Theoretical study on the structures, properties and spectroscopies of fullerene derivatives C66X4 (X = H, F, Cl)

Carbon 45 (2007) 1821–1827 www.elsevier.com/locate/carbon

Theoretical study on the structures, properties and spectroscopies of fullerene derivatives C66X4 (X = H, F, Cl) Qing-Bo Yan, Qing-Rong Zheng, Gang Su

*

College of Physical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049, China Received 18 November 2006; accepted 28 April 2007 Available online 18 May 2007

Abstract The geometrical structures, electronic properties, and spectroscopies of non-IPR (isolated pentagon rule) fullerene C66 and its derivatives C66X4 (X = H, F, Cl) have been studied by the first-principle calculations based on the density functional theory. By searching through all 4478 isomers of C66, the ground state of C66 is observed to bear Cs symmetry and have two pairs of fusion pentagons. It is found that the addition of H, F, Cl atoms to the pentagon–pentagon fusion vertex of C66 cages can form new non-IPR fullerenes such as C66X4, where the molecule C66X4 with C2v symmetry are uncovered to be the most stable among others. The Mulliken charge populations, gap energies between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO), and density of states of these unconventional fullerenes are calculated, showing that different atoms added to non-IPR C66 cages will alter the charge populations remarkably; the chemical deriving could affect the electronic structures distinctly, and improve the stability of the fullerenes. The calculated results of IR, Raman, NMR spectra of C66X4 are also presented.  2007 Elsevier Ltd. All rights reserved.

1. Introduction The geometry of fullerenes (closed-cage carbon molecules of 12 pentagons and several hexagons) is governed by the empirical isolated pentagon rule (IPR) [1,2], which states that the most stable fullerenes are those in which every pentagon is surrounded by five hexagons. The rule has been verified by many experiments (see e.g. [3]), showing that most of the several isolated stable fullerene isomers satisfy the IPR. In fact, due to the geometrical restriction, the fullerenes such as C60, C70, C70+2n, n = 1, 2, 3. . . are able to have all the pentagons isolated in the carbon cage. The fullerenes with other number of carbons may not have all the pentagons isolated, which are coined as non-IPR fullerenes, and believed to be labile and difficult to isolate. However, it has been unveiled recently that some nonIPR fullerenes may be stabilized through metallic endohedral (Sc2@C66 [4], Sc2C2@C68 [5], AxSc3xN@C68 [6,7],

*

Corresponding author. Fax: +86 10 8825 6006. E-mail address: [email protected] (G. Su).

0008-6223/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2007.04.036

La2@C72 [8], etc.). Further investigations [4–8] revealed that the inner metal atoms are bonded to the fused-pentagon pairs, and the electrons transfer from the inner metal core to the carbon cage, which change the electronic structures of the carbon cage, leading to the stabilization of the non-IPR fullerenes and showing special properties. The chemical deriving method has also been used to stabilize the non-IPR fullerenes. Xie et al. [9] had successfully synthesized a new exohedral chemical deriving non-IPR D5h fullerene {50} (say, C50Cl10, with 10 chlorine atoms added to the pentagon–pentagon vertex fusions) in milligram by a graphite arc-discharge process modified by introducing a small amount of carbon tetrachloride (CCl4) in the helium atmosphere. Troshin et al. [10] have nicely obtained two stable seven-membered ring C58 fullerene derivatives C58F17CF3 and C58F18 with milligram quantities by means of the fluorination of C60 at 550 C. Quite recently, a new chemical deriving non-IPR fullerene {64} (namely, C64H4, with 4 hydrogen atoms added to the vertex of a triplet directly fused pentagons) has been successfully prepared by Wang et al. [11] in milligram with the similar method. The fact that C50Cl10 and C64H4 are stabilized

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by the chemical modification on the pentagon–pentagon fusion vertex gives such a hint that the modification of the electronic structures near the fusion-pentagon pairs may be a promising way to stabilize non-IPR fullerenes, enabling to further enrich the bank of stable fullerenes for practical applications. Stimulated by the fact that through the exohedral chemical modification, C64 could be stabilized as C64H4 [11], and through the endohedral metallic atoms, C66 and C68 can be stabilized as Sc2@C66, Sc2C2@C68 and AxSc3xN@C68, one might expect that C66 and C68 may be stabilized as the exohedral chemical derivatives C66Xn or C68Xn. Here, by the first-principle calculations within the density functional theory (DFT) [12], we report that the addition of H, F, Cl atoms to the pentagon–pentagon fusion vertex of C66 cages can form C66X4 (X = H, F, Cl), where the most stable structures are found to have C2v symmetry. The geometrical structures, electronic properties, and spec-

troscopies of C66 and its derivatives C66X4 are investigated in detail. Our study expect to gain an insight for properly understanding the stabilization of non-IPR fullerenes, and stimulating experimental efforts on C66X4 (X = H, F, Cl). 2. Computational details By the spiral algorithm [13], all of the 4478 topologically different isomers of C66 cage have been generated and sorted in terms of the corresponding pentagon–pentagon adjacency (PPA) numbers. Note that one distinct C–C bond shared by two adjacent pentagons in fullerenes is counted as one PPA. Then, by the semiempirical MNDO method [14], which would be called MNDO//MNDO calculations in Gaussian-like terminology, where B//A represents B level energy calculation based on the geometry optimized on A level, C66 isomers with small PPA numbers

Fig. 1. The 9 lowest-energy isomers of C66 obtained at MNDO.

Q.-B. Yan et al. / Carbon 45 (2007) 1821–1827

(NPPA = 2, 3, 4) have been calculated (see Supplementary material). The semiempirical MNDO method has been substantiated to be able to reproduce the ab initio or density functional relative energies of fullerene isomers with useful high accuracy [15,16]. We have chosen nine isomers of C66 with the lowest energies (Fig. 1), and generated their derivatives. The geometries and relative energies of the above nine isomers and their derivatives are obtained within the DFT. The B3LYP functional, which combines the Becke three parameter non-local hybrid exchange potential [17] and the nonlocal correlation functional of Lee–Yang–Parr [18], was applied. In the B3LYP calculations, the basis set 6-31G* was adopted. The gap energies between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) and the harmonic vibrational frequencies were calculated at the B3LYP/6-31G* level, while the nuclear magnetic shielding tensors were calculated at the GIAO-B3LYP/6-31G* level [19]. We have completed all of the calculations by Gaussian 03 [20] apart from the density of states (DOS) of C66X4 which was calculated by means of the ABINIT package [21]. The latter package is coded within the DFT framework based on pseudopotentials and plane waves. It should be pointed out that Troullier–Martins norm conserving pseudopotentials [22] and the Teter parametrization [23] of the Ceperley–Alder exchange-correlation potential were used in our calculations. 3. Results and discussion 3.1. Ground state of C66 The shapes and symmetries of the nine lowest-energy isomers of C66 obtained at MNDO level, labeled as 4478 : n with n being the isomer number in spiral nomenclature [13], are presented in Fig. 1. The geometries have been reoptimized and the relative energies have been recalculated by the B3LYP/6-31G* method, as listed in Table 1. It can be seen from Table 1 that the ground state of C66 is the isomer 4169 (numbering in spiral nomenclature [13]), which is egg-shaped and bears the Cs symmetry. The following are isomers 4348 and 4466, which have C2v and C2 symmetry, respectively. The above-mentioned three isomers with lower energies have two pairs of adjacent pentagons (counted as 2-PPA), while the rest isomers with higher energies all have three couples of adjacent pentagons (counted as 3-PPA). 3.2. Hydro- , fluoro- and chloro- deriving of nine C66 isomers with lowest energies It is believed that the most active sites of the non-IPR fullerene would be the pentagon–pentagon fusion vertices (PPFV) [24], and the chemical modification on the PPFV could effectively release the large steric strain to form stable

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Table 1 MNDO//MNDO, B3LYP/6-31G*//B3LYP/6-31G* relative energies (in eV) of the nine lowest-energy C66 isomers Isomera

1 2 3 4 5 6 7 8 9

(3764) (4007) (4060) (4141) (4169) (4348) (4456) (4462) (4466)

Symm

C1 C1 C1 C1 Cs C2v C2 C1 C2

NPPAb 3 3 3 3 2 2 3 3 2

NPPFVc 6 6 6 6 4 4 6 6 4

Relative Energy MNDOd

B3LYPe

0.9816 0.8723 0.9384 0.9611 0.0000 0.2789 1.0703 1.1517 0.4325

0.7364 0.7055 0.9131 0.8849 0.0000 0.2158 0.8909 0.9475 0.4013

[7] [4] [5] [6] [1] [2] [8] [9] [3]

[5] [4] [8] [6] [1] [2] [7] [9] [3]

a

Labeled as m(n) form, where (n) was the numbering in spiral nomenclature [13]. b Number of pentagon–pentagon adjacency (PPA). c Number of pentagon–pentagon fusion vertex (PPFV). d [n] indicates the stability order on MNDO level. e [n] indicates the stability order on B3LYP/6-31G* level.

structures. On account of this consideration, we attach H, F, and Cl atoms to the PPFV of the above nine C66 isomers to construct their derivatives, and then optimize the geometries and calculate the relative energies of them by the B3LYP/6-31G* method. By noting that the isomers 4169, 4348 and 4466 have 4 PPFV (Table 1), while the others have 6 PPFV, one may find that the derivatives may be C66X4 or C66X6 (X = H, F or Cl). The relative energy cannot be used to determine the relative stability of C66Xn, as the number of the added X atom is not fixed. To overcome this difficulty, we introduce the C–X bond energy DE [25– 27]: 1 DE ¼ ðEC66 þ nEX  EC66 Xn Þ: n This equation tells us that the higher the C–X bond energy DE is, the greater the stability of C66Xn would be. The C–X bond energy DE and relative stability, the LUMO–HOMO gap energies of the hydro-, fluoro- and chloro- derivatives of nine lowest-energy C66 isomers C66Xn (X = H, F or Cl, n = 4 or 6) at the B3LYP/ 6-31G*//B3LYP/6-31G* level are listed in Table 2. It is observed that the stability order is altered when H atoms are added to the C66 isomers. The most stable structure in all C66Hn derivatives is C66H4 4348, which has the largest C–H bond energy, 3.5470 eV. C1 C66H6 4007 and C2 C66H6 4456 follow up. The derivative 4169 has the lowest C–H bond energy, as it is evolved from the ground state of C66 isomers. The addition of F or Cl has an effect similar to that of H. When F and Cl atoms are added to the C66 isomers, the stability order is also changed. The most stable structures are C66F4 and C66Cl4 4348, which have a larger C–F and C–Cl bond energy, 3.8631 eV and 2.2639 eV, respectively. If the C–X bond energy of C66X4 is taken as a criterion for stability, it appears that C66F4 is the most stable, then C66H4 and C66Cl4.

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Table 2 B3LYP/6-31G*//B3LYP/6-31G* bond energies DE (in eV), LUMO–HOMO gap energies (Egap, in eV) of the derivatives of nine lowest-energy C66 isomers Isomer

na

C66Hn DE (B3LYP)

Egap

DE (B3LYP)

Egap

DE (B3LYP)

Egap

1 2 3 4 5 6 7 8 9

6 6 6 6 4 4 6 6 4

3.0662 3.1380 3.0643 3.0255 2.9981 3.5470 3.1193 3.0758 3.0985

1.6354 1.5943 1.3475 1.2983 0.8174 2.3688 1.3913 0.7070 1.0591

3.3919 3.4665 3.4066 3.3456 3.3450 3.8631 3.4674 3.4118 3.4306

1.4977 1.5448 1.2185 1.2174 0.9412 2.2213 1.4531 0.7927 1.0300

1.7596 1.8338 1.7352 1.7116 1.6847 2.2639 1.8743 1.8206 1.8433

1.4577 1.4876 1.1889 1.1946 0.8966 2.2452 1.3989 0.7535 1.0142

(3764) (4007) (4060) (4141) (4169) (4348) (4456) (4462) (4466)

C66Fn [6] [2] [7] [8] [9] [1] [3] [5] [4]

C66Cln [7] [3] [6] [8] [9] [1] [2] [5] [4]

[6] [4] [7] [8] [9] [1] [2] [5] [3]

a The number of added H or Cl atoms, i.e., the number of pentagon–pentagon fusion vertex (PPFV) for each isomer according to the method we generated the derivatives.

In addition, C66H4 4348 has the largest LUMO–HOMO gap energy, 2.3688 eV, while C66H4 4169 has nearly the least LUMO–HOMO gap energy, 0.8174 eV. Among all C66Fn and C66Cln derivatives, C66F4 and C66Cl4 4348 have the largest LUMO–HOMO gap energies, 2.2213 eV and 2.2452 eV, respectively. A large LUMO–HOMO gap energy has been taken as an indication of a high stability of fullerenes [28,29], implying that the non-IPR fullerenes C66X4 (X = H, F, Cl) 4348 with remarkably large LUMO–HOMO gaps show the higher stability. 3.3. Structural and electronic properties of C66X4 (X = H, F, Cl) Let us study the structural and electronic properties of C66X4 (X = H, F, Cl) fullerene derivatives, which are constructed by attaching H, F and Cl atoms to the PPFV of the isomer C66 4348, respectively. The geometrical structures of C66X4 (X = H, F, Cl), as shown in Fig. 2, bear the C2v symmetry, and have two pairs of adjacent-pentagons on the tapering top of C66 cage. The X (X = H, F, Cl) atoms are attached to the pentagon–pentagon fusions to form C–X bonds. For C66H4, the length of the two ˚ , while that of the C–H bonds near the C2v axis is 1.095 A ˚ . The geometrical structwo other C–H bonds is 1.098 A

tures of C66F4 and C66Cl4 are similar, except that the C–F and C–Cl bonds are much longer than the C–H bond. ˚, The lengths of the corresponding C–F bonds are 1.377 A ˚ , and those of C–Cl bonds are 1.808 A ˚ , 1.827 A ˚. 1.385 A The Mulliken atomic charge populations of C66X4 (X = H, F, Cl) are also given in Fig. 2. The charge populations of C66H4 and C66Cl4 are similar. The PPFV C atoms (i.e. those bonded with X atoms) in C66H4 and C66Cl4 are colored in red, suggesting that their charges are rather negative; the other atoms at the tapering top of C66 cage are marked in dark green, indicating that they have small positive charges. The atoms colored in black at bottom are electroneutral. However, the colors of X atoms are distinct, namely light green and dark green for X = H and Cl, respectively, implying that H atoms are rather positive charged, while Cl atoms are less positive charged. For the electron transfers, the PPFV C atoms are electron acceptors, while H and Cl atoms are electron donors. The addition of F atoms leads to a different behavior. Unlike C66H4 and C66Cl4, the PPFV C atoms in C66F4 are positive charged (bright green color), while F atoms are negative charged (light red color), suggesting an inverse electron transfer. Therefore, it seems that a proper chemical modification on the PPFV of the non-IPR carbon cage would give rise to various changes

Fig. 2. Schematic structures and Mulliken atomic charge populations of C2v C66X4 molecules: (a) C66H4, (b) C66F4, (c) C66Cl4. The capital letters indicate the exohedral atoms, and the rest atoms are all C atoms. The colors of the atoms show the Mulliken atomic charge amount in electrons.

Q.-B. Yan et al. / Carbon 45 (2007) 1821–1827

1500

1500

DOS (Arb. Unit)

DOS (Arb. Unit)

DOS Integrated DOS 1000

C

66

500

0 —20

—15

—10

—5

DOS Integrated DOS 1000

66 4

500

0 —20

0

C H

—15

Energy (eV)

DOS (Arb. Unit)

DOS (Arb. Unit)

—5

0

1500 DOS Integrated DOS

C F

66 4

500

0 —20

—10

Energy (eV)

1500

1000

1825

—15

—10

—5

0

Energy (eV)

DOS Integrated DOS 1000

C Cl 66

4

500

0 —20

—15

—10

—5

0

Energy (eV)

Fig. 3. Density of states (DOS) and the integrated DOS (doted line) of electrons as a function of energy for C66 and C66X4 (X = H, F, Cl). The energy zero-point, indicated by the vertical dash-dot line, is taken at the Fermi level.

of electronic properties, depending on the added atoms. Fig. 3 gives the DOS of C66 and C66X4 (X = H, F, Cl) obtained by the Fermi–Dirac smearing of molecular energy levels, for the DOS offers quite useful information of the electronic structure of clusters and solids. It can be observed that from C66 to C66X4 (X = H, F, Cl), the LUMO–HOMO gaps are widened, further indicating that the chemical deriving on C66 isomer 4348 could indeed enhance the stability. 3.4. Spectroscopy of C66X4 (X = H, F, Cl) The spectroscopies of C66X4 (X = H, F, Cl) such as IR, Raman, and NMR spectra are calculated by B3LYP/ 6-31G*, and GIAO-B3LYP/6-31G*, respectively, in order to offer a verifying basis for the experimental identification, as given in Figs. 4 and 5. Figs. 4a and b show that both IR and Raman spectra of C66H4 have two primary regions extending to the frequency larger than 3000 cm1. The two sharp peaks near 3000 cm1 correspond to the C–H stretching modes, which are rather active in both IR and Raman spectra, while the region less than 1700 cm1 corresponds to the C–C stretching, C–C–C bending and C–C–H bending modes. In the interval between 1000 cm1 and 1700 cm1, the IR and Raman spectra have the similar active modes, where the profiles are similar. Below 1000 cm1, there are still some IR active modes, but almost no Raman active modes. Figs. 4c–f give the IR and Raman spectra of C66X4 (X = F, Cl), which are quite different from that of C66H4,

and extend only to the frequency circa 1700 cm1 without obvious separated regions. Unlike C66H4, the spectra of C66X4 (X = F, Cl) do not have a clear region of C–X stretching modes. The reason may be that the C–H stretching modes can be separated from other modes caused by C atoms as H atom is much lighter than C atom, resulting in the corresponding peaks appear in a region with a very high frequency, while F and Cl atoms are heavier than C atom, F and Cl atoms might couple strongly with C atoms, leading to the IR and Raman spectra of C66F4 and C66Cl4 do not have obvious separated regions. The main IR peaks of C66F4 are located between 1000 cm1 and 1200 cm1, which may be related to the C–F stretching and the vibration of the other part of C66F4. However, the Raman peaks located between 1200 cm1 and 1600 cm1 might correspond to the C–C stretching and C–C–C bending modes, where the vibrations of F atoms are not observed. Similar to C66F4, the main IR and Raman peaks of C66Cl4 might correspond to the Cl-involved modes and Cl-not-involved modes, respectively. From C66F4 to C66Cl4, the main peaks of IR spectra are located at different frequencies, and appear to be red shifted. The Raman spectra show more similarity between C66F4 and C66Cl4, namely, the profiles are very similar, and the main peaks are both located between 1200 cm1 and 1600 cm1. The Raman spectrum of C66H4 below 1600 cm1 is also similar to those of C66X4 (X = F, Cl). The above observation tells us that the IR spectra are more sensitive to different added X atoms than Raman spectra in C66X4 molecules.

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Fig. 5. NMR spectra of C2v C66X4 (X = H, F, Cl), scaled by referenced shifts, where the inset of (a) shows the chemical shifts of H atoms, and others show that of C atoms.

the PPFV carbon atoms. In the middle region, 12 of which have the same degeneracy 4, and the other 3 have the half of the degeneracy, which can be ascribed to the other 54 sp2 (12 · 4; 3 · 2) C atoms. 4. Summary Fig. 4. IR and Raman spectra of C2v C66X4 (X = H, F, Cl), which are scaled by a factor of 0.9613.

The NMR spectra of C66X4 (X = H, F, Cl) are also calculated, as presented in Fig. 5. The C2v C66X4 have 19 unique types of C atoms [62 sp2 C atoms (14 · 4; 3 · 2); 4 sp3 C atoms (2 · 2)] and 2 unique types of X atoms [total 4 X atoms (2 · 2)], where a · b represents a unique types, and in one type there are b symmetrical equivalent atoms. The calculated 13C NMR spectra of C66H4, C66F4 and C66Cl4 are similar, despite of some quantitative differences. These spectra can be sorted out in three regions: the left and right regions both with two peaks, and the middle region with 15 peaks. The right region contains two peaks with the same degeneracy 2. This feature can be ascribed to the sp3 (2 · 2) C atoms which are bonded to the X atoms (i.e. PPFV). The two peaks of the left region have the same degeneracy 4, corresponding to the 8 sp2 atoms (2 · 4) that are bonded with

The geometrical structures, electronic properties and spectroscopies of the non-IPR fullerene C66 and its derivatives C66X4 (X = H, F, Cl) have been investigated by the first-principle calculations within the density functional theory. It has been uncovered that the ground state of C66 should be an egg-shaped, Cs symmetrical isomer with spiral number 4169. The addition of the three X (X = H, Cl, F) atoms to the pentagon–pentagon fusion vertex of C66 cage is observed to have effects on the electronic structures and to enhance the stability of the fullerenes. C66X4 (X = H, F, Cl) are found to be stable, as they have large LUMO–HOMO gap energies and large C–X bond energies. As the C–F bond energy of C66F4 is higher than those of the other two, it seems that C66F4 is the most stable among them. In order for the convenience to further experimental efforts, the IR, Raman, NMR spectra of C66X4 (X = H, F, Cl) are also presented. Since the isolation of C64H4 has been realized recently, we expect that the molecule C66X4 (X = H, F, Cl) could also be obtained experimentally in near future.

Q.-B. Yan et al. / Carbon 45 (2007) 1821–1827

Acknowledgements The authors are grateful to X. Chen, B. Gu, and H. F. Mu for helpful discussions. All of the calculations are completed on the supercomputer NOVASCALE 6800 in Virtual Laboratory of Computational Chemistry, Computer NetWork Information Center (Supercomputing Center) of Chinese Academy of Sciences. This work is supported in part by the National Science Foundation of China (Grant Nos. 90403036, 20490210), the National Science Fund for Distinguished Young Scholars of China (Grant No. 10625419), and by the MOST of China (Grant No. 2006CB601102).

[11]

[12] [13] [14]

[15]

[16]

Appendix A. Supplementary material [17]

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2007. 04.036.

[18]

[19]

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