A novel route for designing C60 derivatives with large first hyperpolarizability: Cage-opened cases

Synthetic Metals 161 (2011) 2185–2191

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A novel route for designing C60 derivatives with large first hyperpolarizability: Cage-opened cases Liang Zhao, Min Zhang, Lili Shi, Shiling Sun, Shuixing Wu, Chunguang Liu, Zhongmin Su ∗ Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun 130024, PR China

a r t i c l e

i n f o

Article history: Received 10 March 2011 Received in revised form 26 June 2011 Accepted 6 July 2011 Available online 25 September 2011 Keywords: Open-cage fullerene C55 O5 C54 O6 NLO First hyperpolarizability Sum-over-state

a b s t r a c t Systematic density functional investigations on the structural and electronic properties of C55 O5 and C54 O6 , two open-cage oxo-fullerene derivatives, have been performed. Those formed from topmost pen˚ tagon and hexagon of C60 cleaved with oxygen atoms, have a large circular opening 4.92 A˚ and 5.99 A, respectively. The size of the opening is large enough to allow guest atoms or small molecules penetrating, thus C55 O5 and C54 O6 may act as promising candidates for fuel storage. The calculations on their nonlinear optical (NLO) properties with ZINDO/SCI–SOS method show that the investigated compounds possess remarkably larger static first hyperpolarizability (ˇ) values amounting to −239.48 and −339.83 × 10−30 esu for C55 O5 and C54 O6 , respectively, which are comparable to the reported exohedral C60 derivatives. It opens a new route to explore new type of NLO materials based on C60 derivatives. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Since the discovery of C60 in 1985 [1], numerous studies of chemical modification of the exterior of fullerene cages utilizing the ␲ bond reactivity have been reported [2–5]. The formation of open-cage fullerene is in a rapid progress and quite promising [6–10] since endohedral fullerenes can be exploited for various purposes from molecular electronics [11,12] to biomedical applications [13,14]. However, it is also challenging for the synthesis of yet-unknown endohedral fullerenes in fullerene chemistry. The molecular surgical approach for the synthesis of innovative endohedral fullerenes has been witnessed a dramatic growth in recent years [15–20] which overcomes the drawbacks of the other modifications because the orifice in the fullerene considerably lowers the activation barrier for insertion of the dopant molecule. It involves creation of an opening on the fullerene cage, insertion of a small guest through the opening, and closure of the opening with retention of the guest inside the fullerene. Gan and his coworkers reported the synthesis of fullerene-mixed peroxides and found that these oxygen-rich compounds are good precursors for cageopened fullerene derivatives with carbonyl groups on the rim of the orifice. They synthesized a cage-opened fullerene derivative with three oxygen atoms directly attached to carbon atom of fullerene [21,22]. They attempt to realize the synthesis of a pentagon of the

∗ Corresponding author. Tel.: +86 431 85099108; fax: +86 431 85894009. E-mail address: [email protected] (Z. Su). 0379-6779/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.synthmet.2011.07.004

C60 cage replaced by five oxygen atoms to form C55 O5 . In this paper, we discuss the synthetical possibility of C55 O5 theoretically. The C60 derivatives with relatively larger ˇ values only can be obtained by breaking the centrosymmetric structure. Most of the previous studies concerning the first hyperpolarizability of C60 derivatives have been focused on the forming of charge-transfer complexes between fullerenes and electron donor, such as ferrocene, aniline or TTF [23–25]. It should be noted that when the cage of fullerene is opened, the first hyperpolarizability is induced simultaneously. Accordingly, we also investigate the NLO properties of cage-opened fullerene derivative C55 O5 . The stability and the NLO properties of C54 O6 , another opencage derivative formed by replaced a hexagon of the C60 cage with six oxygen atoms are also predicted. In order to compare with C55 O5 and C54 O6 , the two compounds C55 and C54 were discussed. It is helpful to elucidate the stability and electronic properties of cageopened oxo derivatives. They are generated by removing adjacent five or six carbon atoms from a pentagon or hexagon ring of C60 , and are also regarded as the predecessors of C55 O5 and C54 O6 by removing the attached oxygen atoms. Our study provides a novel route for designing appropriate C60 derivatives with larger ˇ values. 2. Computational procedures In this paper, all the four fullerene derivatives were optimized with the density functional theory level with the B3LYP [26,27] at 6-31G(d) basis set level. No symmetry or other coordinate constraints were adopted during optimization. The larger orbital basis

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Fig. 1. Optimized structures of studied compounds.

set 6-31+G(d) was employed for the energy calculations using the B3LYP/6-31G(d) optimized geometry. All these calculations were carried out with the Gaussian 03 program suite [28]. Based on the optimized structures, the ground state one-photon absorption spectra, including the transition dipole moment and the corresponding transition energy were calculated with ZINDO/SCI method. For all the molecules, the CI-active spaces were restricted to the thirty highest occupied and the thirty lowest unoccupied orbitals for singly excited configuration (SCI) resulting in 901 configurations including the ground state. The static first hyperpolarizability was obtained using the sum-over-states (SOS) formula according to Eq. (1) [29]:

ˇijk =

1 2

4¯h

 ×

p(i, j, l; −ω , ω1 , ω2 )



m= / gn = / g

      g i  mm ∗  nn k  g (ωmg − ω − img )(ωng − ω1 − ing )

 (1)

 

Here g i  m is an electronic transition moment along the i-axis of the Cartesian component,   between the ground state g|





and the excited state |m; m ∗j  n denotes the dipole difference

operator; ωmg is the transition energy ω1 and ω2 are the frequencies of the perturbation radiation fields, and ω = ω1 + ω2 is the polarization response frequency; P(i, j, l ; − ω , ω1 , ω2 ) indicates all permutations of ω1 , ω2 , and ω along with associated indices i, j, k;  mg is the damping factor. Furthermore, the reliability of the ZINDO/SOS method has been validated for the NLO properties for fullerene as well as its derivatives [30–33].

3. Results and discussion 3.1. Molecular structure and stability The optimized configurations of the investigated systems are displayed in Fig. 1. A harmonic vibration frequency analysis performed at the 6-31G(d) level using the same B3LYP method produced no imaginary frequencies for all the four systems. It demonstrates that the optimized structures of C55 O5 (C55 ) with C5v symmetry and C54 O6 (C54 ) with C3v symmetry are energetically stable. The optimized parameters of C55 O5 and C54 O6 are presented in Table 1. It can be seen that the main geometrical parameters of optimized C55 O5 are in good agreement with the crystal data of an open-cage fullerene derivative named 13 synthesized by Gan et al. [21]. The difference of C O bond length for C55 O5 between calcu˚ The C O lated and average experimental observed is only 0.004 A. bond length of C54 O6 is a little larger than that of C55 O5 . Owing to the high Ih symmetry, there exist only two kinds of carbon–carbon bonds in C60 : R6–6 = 1.401 A˚ and R5–6 = 1.458 A˚ in experiment measurement [34]. From Table 1, except for the C–C bond linked with oxygen behaving typical single-fold bond character, the other bond lengths hardly change compared to original C60 . Generally, such molecular decoration does not deform the collective ␲-bond delocalization in C60 framework, except the direct oxo-bonding carbon atoms. Mulliken charge analysis of C55 O5 and C54 O6 showed that the oxygen atom has negative charges of 0.38|qe| and the direct oxobonding carbon atom has positive charges of 0.38|qe|, while the remaining carbon atoms have tiny negative or positive charges. The oxygen atoms can thus be considered as sites of electron acceptors, while the open-cage fullerene with delocalized ␲ electrons as donors.

L. Zhao et al. / Synthetic Metals 161 (2011) 2185–2191

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−33.45 −49.79 0.00 −140.21 123.92 −28.65 1.87

4 2

-2

Energy(eV)

1–5–6–7 2–7–8–12 7–8–12–13 5–6–7–8 6–7–8–12 6–7–8–9 12–8–9–10

Dihedral

0

-4

2.76eV

LUMO 2.84eV

1.81eV

-6

1.25eV 2.17eV

HOMO

-10

1–5–6 2–7–6 4–5–6 5–6–7 9–8–12 8–9–10 7–8–12

-12

1–5 5–6 6–7 6–14 7–8 8–9 10–11

1.2049(1.1952) 1.5290(1.5343) 1.4408(1.4487) 1.3862(1.3937) 1.3941(1.3861) 1.4414(1.4359) 1.4524(1.4553)

1–5–6 2–13–14 4–5–6 5–6–7 12–13–14 13–12–11 7–6–14

128.18(126.53) 128.18(128.26) 103.49(104.73) 107.26(106.91) 103.49(103.52) 107.26(107.89) 118.85(117.99)

1–5–6–14 6–14–13–2 4–5–6–7 12–13–14–10 5–6–14–13 6–7–8–9 8–9–10–11

−43.23(−41.44) 43.23(41.67) −17.99(−18.37) 17.99(17.11) 0.00(0.00) −5.34(−4.16) −138.58(−139.27)

1–5 5–6 8–9 9–10 11–12 8–12 15–16

1.2136 1.5164 1.4718 1.4379 1.4718 1.3841 1.4667

Bond angles Bond lengths

C54 O6

Dihedral Bond angles Bond lengths

C55 O5

Table 1 Optimized geometric parameters with B3LYP/6-31G(d) method of C55 O5 and C54 O6 (bond distance: angstrom, bond angel and dihedral: degree, experimental data in parentheses).

123.28 123.28 112.47 119.91 107.81 109.54 127.99

-8

C60

C55O5

C55

C54O6

C54

Fig. 2. Molecular orbital energy diagram calculated by B3LYP/6-31G(d).

The cage-opening C55 O5 and C54 O6 provide a wide circular ˚ respectively. opening, with a diameters of about 4.92 and 5.99 A, Calculated hole diameter of the most stable C58 isomer by Hu and Ruckenstein is 3.22 Å [35]. Iwamatsu et al. synthesized a bowl-shaped C60 derivative containing a 20-membered ring with an orifice of 6.5 A˚ along the long axis and 4.2 A˚ along the short axis defined at the B3LYP/6-31G(d) level [36]. Hence the holes of C55 O5 and C54 O6 are much larger compared to the reported results, showing that the holes are large enough for single atoms or small molecules and clusters including a couple of atoms to pass through. Consequently, C55 O5 and C54 O6 may be promising potential candidates for fuel (such as H2 ) storage. The systems of C55 and C54 possess five and six unsaturated carbon atoms, respectively. They are the isomers with maximal number of unsaturated carbon atoms generated by removing five or six adjacent carbon atoms from C60 . Moreover, there exists a non-closed ring with a 15-membered-ring orifice in them. It is well known that C60 cluster has a unique icosahedral structure, consisting of twelve five-membered rings and twenty six-membered rings. When C60 was transformed into cage-opened compounds, one five-membered ring is removed and adjacent five conjugated six-membered rings are destroyed for C55 . It is similar situation for C54 . The whole ␲ electrons cannot delocalize in the whole remaining fragments of C55 and C54 , due to lacking of one five- or six-membered bridge-linked ring. The C55 O5 and C54 O6 are more stable than C55 and C54 , because the oxygen atoms saturate the dangling terminated carbon atoms. In addition, C55 O5 and C54 O6 do not contain unsaturated carbon atoms, and therefore, C55 O5 and C54 O6 are stable in light of Schmalz’s criteria for stable fullerene cluster [37]. The energies of frontier molecular orbital predicted with the B3LYP/6-31G(d) method are schematically plotted in Fig. 2. Comparing the HOMO–LUMO energy gaps of these molecules from Fig. 2, we find that the calculated HOMO–LUMO gap of C54 O6 is 2.17 eV, which is lower than that of C60 . On the contrary, the calculated HOMO–LUMO gap of C55 O5 is 0.08 eV larger than that of C60 . It is known that the HOMO–LUMO gap is qualitative to describe the dynamic stability for a series of molecules, so it should be believed that C55 O5 should be a stable open-cage structure with high dynamic stability, probably more stable than C60 [38,39]. 3.2. Electronic properties The calculated vertical ionization potential (VIP), vertical electron affinity (VEA), total energy, cohesive energy and reaction energy of studied compounds using B3LYP/6-31+G(d) are summarized in Table 2. The cohesive energy defined here as the energy

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Table 2 Computed vertical ionization potential (VIP, eV), vertical electron affinity (VEA, eV), total energy (TE, au), cohesive energy (Ecoh , au), reaction energy (Erea , kcal mol−1 ) at the B3LYP/6-31+G(d) level. a

Structure

VIP

VEA

TE

Ecoh

C60 C55 O5 C54 O6

7.58 7.98 8.18

2.52 2.86 3.74

−2286.22205 −2471.79701 −2508.83777

−19.12 −18.79 −18.65

Erea

b

0.00 208.13 296.34

a Carbon atom energy and oxygen atom energy at B3LYP/6-31+G(d) level are −37.78503 Hartree and −74.96636 Hartree, respectively. b Erea was defined as the reaction energy from C60 to the target compound. The reaction pathways are defined as C60 − 5C + 5O → C55 O5 and C60 − 6C + 6O → C54 O6 .

difference between the total molecular energy and the sum of isolated atomic energy, is an important standard to understand the trends in the formation of fullerene-like moleculese [40,41] reported experimentally and theoretically results [38,41–43]. The LUMO eigenvalue of C55 O5 and C54 O6 are lower than that of C60 . This suggests that C55 O5 and C54 O6 should have a larger electron affinity than C60 . As expected, the theoretical VEAs and VIPs of C55 O5 and C54 O6 are larger relative to that of C60 at the same calculation level, further indicating that both of the oxo derivatives are good electron acceptors, especially for C54 O6 . 3.3. Electronic spectra Based on the optimized geometries, the electronic spectra of C55 O5 and C54 O6 are anticipated by ZINDO/SCI method. The reliability of this method for predicting the one-photon absorption spectra of fullerene derivatives has been widely accepted [30–32]. The absorption spectra of C55 O5 and C54 O6 have more distinct peaks than that C60 due to lower symmetry. However, the important characteristic transition peaks for the super-delocalized ␲-bond similar in C60 at 4.84, 5.41, and 5.96 eV are still very apparent in Fig. 3 [44]. The more dipole allowed electron excitations emerge partially ascribed to the ␲–␲* excitation between the fullerene skeleton and C O part. For example, in Fig. 3, an obvious absorption peak located at around 3.6 eV exists for C55 O5 and C54 O6 , which doesnot occur in pristine C60 and defect C60 (C55 and C54 ). The major electronic absorption peaks of C55 O5 and C54 O6 appear in the range from 3 to 7 eV with the strongest absorption peak at 5.48 and 4.92 eV as presented in Fig. 3. Compared with the absorption spectra of C55 O5 , the absorption maximum of C54 O6 shows a bathochromic shift of ∼ 22 nm, in accordance with the HOMO–LUMO gap. Owing to the expanded CI, significant absorption peaks lying below 6.19 eV can also be found from Fig. 3. Taking C55 O5 as an example, it shows several dominant absorption peaks located at 6.92, 7.09, 8.34 and 8.58 eV. In comparison, major electronic absorption at 6.53, 8.41, 8.49 and 8.71 eV can be seen from C55 . 3.4. Dipole polarizability Investigating the physical mechanism concerning determination of the dipole polarizability (˛) is important for the discussion of the first hyperpolarizability. At the B3LYP/6-31G(d) level, static dipole polarizabilities defined by Eq. (2) of C55 O5 and C54 O6 as well as their counterparts are listed in Table 3. The polarizability Table 3 B3LYP/6-31G(d) static polarizability (˛, in Å3 ) of investigated compounds.

˛xx (˛yy ) ˛zz |˛|

C55 O5

C55

C54 O6

C54

C60

67.81 77.30 70.98

72.18 70.21 71.53

70.42 78.96 73.27

71.32 66.00 69.55

69.24 69.24 69.24

Table 4 Calculated static first hyperpolarizabilities (×10−30 esu) by ZINDO/SOS method. polarizability

C55 O5

C55

C54 O6

C54

ˇzxx ˇzyy ˇzzz ˇvec |ˇzzz /ˇvec |

47.35 47.33 144.81 −239.48 0.60

39.49 9.47 104.25 −183.22 0.57

66.73 66.69 206.41 −339.83 0.61

45.12 45.09 46.14 −136.35 0.34

of C60 and its derivative have been investigated theoretically and experimentally [30,45,46]. Our calculated average polarizability, |a| = 69.24 × 10−30 m3 for C60 is fairly consistent with the experimental value, (76.5 ± 8.0) × 10−30 m3 [45]: ˛=

1 (˛xx + ˛yy + ˛zz ) 3

(2)

Only the diagonal dipole polarizability tensors ˛xx , ˛yy , and ˛zz are nonzero because of the C5v symmetry of C55 O5 and C3v symmetry of C54 O6 . Due to the molecular dipole moment along z-axis, the polarizability component along the z direction is larger than those along x and y directions for C55 O5 and C54 O6 . Nevertheless, the larger polarizability component points to x and y directions for C55 and C54 . Generally, all of the open-fullerene structures have slightly higher polarizabilities than C60 . The results indicate the electron delocalization in fullerene skeleton is destroyed to a certain extent in open-fullerene structures and then bring much larger NLO response under electric field. 3.5. Static first hyperpolarizability As known, second-order NLO effects in organic and polymer materials are more adequate for device applications such as optoelectronic integrated circuits and second harmonic generation; moreover, the static first hyperpolarizability is an estimate for the intrinsic molecular hyperpolarizability in the absence of any resonance effect. In this part, the static first hyperpolarizabilities of cage-opened fullerene derivatives are systematically discussed. For a compound with its dipole moment along z-axis, the ˇvec is defined as ˇvec =

1 3



(ˇzii + ˇizi + ˇiiz )

(3)

i=x,y,z

Owing to the C5v symmetry of C55 O5 , there are 10 nonzero components of ˇ among the 27 components. However, only 4 tensor components are independent, because ˇxxz = ˇxzx = ˇzxx , ˇyyz = ˇzyy = ˇyzy , and ˇzzy = ˇzyz = ˇyzz . Out of the 4 independent components, the main contribution to ˇvec is ˇzzz , which is along the direction of C5 axis (z-direction). For C54 O6 , Owing to the C3v symmetry, the independent individual first hyperpolarizability components are similar to that of C55 O5 . The main contribution to ˇvec comes also from ˇzzz pointing to the direction of C3 axis (z-direction). These indicate that the main charge transfer (CT) is along the z-direction for C55 O5 and C54 O6 . Therefore, the ˇvec can be simplified as the following equation: ˇvec = ˇzzz + ˇzxx + ˇzyy

(4)

The static ˇvec of C55 O5 and C54 O6 are reported in Table 4. The calculated ˇ0 value is comparable to those of C60 exohedral derivatives. In comparison, the ZINDO/SCI–SOS calculated ˇ0 value of C60 /aniline and C60PY–TTF are 20.42 × 10−30 and 48.69 × 10−30 esu respectively [23,25]. Yamamoto et al. reported the NLO properties of C60 –acetylene–ferrocene with an intrinsic hyperpolarizability ˇ0 value of 97 × 10−30 esu by the Oudar–Chemla equation [25]. For example, our calculated ˇ0 value of C60 –acetylene–ferrocene is −179 × 10−30 esu with ZINDO/SCI–SOS method (Supporting

L. Zhao et al. / Synthetic Metals 161 (2011) 2185–2191

2189

0

0

-50

-120

1.0

-150

0.8

-180

0.6

-210

0.4

C54O6

-150

0.6

-200 -250

0.4

-300 0.2

-240

0.2

-100

0.8

-30

1.2

-30

-90

Oscillator strength

-60

C55O5

1.4

βvec(10 esu)

-350

-270

2

3

4

5

6

7

8

9

10

2

3

4

5

Energy(ev)

-90

0.6

-120 0.4

-150

Oscillator strength

C55

-30

-60

βvec(10 esu)

-30

Oscillator strength

7

8

9

10

1.2

0

1.0

-30

C54

0.8

-60

-30

0

1.0

0.8

6

Energy(ev)

βvec(10 esu)

Oscillator strength

1.0

-30

1.6

βvec(10 esu)

1.8

0.6

-90

0.4 -120

-180

0.2 2

3

4

5

6

7

8

9

0.2

-210 10

1

Energy(ev)

2

3

4

5

6

7

8

9

-150 10

Energy(ev)

Fig. 3. Calculated electronic spectra with ZINDO/SCI and static hyperpolarizabilities by ZINDO/SOS.

Information). Consequently, it is convinced from normalized ˇ0 values that the open-cage fullerene derivatives have excellent second-order NLO response in contrast to the C60 exohedral derivatives. When the unsaturated carbon atoms are all saturated with oxygen atoms forming C55 O5 and C54 O6 , the increase of ˇ0 values amounts to 30.71% and 149.2% related to C55 and C54 . The relatively larger geometric variation of C54 compared to C54 O6 than that of C55 compared to C55 O5 are responsible for the different increment. Cleaving a single five- or six-membered ring from C60 and then saturated with oxygen atoms exhibits different intensities on the ˇ0 value of C55 O5 and C54 O6 , the ratio of ˇC0 O /ˇC0 O 55 5 54 6 is 1.42. In order to make this point clear, the two-level model for static first hyperpolarizability is considered [47,48]. The static first hyperpolarizability can be expressed by the following expression [49]: ˇCT ∝

eg feg 3 Ege

(5)

where eg = e − g is the change of dipole moment between the ground and excited (CT) state, Ege is the corresponding transition energy and feg is the oscillator strength. The model is valid for analysis of C55 O5 and C54 O6 due to their large energy gaps. The main contributions of the main transition states to ˇvec are calculated and listed in the Supporting Information. Taking the largest contribution of C55 O5 and C54 O6 to the NLO response as an example, according  model of first hyperpolarizability, the  to two-level 3  value of C O and C O are 0.018 and calculated (eg feg )/Ege 55 5 54 6 0.022, respectively. It reconfirms that C54 O6 shows relatively larger ˇ0 value in contrast with C55 O5 . It also can be explained from the

relatively smaller transition energy contributing to the secondorder polarizability for C54 O6 compared to C55 O5 . The convergence of ˇ0 with respect to the electron excitation is investigated first. The calculated ˇ0 values include the contributions from all the lowest-lying excited states with nonzero oscillator strength. The number of active molecular orbitals in the SCI calculations and excited states involved in the SOS formula are enough to present well-converged ˇ0 values for the discussed molecules because further enlargement of CI will extend to the far ultraviolet region (above 10 eV) as shown in Fig. 3. The predicted ˇ0 converges to −239.48 and −339.83 (×10−30 esu) for C55 O5 and C54 O6 . The size of our CI is appropriate that the excitations above 6.2 eV still make a large proportion to the total ˇ0 values. For example, the excitations above 6.2 eV make a contribution of 20% and 18% to the total ˇ0 values for C55 O5 and C54 O6 , respectively. After the excitations above 8.0 eV, the ˇ0 values begin to converge slowly. When above 9.0 eV, the excitations almost contribute nothing to ˇ0 values. The largest contributions to ˇ0 values of C55 O5 and C55 O6 originate from their strongest absorption peak at 5.48 eV and 4.92 eV. Fig. 4 shows the main orbitals which correspond to high CT peaks and contribute significantly to the ˇ0 values. The major CI contribution to the ˇ0 values of C55 O5 and C54 O6 still takes place in the delocalized ␲ skeleton of C60 and the contribution concerning oxygen atom is less. In addition, the main contributions for C55 O5 and C54 O6 benefit from the CT along z-axis direction significantly. But those for C55 and C54 involve the CT between the new-formed 15membered ring and the remaining aromatic fragment (Supporting Information).

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L. Zhao et al. / Synthetic Metals 161 (2011) 2185–2191

Fig. 4. Molecular orbitals making the main contributions to the NLO response of C55 O5 and C54 O6 .

4. Conclusions

Appendix A. Supplementary data

In this paper, the structural and electronic properties of two open-cage oxo fullerene derivatives: C55 O5 and C54 O6 have been theoretically investigated. Calculation results indicate that C55 O5 is chemically stable with relatively larger band gap compared to C60 . The cohesive energy and reaction energy calculations reveal that the formation of C55 O5 may be easier than that of C54 O6 , which is a useful guidance for synthetic chemists. Therefore, it is to be believed that the experimental synthesis of C55 O5 will certainly be accomplished in the near future. The large openings in diameter of C55 O5 and C54 O6 satisfy one of the main criteria required for fuel storage, predicting their potential application in such field. Analysis of the main contributions to the second-order NLO response of C55 O5 and C54 O6 reveals that charge transfer along the z-axis is the key direction. The larger second-order nonlinear optical response of cage-opened fullerene derivatives also offers a novel opportunity to explore new type of fullerene NLO materials. Further theoretical design and investigations on other kinds of open-cage fullerenes are now ongoing in our team.

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.synthmet.2011.07.004.

Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Project Nos. 21003019 and 20971020), Changjiang Scholars Program (2006), Program for Changjiang Scholars and Innovative Research Team in University (IRT0714).

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