [62]. The value of *λ*<sup>0</sup>

**5. Reorganization energies and rate constants**

because of its electronic degeneracy [58, 59]. C<sup>+</sup>

Jahn–Teller effect [60–62] in which the values of *λ*<sup>+</sup>

<sup>h</sup> of C<sup>+</sup>

 

H H H H

 

 

### **4. Isomers of hydrogenated fullerenes**

### **4.1. Low hydrogenation: C**60**H**<sup>2</sup> − **C**60**H**<sup>8</sup>

There are 23 isomers for C60H2 [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 C60H2 is already shown in the figure. The second hydrogen atom is added to one of the carbon atoms labeled 1–11. These isomers are named **1**–**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].

Although there are a total of 4190 isomers for C60H4 [53], we consider eight isomers originating from two H2 additions to [6,6]-ring fusions (see Figure 5 (b)) [54]. In other words, these isomers result from 1,2-addition to C60H2-**1**. In Figure 5 (b), the second H2 pair is added to one of the carbon atom pairs labeled 1–8 and these isomers are named **1**–**8**. Experimentally, some of the eight isomers have been synthesized, and four isomers (**1**, **4**, **6**, and **8**) among them were identified [36, 39–41, 55–57].

Among a total of 418470 isomers of C60H6 [53], we consider only 16 isomers in Figure 5 (c) originating from one H2 addition to C60H4-**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 C60H8 in Figure 5 (d) originating from H2 addition to C60H6-**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**.

### **4.2. High hydrogenation: C**60**H**<sup>52</sup> − **C**60**H**<sup>60</sup>

As highly hydrogenated fullerenes, we consider C60H52, C60H54, C60H56, C60H58, and C60H60. C60H60 has *Ih* symmetry. We consider 11, 8, 16, and 6 isomers for C60H58, C60H56, C60H54, and C60H52, respectively. For these highly hydrogenated isomers, hydrogenated carbon atoms in Figure 5 are to be considered the nonhydrogenated carbon atoms.

**Figure 5.** Isomers of (a) C60H2, (b) C60H4, (c) C60H6 (2 figures), and (d) C60H8. Hydrogen atoms are bonded to the labeled carbon atoms. Figures (a), (b), (c), and (d) also correspond to isomers of C60H58, C60H56, C60H54, and C60H52, respectively.

### **5. Reorganization energies and rate constants**

#### **5.1. C**<sup>60</sup>

8 Hydrogenation

reduction with 10-methyl-9,10-dihydroacridine [43, 44], and ultrasonic irradiation in decahydronaphthalene [45]. In many cases, a mixture of C60, C60H2, and C60H*<sup>n</sup>* (*n >* 2) is obtained [46]. Birch reduction [47] and transfer hydrogenation [48] of C60 produce C60H18 and C60H36. In the ruthenium-catalyzed hydrogenation, other types of C60H*<sup>n</sup>* (*n* = 10, 12, 34, 36, 38, and 40) were observed using a field-desorption (FD) mass spectrometer [49]. Direct hydrogenation of C60 was achieved without the use of a catalyst by exposing solid-phase fullerenes to high-pressure hydrogen gas, and many types of C60H*<sup>n</sup>* (*n* = 2−18) were identified by laser-desorption Fourier-transform mass spectrometry [50]. Unfortunately, highly hydrogenated fullerenes discussed in this chapter, C60H52 − C60H60, have not been

There are 23 isomers for C60H2 [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 C60H2 is already shown in the figure. The second hydrogen atom is added to one of the carbon atoms labeled 1–11. These isomers are named **1**–**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

Although there are a total of 4190 isomers for C60H4 [53], we consider eight isomers originating from two H2 additions to [6,6]-ring fusions (see Figure 5 (b)) [54]. In other words, these isomers result from 1,2-addition to C60H2-**1**. In Figure 5 (b), the second H2 pair is added to one of the carbon atom pairs labeled 1–8 and these isomers are named **1**–**8**. Experimentally, some of the eight isomers have been synthesized, and four isomers (**1**, **4**, **6**, and **8**) among them

Among a total of 418470 isomers of C60H6 [53], we consider only 16 isomers in Figure 5 (c) originating from one H2 addition to C60H4-**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 C60H8 in Figure 5 (d) originating from H2 addition to C60H6-**1** at a [6,6]-ring fusion. One hydrogen pair is added to one of the carbon atom pairs labeled 1–6

As highly hydrogenated fullerenes, we consider C60H52, C60H54, C60H56, C60H58, and C60H60. C60H60 has *Ih* symmetry. We consider 11, 8, 16, and 6 isomers for C60H58, C60H56, C60H54, and C60H52, respectively. For these highly hydrogenated isomers, hydrogenated carbon atoms in

synthesized.

methods [52].

were identified [36, 39–41, 55–57].

and these isomers are named **1**–**6**.

**4.2. High hydrogenation: C**60**H**<sup>52</sup> − **C**60**H**<sup>60</sup>

Figure 5 are to be considered the nonhydrogenated carbon atoms.

**4. Isomers of hydrogenated fullerenes**

**4.1. Low hydrogenation: C**60**H**<sup>2</sup> − **C**60**H**<sup>8</sup>

The electronic structure of C<sup>+</sup> <sup>60</sup> has been investigated both experimentally and theoretically because of its electronic degeneracy [58, 59]. C<sup>+</sup> <sup>60</sup> has an *Hu* degenerate electronic state so that symmetry lowering because of the Jahn–Teller effect [21] stabilizes C<sup>+</sup> <sup>60</sup>. The most stable structure of C<sup>+</sup> <sup>60</sup> was calculated as having *<sup>D</sup>*5*<sup>d</sup>* symmetry, and its *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> is 95 meV in our calculation. The result of *λ*<sup>+</sup> <sup>h</sup> is qualitatively consistent with previous works based on the static Jahn–Teller effect [60–62] in which the values of *λ*<sup>+</sup> <sup>h</sup> were calculated as 351 [60], 35 [61], and 71 meV [62]. The value of *λ*<sup>0</sup> <sup>h</sup> of C<sup>+</sup> <sup>60</sup>(*D*5*d*) was calculated as 74 meV. Thus, the reorganization energy of the hole transport, *<sup>λ</sup>*h, is 169 meV. It should be noted that the value of *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> is much larger than that of *λ*<sup>0</sup> <sup>h</sup>. 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.

### **5.2. C**60**H**<sup>2</sup> **– C**60**H**<sup>8</sup>

On average, *λ*<sup>+</sup> <sup>h</sup> of C60H2 is 84 meV, which is smaller than that of C60 by 11 meV and *<sup>λ</sup>*<sup>0</sup> <sup>h</sup> of C60H2 is 90 meV, which is larger than that of C60 by 16 meV [12, 13]. The average value of *λ*<sup>h</sup> of C60H2 (174 meV) is almost as large as that of C60 (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 C60H2 (**1**, **4**, **5**, **6**, **8**, and **9**) have a smaller *λ*<sup>h</sup> than C60. In particular, isomer **6** has the smallest *λ*<sup>h</sup> (101 meV), which is over 40% less than that of C60. In addition, the *k* <sup>h</sup> of **6** is about 2.5 times as large as that of C60. From the viewpoint of practical use, it should be noted that the values of *λ*<sup>h</sup> for the two synthesized isomers, **1** and **5**, are 133 and 142 meV, respectively, which are about 20% smaller than that of C60. The values of *k* <sup>h</sup> for these isomers are about 1.5 times as large as that of C60. These results indicate that hydrogenation can be an effective method for modifying the hole-transport properties of C60. Two synthesized isomers of C60H2, **1** and **5**, have potential utility as hole-transport materials. For almost all isomers of C60H2, *λ*<sup>+</sup> <sup>h</sup> is almost equal to *λ*<sup>0</sup> <sup>h</sup>. 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 C60.

C60H8 *λ*<sup>+</sup>

**Table 1.** Reorganization energies (*λ*<sup>h</sup> in meV) and rate constants (*k*

**Table 2.** Reorganization energies (*λ*<sup>h</sup> in meV) and rate constants (*k*

176 meV, which is much larger than that of C60 by 81 meV, and *λ*<sup>0</sup>

140 meV, which is much larger than that of C60 by 45 meV, and *λ*<sup>0</sup>

average value over six C60H52 isomers is also shown.

and there is not so large a difference.

much larger than that of C60 by 27 meV, and *λ*<sup>0</sup>

as that of C60.

*λ*<sup>h</sup> and *k*

**5.3. C**60**H**<sup>52</sup> **– C**60**H**<sup>58</sup>

has *λ*<sup>h</sup> as large as C60.

Values of *λ*<sup>h</sup> and *k*

Values of *λ*<sup>h</sup> and *k*

as that of C60. Isomer **6** with the second smallest *λ*<sup>h</sup> has a value of *k*

<sup>h</sup> of C60H52 are shown in Table 2. On average, *<sup>λ</sup>*<sup>+</sup>

for the original C60 and an averaged value over the six C60H8 isomers are also shown.

<sup>h</sup> *<sup>λ</sup>*<sup>0</sup>

than that of C60 by 58 meV. The average value of *λ*<sup>h</sup> of C60H52 (254 meV) is much larger than that of C60 (169 meV). Hydrogenation leads to a large difference in *λ*h, 175–441 meV. Isomer **6**

<sup>h</sup> *<sup>λ</sup>*<sup>0</sup>

 163 174 337 0.14 204 237 441 0.04 100 104 204 0.65 86 94 180 0.87 92 96 188 0.78 86 89 175 0.92 Average 122 132 254 0.36

<sup>h</sup> for C60H54 isomers are shown in Table 3. On average, *<sup>λ</sup>*<sup>+</sup>

<sup>h</sup> for C60H56 isomers are shown in Table 4. On average, *<sup>λ</sup>*<sup>+</sup>

is much larger than that of C60 by 107 meV. The average value of *λ*<sup>h</sup> of C60H54 (357 meV) is much larger than that of C60. It is interesting that the values of *λ*<sup>h</sup> are in the range 254–397 meV

is much larger than that of C60 by 80 meV. The average value of *λ*<sup>h</sup> for C60H56 (294 meV) is

<sup>h</sup> *λ*<sup>h</sup> *k* h

C60H52 *λ*<sup>+</sup>

<sup>h</sup> *λ*<sup>h</sup> *k* h

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 319

<sup>h</sup>) for hole transport in C60H8. Values

<sup>h</sup> of C60H52 is 122 meV, which is

<sup>h</sup>) for hole transport in C60H52. The

<sup>h</sup> of C60H54 is 181 meV, which

<sup>h</sup> of C60H56 is 154 meV, which

<sup>h</sup> of C60H54 is

<sup>h</sup> of C60H56 is

<sup>h</sup> of C60H52 is 132 meV, which is much larger

<sup>h</sup> that is 3.23 times as large

On average, *λ*<sup>+</sup> <sup>h</sup> of C60H4 is 65 meV, which is smaller than that of C60 by 30 meV and *<sup>λ</sup>*<sup>0</sup> <sup>h</sup> of C60H4 is 68 meV, which is smaller than that of C60 by 6 meV [12, 14]. The average value of *λ*<sup>h</sup> of C60H4 (134 meV) is much smaller than that of C60 (169 meV) and is almost as large as that of C60H2-**1** (133 meV). The addition of two H atoms to C60H2-**1** results in the large difference in *λ*h, 83–183 meV. Seven isomers of C60H4 (**1**, **3**, **4**, **5**, **6**, **7**, and **8**) have smaller *λ*<sup>h</sup> than C60. Remarkably, the major product **1** has the smallest *λ*<sup>h</sup> (83 meV), which is over 50% less than that of C60. In addition, *k* <sup>h</sup> of **1** is 3.28 times as large as that of C60, and more than twice as large as that of the synthesized C60H2-**1** [13]. Isomer **7** with the second smallest *λ*<sup>h</sup> has a value for *k* <sup>h</sup> that is 2.83 times as large as that of C60. Other identified isomers **4**, **6**, and **8** also have small *λ*<sup>h</sup> (138, 150, and 126 meV, respectively), and *k* <sup>h</sup> of these isomers are respectively 1.49, 1.26, and 1.74 times larger than that of C60. Synthesized isomers of C60H4, especially the major product **1**, have potential utility as useful hole-transport materials.

On average, *λ*<sup>+</sup> <sup>h</sup> of C60H6 is 61 meV, which is much smaller than that of C60 by 34 meV and *<sup>λ</sup>*<sup>0</sup> h of C60H6 is 66 meV, which is smaller than that of C60 by 8 meV [12]. The average value of *λ*<sup>h</sup> for C60H6 (127 meV) is much smaller than that for C60 (169 meV); however, it is much larger than that for C60H4-**1** (83 meV). Further addition of two H atoms to C60H4-**1** leads to a large difference in *λ*h, 71–182 meV. 14 of the 16 isomers have smaller *λ*<sup>h</sup> than C60. Isomer **1** has the smallest *λ*<sup>h</sup> (71 meV), which is about 60% less than that of C60. In addition, *k* <sup>h</sup> of **1** is 3.94 times as large as that of C60. Isomer **4** with the second smallest *λ*<sup>h</sup> has a value of *k* <sup>h</sup> that is 3.22 times as large as that of C60.

*λ*<sup>h</sup> and *k* <sup>h</sup> of C60H8 are shown in Table 1. On average, *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> of C60H8 is 51 meV, which is much smaller than that of C60 by 44 meV, and *λ*<sup>0</sup> <sup>h</sup> of C60H8 is 62 meV, which is smaller than that of C60 by 12 meV. The average value of *λ*<sup>h</sup> for C60H8 (113 meV) is much smaller than that for C60 (169 meV); however, it is much larger than that for C60H6-**1** (71 meV). Further addition of two H atoms to C60H6-**1** leads to a large difference in *λ*h, 81–175 meV. Five of the six isomers have smaller *λ*<sup>h</sup> than C60. Isomer **5** has the smallest *λ*<sup>h</sup> (81 meV), and *k* <sup>h</sup> of **5** is 3.39 times as large


**Table 1.** Reorganization energies (*λ*<sup>h</sup> in meV) and rate constants (*k* <sup>h</sup>) for hole transport in C60H8. Values for the original C60 and an averaged value over the six C60H8 isomers are also shown.

as that of C60. Isomer **6** with the second smallest *λ*<sup>h</sup> has a value of *k* <sup>h</sup> that is 3.23 times as large as that of C60.

### **5.3. C**60**H**<sup>52</sup> **– C**60**H**<sup>58</sup>

10 Hydrogenation

C60H2 is 90 meV, which is larger than that of C60 by 16 meV [12, 13]. The average value of *λ*<sup>h</sup> of C60H2 (174 meV) is almost as large as that of C60 (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 C60H2 (**1**, **4**, **5**, **6**, **8**, and **9**) have a smaller *λ*<sup>h</sup> than C60. In particular, isomer **6** has the smallest

as large as that of C60. From the viewpoint of practical use, it should be noted that the values of *λ*<sup>h</sup> for the two synthesized isomers, **1** and **5**, are 133 and 142 meV, respectively, which are

large as that of C60. These results indicate that hydrogenation can be an effective method for modifying the hole-transport properties of C60. Two synthesized isomers of C60H2, **1** and **5**,

the same curvature around the minima because the hydrogenation removes the electronic

C60H4 is 68 meV, which is smaller than that of C60 by 6 meV [12, 14]. The average value of *λ*<sup>h</sup> of C60H4 (134 meV) is much smaller than that of C60 (169 meV) and is almost as large as that of C60H2-**1** (133 meV). The addition of two H atoms to C60H2-**1** results in the large difference in *λ*h, 83–183 meV. Seven isomers of C60H4 (**1**, **3**, **4**, **5**, **6**, **7**, and **8**) have smaller *λ*<sup>h</sup> than C60. Remarkably, the major product **1** has the smallest *λ*<sup>h</sup> (83 meV), which is over 50% less than

large as that of the synthesized C60H2-**1** [13]. Isomer **7** with the second smallest *λ*<sup>h</sup> has a value

1.26, and 1.74 times larger than that of C60. Synthesized isomers of C60H4, especially the major

of C60H6 is 66 meV, which is smaller than that of C60 by 8 meV [12]. The average value of *λ*<sup>h</sup> for C60H6 (127 meV) is much smaller than that for C60 (169 meV); however, it is much larger than that for C60H4-**1** (83 meV). Further addition of two H atoms to C60H4-**1** leads to a large difference in *λ*h, 71–182 meV. 14 of the 16 isomers have smaller *λ*<sup>h</sup> than C60. Isomer **1** has the

C60 by 12 meV. The average value of *λ*<sup>h</sup> for C60H8 (113 meV) is much smaller than that for C60 (169 meV); however, it is much larger than that for C60H6-**1** (71 meV). Further addition of two H atoms to C60H6-**1** leads to a large difference in *λ*h, 81–175 meV. Five of the six isomers have

<sup>h</sup> that is 2.83 times as large as that of C60. Other identified isomers **4**, **6**, and **8** also have

<sup>h</sup> of C60H6 is 61 meV, which is much smaller than that of C60 by 34 meV and *<sup>λ</sup>*<sup>0</sup>

<sup>h</sup>. This means that the potential curves of the ionic and neutral states have almost

<sup>h</sup> of C60H4 is 65 meV, which is smaller than that of C60 by 30 meV and *<sup>λ</sup>*<sup>0</sup>

<sup>h</sup> of **1** is 3.28 times as large as that of C60, and more than twice as

have potential utility as hole-transport materials. For almost all isomers of C60H2, *λ*<sup>+</sup>

*λ*<sup>h</sup> (101 meV), which is over 40% less than that of C60. In addition, the *k*

about 20% smaller than that of C60. The values of *k*

small *λ*<sup>h</sup> (138, 150, and 126 meV, respectively), and *k*

product **1**, have potential utility as useful hole-transport materials.

<sup>h</sup> of C60H8 are shown in Table 1. On average, *<sup>λ</sup>*<sup>+</sup>

smaller *λ*<sup>h</sup> than C60. Isomer **5** has the smallest *λ*<sup>h</sup> (81 meV), and *k*

smallest *λ*<sup>h</sup> (71 meV), which is about 60% less than that of C60. In addition, *k*

as large as that of C60. Isomer **4** with the second smallest *λ*<sup>h</sup> has a value of *k*

<sup>h</sup> of C60H2 is 84 meV, which is smaller than that of C60 by 11 meV and *<sup>λ</sup>*<sup>0</sup>

<sup>h</sup> of

<sup>h</sup> of **6** is about 2.5 times

<sup>h</sup> is almost

<sup>h</sup> of

h

<sup>h</sup> of **1** is 3.94 times

<sup>h</sup> that is 3.22 times

<sup>h</sup> for these isomers are about 1.5 times as

<sup>h</sup> of these isomers are respectively 1.49,

<sup>h</sup> of C60H8 is 51 meV, which is much

<sup>h</sup> of **5** is 3.39 times as large

<sup>h</sup> of C60H8 is 62 meV, which is smaller than that of

**5.2. C**60**H**<sup>2</sup> **– C**60**H**<sup>8</sup>

On average, *λ*<sup>+</sup>

equal to *λ*<sup>0</sup>

for *k*

On average, *λ*<sup>+</sup>

On average, *λ*<sup>+</sup>

as large as that of C60.

smaller than that of C60 by 44 meV, and *λ*<sup>0</sup>

*λ*<sup>h</sup> and *k*

degeneracy in ionic states of C60.

that of C60. In addition, *k*

*λ*<sup>h</sup> and *k* <sup>h</sup> of C60H52 are shown in Table 2. On average, *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> of C60H52 is 122 meV, which is much larger than that of C60 by 27 meV, and *λ*<sup>0</sup> <sup>h</sup> of C60H52 is 132 meV, which is much larger than that of C60 by 58 meV. The average value of *λ*<sup>h</sup> of C60H52 (254 meV) is much larger than that of C60 (169 meV). Hydrogenation leads to a large difference in *λ*h, 175–441 meV. Isomer **6** has *λ*<sup>h</sup> as large as C60.


**Table 2.** Reorganization energies (*λ*<sup>h</sup> in meV) and rate constants (*k* <sup>h</sup>) for hole transport in C60H52. The average value over six C60H52 isomers is also shown.

Values of *λ*<sup>h</sup> and *k* <sup>h</sup> for C60H54 isomers are shown in Table 3. On average, *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> of C60H54 is 176 meV, which is much larger than that of C60 by 81 meV, and *λ*<sup>0</sup> <sup>h</sup> of C60H54 is 181 meV, which is much larger than that of C60 by 107 meV. The average value of *λ*<sup>h</sup> of C60H54 (357 meV) is much larger than that of C60. It is interesting that the values of *λ*<sup>h</sup> are in the range 254–397 meV and there is not so large a difference.

Values of *λ*<sup>h</sup> and *k* <sup>h</sup> for C60H56 isomers are shown in Table 4. On average, *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> of C60H56 is 140 meV, which is much larger than that of C60 by 45 meV, and *λ*<sup>0</sup> <sup>h</sup> of C60H56 is 154 meV, which is much larger than that of C60 by 80 meV. The average value of *λ*<sup>h</sup> for C60H56 (294 meV) is


C60H58 *λ*<sup>+</sup>

**Table 5.** Reorganization energies (*λ*h) and rate constants (*k*�

(140 meV). Only C60H60 has a smaller *λ*<sup>h</sup> than C60.

value over 16 C60H58 isomers is also shown.

hole-transport materials.

**5.4. C**60**H**<sup>60</sup>

and its *λ*<sup>+</sup>

that of C60.

**5.5. Summary**

stabilizes C60H<sup>+</sup>

is much larger than *λ*<sup>0</sup>

C60H<sup>+</sup>

<sup>h</sup> *<sup>λ</sup>*<sup>0</sup>

These results mean that highly hydrogenated C60H52 − C60H58 are generally not suited for

degenerate electronic state, and symmetry lowering because of the Jahn–Teller effect [21]

40 meV. Thus, the reorganization energy for hole transport, *<sup>λ</sup>*h, is 140 meV. Similar to C60, *<sup>λ</sup>*<sup>+</sup>

Figure 6 shows minimum and average values of *λ<sup>h</sup>* for C60H*n*. C60 and C60H60 have only one isomer so that the minimum values are equal to the average values. From the systematic discussion through C60H*<sup>n</sup>* (*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*<sup>h</sup> decrease as the number of hydrogen atoms increases: C60 (169 meV) → C60H2-**6** (101 meV) → C60H4-**1** (83 meV) → C60H6-**1** (71 meV). However, *λ*<sup>h</sup> increases for C60H8-**5** (81 meV). The average values of *λ*<sup>h</sup> change as C60 (169 meV) → C60H2 (174 meV) → C60H4 (134 meV) → C60H6 (127 meV) → C60H8 (113 meV). The average *λ*<sup>h</sup> of C60H4 (134 meV) is almost as large as that of C60H2-**1** (133 meV), but the average *λ*<sup>h</sup> of C60H6 (127 meV) is much larger than that of C60H4-**1** (83 meV), and the average *λ*<sup>h</sup> of C60H8 (113 meV) is much larger than that of C60H6-**1** (71 meV). Highly hydrogenated C60H*<sup>n</sup>* generally has large *λ*h. The average *λ*<sup>h</sup> is C60H52 (254 meV), C60H54 (357 meV), C60H56 (294 meV), C60H58 (1074 meV), and C60H60

<sup>60</sup> has nine electrons in fivefold degenerate *hu* orbitals. Thus, C60H<sup>+</sup>

<sup>h</sup> because of the Jahn–Teller effect. *k*�

60. The most stable structure of C<sup>+</sup>

<sup>h</sup> is 101 meV in our calculation. The value of *<sup>λ</sup>*<sup>0</sup>

<sup>h</sup> *λ*<sup>h</sup> *k*�

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 321

h

<sup>h</sup>) for hole transport in C60H58. The average

<sup>60</sup> was calculated as having *D*3*<sup>d</sup>* symmetry,

<sup>h</sup> for C<sup>+</sup>

<sup>h</sup> of C60H<sup>+</sup>

<sup>60</sup> has an *Hu*

h

<sup>60</sup>(*D*3*d*) was calculated as

<sup>60</sup> is 1.44 times as large as

**Table 3.** Reorganization energies (*λ*<sup>h</sup> in meV) and rate constants (*k* <sup>h</sup>) for hole transport in C60H54. The average value over 16 C60H54 isomers is also shown.

much larger than that for C60. The values of *λ*<sup>h</sup> are in the range 230–501 meV. Isomer **2** has the largest *λ*<sup>h</sup> of more than 500 meV.


**Table 4.** Reorganization energies (*λ*h) and rate constants (*k* <sup>h</sup>) for hole transport in C60H56. The average value over eight C60H56 isomers is also shown.

*λ*<sup>h</sup> and *k* <sup>h</sup> of C60H58 are shown in Table 5. On average, *<sup>λ</sup>*<sup>+</sup> <sup>h</sup> of C60H58 is 606 meV, which is much larger than that of C60 by 511 meV and *λ*<sup>0</sup> <sup>h</sup> of C60H58 is 468 meV, which is much larger than that of C60 by 394 meV. The average value of *λ*<sup>h</sup> of C60H58 (1074 meV) is much larger than that of C60. It is interesting that the values of *λ*<sup>h</sup> are in the range 392–2411 meV. Isomers **1**, **2**, and **4** have smaller *λ*h.


**Table 5.** Reorganization energies (*λ*h) and rate constants (*k*� <sup>h</sup>) for hole transport in C60H58. The average value over 16 C60H58 isomers is also shown.

These results mean that highly hydrogenated C60H52 − C60H58 are generally not suited for hole-transport materials.

### **5.4. C**60**H**<sup>60</sup>

12 Hydrogenation

<sup>h</sup> *<sup>λ</sup>*<sup>0</sup>

much larger than that for C60. The values of *λ*<sup>h</sup> are in the range 230–501 meV. Isomer **2** has the

<sup>h</sup> *<sup>λ</sup>*<sup>0</sup>

than that of C60 by 394 meV. The average value of *λ*<sup>h</sup> of C60H58 (1074 meV) is much larger than that of C60. It is interesting that the values of *λ*<sup>h</sup> are in the range 392–2411 meV. Isomers

<sup>h</sup> *λ*<sup>h</sup> *k* h

C60H56 *λ*<sup>+</sup>

<sup>h</sup> *λ*<sup>h</sup> *k* h

<sup>h</sup>) for hole transport in C60H54. The

<sup>h</sup>) for hole transport in C60H56. The average

<sup>h</sup> of C60H58 is 468 meV, which is much larger

<sup>h</sup> of C60H58 is 606 meV, which is

C60H54 *λ*<sup>+</sup>

**Table 3.** Reorganization energies (*λ*<sup>h</sup> in meV) and rate constants (*k*

average value over 16 C60H54 isomers is also shown.

**Table 4.** Reorganization energies (*λ*h) and rate constants (*k*

much larger than that of C60 by 511 meV and *λ*<sup>0</sup>

<sup>h</sup> of C60H58 are shown in Table 5. On average, *<sup>λ</sup>*<sup>+</sup>

value over eight C60H56 isomers is also shown.

**1**, **2**, and **4** have smaller *λ*h.

*λ*<sup>h</sup> and *k*

largest *λ*<sup>h</sup> of more than 500 meV.

C60H<sup>+</sup> <sup>60</sup> has nine electrons in fivefold degenerate *hu* orbitals. Thus, C60H<sup>+</sup> <sup>60</sup> has an *Hu* degenerate electronic state, and symmetry lowering because of the Jahn–Teller effect [21] stabilizes C60H<sup>+</sup> 60. The most stable structure of C<sup>+</sup> <sup>60</sup> was calculated as having *D*3*<sup>d</sup>* symmetry, and its *λ*<sup>+</sup> <sup>h</sup> is 101 meV in our calculation. The value of *<sup>λ</sup>*<sup>0</sup> <sup>h</sup> for C<sup>+</sup> <sup>60</sup>(*D*3*d*) was calculated as 40 meV. Thus, the reorganization energy for hole transport, *<sup>λ</sup>*h, is 140 meV. Similar to C60, *<sup>λ</sup>*<sup>+</sup> h is much larger than *λ*<sup>0</sup> <sup>h</sup> because of the Jahn–Teller effect. *k*� <sup>h</sup> of C60H<sup>+</sup> <sup>60</sup> is 1.44 times as large as that of C60.

#### **5.5. Summary**

Figure 6 shows minimum and average values of *λ<sup>h</sup>* for C60H*n*. C60 and C60H60 have only one isomer so that the minimum values are equal to the average values. From the systematic discussion through C60H*<sup>n</sup>* (*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*<sup>h</sup> decrease as the number of hydrogen atoms increases: C60 (169 meV) → C60H2-**6** (101 meV) → C60H4-**1** (83 meV) → C60H6-**1** (71 meV). However, *λ*<sup>h</sup> increases for C60H8-**5** (81 meV). The average values of *λ*<sup>h</sup> change as C60 (169 meV) → C60H2 (174 meV) → C60H4 (134 meV) → C60H6 (127 meV) → C60H8 (113 meV). The average *λ*<sup>h</sup> of C60H4 (134 meV) is almost as large as that of C60H2-**1** (133 meV), but the average *λ*<sup>h</sup> of C60H6 (127 meV) is much larger than that of C60H4-**1** (83 meV), and the average *λ*<sup>h</sup> of C60H8 (113 meV) is much larger than that of C60H6-**1** (71 meV). Highly hydrogenated C60H*<sup>n</sup>* generally has large *λ*h. The average *λ*<sup>h</sup> is C60H52 (254 meV), C60H54 (357 meV), C60H56 (294 meV), C60H58 (1074 meV), and C60H60 (140 meV). Only C60H60 has a smaller *λ*<sup>h</sup> than C60.

**Figure 6.** Dependence of minimum and average values of *λ*<sup>h</sup> on the degree of hydrogenation. The average value of *λ*<sup>h</sup> for C60H58 is very large (1074 meV), therefore it is not shown in the figure.

#### **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 [64–66]. The strong forces on the nuclei generally result in large *λ* and geometrical relaxation. In our previous publications, we defined parameters Δ*r* that characterize the geometrical relaxation as

$$
\Delta r = \sum\_{i} |\Delta r\_i| \,\tag{7}
$$

0.2 0.3 0.4 0.5 0.8 Δr (Å)

0.6 0.7

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation 323

λ<sup>h</sup>

transport in C60H*<sup>n</sup>* (*n* = 8, 52, 54, 56, 58, and 60).

**Figure 8.** HOMOs of isomer-**1** of C60H*n*.

0

500

1000

1500

2000

2500

C60H8

C60H58 C60H60

C60H52, C60H54, C60H56

**Figure 7.** Relationship between reorganization energy (*λ*) and geometrical relaxation (Δ*r*) for hole

The HOMOs of isomer-**1** of C60H*<sup>n</sup>* are shown in Figure 8. The HOMOs of C60H8-**1** and other lowly hydrogenated fullerenes [11, 13, 14] are distributed over the whole molecule. In

C60H8-**1** C60H52-**1** C60H54-**1**

C60H56-**1** C60H58-**1** C60H60

(meV)

where Δ*ri* is the difference in the *i*th 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 Δ*r* and *λ*<sup>h</sup> for C60H*<sup>n</sup>* (*n* = 2, 4, and 6) [11]. Figure 7 shows the relationship between *λ* and Δ*r* for hole transport in C60H8, C60H52, C60H54, C60H56, C60H58, and C60H60. A linear relationship between Δ*r* and *λ*<sup>h</sup> is observed for C60H8 and C60H58. A clear linear relationship is not found for C60H52, C60H54, and C60H56 because the values of the reorganization energy for these species are almost the same. When the values of Δ*r* are the same, C60H8 has a smaller reorganization energy but C60H58 has a larger reorganization energy.

#### **6.2. 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 C60H*n*. The HOMO of C60, which is originally fivefold degenerate, splits because of the interaction between C60 and the H atoms. The distribution of the HOMO easily changes depending on the interaction between C60 and the H atoms.

**Figure 7.** Relationship between reorganization energy (*λ*) and geometrical relaxation (Δ*r*) for hole transport in C60H*<sup>n</sup>* (*n* = 8, 52, 54, 56, 58, and 60).

The HOMOs of isomer-**1** of C60H*<sup>n</sup>* are shown in Figure 8. The HOMOs of C60H8-**1** and other lowly hydrogenated fullerenes [11, 13, 14] are distributed over the whole molecule. In

**Figure 8.** HOMOs of isomer-**1** of C60H*n*.

14 Hydrogenation

average minimum

Degree of Hydrogenation: n

**Figure 6.** Dependence of minimum and average values of *λ*<sup>h</sup> on the degree of hydrogenation. The average value of *λ*<sup>h</sup> for C60H58 is very large (1074 meV), therefore it is not shown in the figure.

The reorganization energy is a stabilization energy by geometrical relaxation originating from the change in electronic structure [64–66]. The strong forces on the nuclei generally result in large *λ* and geometrical relaxation. In our previous publications, we defined parameters Δ*r*

> Δ*r* = ∑ *i*

where Δ*ri* is the difference in the *i*th 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 Δ*r* and *λ*<sup>h</sup> for C60H*<sup>n</sup>* (*n* = 2, 4, and 6) [11]. Figure 7 shows the relationship between *λ* and Δ*r* for hole transport in C60H8, C60H52, C60H54, C60H56, C60H58, and C60H60. A linear relationship between Δ*r* and *λ*<sup>h</sup> is observed for C60H8 and C60H58. A clear linear relationship is not found for C60H52, C60H54, and C60H56 because the values of the reorganization energy for these species are almost the same. When the values of Δ*r* are the same, C60H8 has a smaller reorganization energy but C60H58 has a larger reorganization

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 C60H*n*. The HOMO of C60, which is originally fivefold degenerate, splits because of the interaction between C60 and the H atoms. The distribution of the HOMO easily changes depending on

2 4 6 8 52 54 56 58 60 ...


0

0

100

200

λ<sup>h</sup>

**6. Analysis for molecular design**

that characterize the geometrical relaxation as

**6.1. Geometrical relaxation**

**6.2. Molecular orbital pattern**

the interaction between C60 and the H atoms.

energy.

(meV)

300

400

contrast, the HOMOs of C60H52-**1**, C60H54-**1**, C60H56-**1**, and C60H58-**1** are localized around the nonhydrogenated C atoms. Therefore, highly hydrogenated C60 has a large reorganization energy. In particular, the HOMO of C60H58-**1** is localized on two carbon atoms, therefore the reorganization energy is very large. The HOMO of C60H60 is delocalized over the whole molecule because C60H60 has high symmetry, so that the value of *λ*<sup>h</sup> is smaller than that for other highly hydrogenated fullerenes.

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### **7. Summary**

Systematic analyses of reorganization energies of hydrogenated fullerenes C60H*<sup>n</sup>* (*n* = 2, 4, 6, 8, 52, 54, 56, 58, and 60) give us very important knowledge for efficient design of useful C60 materials:


### **Acknowledgments**

This work was supported by Grant-in-Aid for Scientific Research on Innovation Areas from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 20118007) and Grant-in-Aid for Scientific Research (C) from Japan Society for Promotion of Sciences (No. 24560930). The author would like to thank Dr. Shigekazu Ohmori of the National Institute of Advanced Industrial Science and Technology (AIST) and Dr. Hiroshi Kawabata of Hiroshima University for collaboration in this research theme and helpful comments on this chapter. Theoretical calculations were mainly carried out using the computer facilities at the Research Institute for Information Technology, Kyushu University.

### **Author details**

Ken Tokunaga *Division of Liberal Arts, Kogakuin University, Tokyo, Japan*

### **8. References**


contrast, the HOMOs of C60H52-**1**, C60H54-**1**, C60H56-**1**, and C60H58-**1** are localized around the nonhydrogenated C atoms. Therefore, highly hydrogenated C60 has a large reorganization energy. In particular, the HOMO of C60H58-**1** is localized on two carbon atoms, therefore the reorganization energy is very large. The HOMO of C60H60 is delocalized over the whole molecule because C60H60 has high symmetry, so that the value of *λ*<sup>h</sup> is smaller than that for

Systematic analyses of reorganization energies of hydrogenated fullerenes C60H*<sup>n</sup>* (*n* = 2, 4, 6, 8, 52, 54, 56, 58, and 60) give us very important knowledge for efficient design of useful C60

• Considering only 1,2-addition, C60H6-**1** has the smallest reorganization energy (71 meV).

• Highly hydrogenated fullerenes, especially C60H58, have very large reorganization energies because the HOMOs are localized around nonhydrogenated carbon atoms.

• However, C60H60 has a smaller reorganization energy than other highly hydrogenated fullerenes and C60 because the HOMO of C60H60 is distributed over the whole molecule. • There is a linear relationship between the reorganization energy and the geometrical relaxation. When the values of Δ*r* are the same, lowly hydrogenated fullerenes have

This work was supported by Grant-in-Aid for Scientific Research on Innovation Areas from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 20118007) and Grant-in-Aid for Scientific Research (C) from Japan Society for Promotion of Sciences (No. 24560930). The author would like to thank Dr. Shigekazu Ohmori of the National Institute of Advanced Industrial Science and Technology (AIST) and Dr. Hiroshi Kawabata of Hiroshima University for collaboration in this research theme and helpful comments on this chapter. Theoretical calculations were mainly carried out using the computer facilities at the Research

Further hydrogenation does not reduce the reorganization energy.

Therefore, these C60 derivatives are not suited for hole-transport materials.

smaller reorganization energies than highly hydrogenated fullerenes.

Institute for Information Technology, Kyushu University.

*Division of Liberal Arts, Kogakuin University, Tokyo, Japan*

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[3] Brédas JC, Beljonne D, Coropceanu V, Cornil J (2004) Chem. rev. 104: 4971.

other highly hydrogenated fullerenes.

**7. Summary**

**Acknowledgments**

**Author details**

Ken Tokunaga

**8. References**

materials:


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### *Edited by Iyad Karamé*

The domain of catalytic hydrogenation continues to grow fast, reflecting the wide range of chemical applications that can be enhanced by the easy use of molecular hydrogen. The advances in characterization techniques and their application have improved our understanding of the catalytic processes and mechanisms occurring in both homogeneous and heterogeneous catalysis. The aim of this volume, although not exhaustive, is to provide a general overview of new progress of the hydrogenation reactions. This volume comprises a series of various contributions, as reviews or original articles, treating heterogeneously and homogeneously catalyzed hydrogenation reactions. It is composed of three parts: hydrogenation reactions in fine organic chemistry, hydrogenation reactions in environmental chemistry and renewable energy, and special topics in hydrogenation.

Hydrogenation

Hydrogenation

*Edited by Iyad Karamé*

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