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A relativistic DFT study on the structure and property of M(M = Ba, Sr) @ C74 (D3h)
Computational and Theoretical Chemistry 1020 (2013) 57–62
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A relativistic DFT study on the structure and property of M(M = Ba, Sr) @ C74 (D3h) Dongxu Tian ⇑, Wei Zheng, Suzheng Ren, Ce Hao ⇑ State Key Laboratory of Fine Chemicals, Dalian University of Technology, Dalian 116024, People’s Republic of China
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Article history: Received 20 March 2013 Received in revised form 17 July 2013 Accepted 17 July 2013 Available online 26 July 2013 Keywords: M@C74 Relativistic DFT Energy potential surface Dynamic NMR Raman
a b s t r a c t The interaction between M (M = Ba, Sr) and C74 (D3h) was investigated by the relativistic DFT. With the representative patch of C74 (D3h), all the possible isomers, transition states, and energy barriers were studied. Optimized structures show that there are three equivalent isomers, with Ba or Sr located about 1.7 Å off-center. According to the minimum energy pathway, the possible movement trajectory of Ba or Sr in the C74 (D3h) cage was predicted. The energy barriers for Ba and Sr hopping from one stable site to another are 8.30 and 7.88 kcal mol1, respectively. According to the trajectory, the NMR spectra of M@C74 (M = Ba, Sr) was predicted. When the Ba or Sr was encapsulated into the C74 cage, the symmetry of M@C74 (M = Ba, Sr) changes from D3h to C2v, and the blue shift of the Raman vibrational mode within 100–200 cm1 of M@C74 was found. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Since the first extraction of metallofullerene La@C82 [1], endohedral metallofullerenes (EMFs) have attracted considerable attention [2–11] due to their promising properties and applications in material and biological science. The C74 cage is stabilized when a divalent metal is inserted, with two electrons transferred from the metal to the C74 [2–11]. Experimentally, some divalent M2+@C74 EMFs (M = Ba [3–4], Eu [5], Sm [6–8], Ca [9,10], Sr [4], or Yb [11]) have been isolated. Andreas et al. [12] observed that the Ba atom is located at a 130–150 ppm off-center position by employing a combination of X-ray diffraction, XANES spectroscopy, and theoretical calculations. Slanina et al. [13–15] found that both of the Ba@C74 and Sr@C74 derived from the sole D3h–C74 cage by calculating the Gibbs energies. On the basis of Slanina’s work, Tang et al. [16] found that the most favorable site for a Ba atom is off-center under a [6,6] double bond along the C2 axis on the rh plane. The position and motion of the encapsulated metal atoms are important for the properties of EMFs. Experimental and theoretical works have studied the behavior of the encapsulated metal atoms [17–27]. Miyaka et al. [17] have used 45Sc solution NMR spectroscopy to study the internal motion of the Sc in Sc2@C84. The two Sc in Sc2@C84 have a D2d symmetry and rapidly change their positions with changing temperature. Nishibori et al. [18] showed that the
⇑ Corresponding authors. Tel.: +86 4113352216890; fax: +86 41184986335. E-mail addresses: [email protected] (D. Tian), [email protected] (C. Hao). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.07.020
trajectory of La atoms inside C82 cage is like a bowl at room temperature using the maximum entropy method. Similar dynamical motion of divalent metals in C74 (D3h) cages has been observed [19]. The 13C NMR spectra of Ca@C74 indicates that the Ca atom hops inside the cage [19]. Yamada et al. [20] reported the synthesis of La2@C80(CH2)2NTrt, suggesting that two La atoms can rotate freely in fullerene. Recently, 13C NMR spectroscopy suggests that two encapsulated Lu atoms rapidly rotate in Td–C76 fullerene cages [21]. The motion of metal atoms inside the fullerene cages has also been found by computational studies [22–26]. Andreoni and Curioni [22] obtained the dynamic trajectory of La inside C60 using ab initio molecular dynamics. The dynamic behavior of europium in C74 was investigated by quasi-relativistic DFT by Vietze et al. [23]. Heine et al. [24] calculated the dynamic NMR spectra of Sc3N@C80. Xu et al. [2] calculated the 13C NMR spectra of Yb@C74 and found that the motion of Yb atom is similar to Ca atom in C74 (D3h). Jin et al. [25] showed that the La atom probably undergoes boat-shaped movement at high temperatures. Recently, Zhang et al. [26] reported that the two La ions of La2@C80 form a pentagonal-dodecahedral path. And, what is the dynamic properties of the Ba and Sr in C74 (D3h) cage? In present study, the stable isomers and transition states (TS) of Ba@C74 and Sr@C74 were investigated using relativistic density function theory. With the aid of the potential energy surface (PES), we obtained the trajectory of the Ba atom and Sr atom in the C74 (D3h) cage respectively and forecasted the dynamic NMR spectra of Ba@C74 and Sr@C74. The Raman spectra of Sr@C74 and the hollow C74 cage were calculated and the vibration modes were analyzed.
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2. Computational details Using ADF program [27–36], the relativistic density functional theory calculations were carried out for Ba@C74 and Sr@C74 EMFs. The geometry optimization, Raman frequency analysis as well as the line transition (LT) [37] of the configurations was calculated by the zeroth-order regular approximation (ZORA) basis sets, in which the relativistic effects are considered. All calculations employed the Becke Perdew within the generalized gradient approximation (GGA), with the DZP basis sets used for C atoms and the TZP basis sets for Ba and Sr atoms. In addition, the frozen-core approximation up to the 1s orbital for C atoms and the 4d orbital for Ba atom while the 4p orbital for Sr atom was used. In the calculation of scanning the potential energy curves and the potential energy surface, the coordinate of the hollow C74 cage was fixed. The NMR spectra of Ba@C74 and Sr@C74 were calculated with the BLYP exchange correlation functional within generalized gradient approximation (GGA), and the TZP basis sets.
optimized geometric parameters were shown in Table 1. The point group symmetry of Ba@C74 and Sr@C74 changes from D3h to C2v upon encapsulation of the Ba or Sr atom. The Ba or Sr atom is located about 1.34 Å off-center and under a [6,6] double bond along a C2 axis on the rh plane. Three symmetrically equivalent stable sites for the Ba or Sr atom were found inside the cage along the three C2 axes on the rh plane due to the D3h symmetry of the C74 cage. Because there are three equivalent sites for Ba or Sr atom, which are linked by rotation around the threefold axis, there is a transition state (TS) between two such equivalent minima as shown in Fig. 1b. The vibrational frequencies of transition states for Ba@C74 and Sr@C74 were computed to ensure that the configurations were the saddle points. The transition state structure (Fig. 1b) shows that Ba and Sr are located about 1.10 Å off-center along the C2 axis, and are under a hexagon opposite to the C–C double bond on the rh plane. The activation energy between the minimum energy
Table 1 Geometry parameters and energies of most stable structures and transition states of Sr@C74 (C2v) and Ba@C74 (C2v).
3. Results and discussion 3.1. Geometry optimization and transition state search The hollow C74 cage with D3h symmetry was optimized, and then full geometry optimizations were carried out for Ba@C74 and Sr@C74 to find the favorable position for the metal atoms, with the most stable structures of Ba@C74 and Sr@C74 shown in Fig. 1a. The vibrational frequencies were computed and all turned out to be real, ensuring that the configuration was a true minimum. The
M2+@C2 74
Structure
Relative energies (kcal mol1)
The distance of M-Center (Å)
Number of imaginary frequencies
Sr@C74
C2v(a) C2v(b)
0 7.88
1.34 1.19
0 1
Ba@C74
C2v(a) C2v(b)
0 8.30
1.34 1.10
0 1
(a)
(b) Fig. 1. (a) Relativistic DFT optimized geometry of Sr@C74 and Ba@C74. (b) Optimized transition states.
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point and the saddle points are 7.88 and 8.30 kcal mol1 for Ba@C74 and Sr@C74, respectively. This indicates that the configurations of the energy minimum point are easy to convert from one to another. 3.2. The interaction between Ba/Sr and C74 (D3h)
3.2.1. A representative patch for C74 (D3h) C74 fullerene has only one isomer that satisfies the isolated pentagon rule with D3h symmetry. A right angle patch under a circumspherical surface was taken as a representative patch of the C74 (D3h) cage to describe the C74 (D3h) cage simply as shown in Fig. 2. The area of the patch ABC is equal to 1/12 of the total surface area. There are 27 key points on the C74(D3h) representative patch. Points C1 to C9 represent nine different types of carbon atoms: C1 has C3v local symmetry; C2, C5, C7, C9 have Cs local symmetry; and C3, C4, C6, C8 have C1 local symmetry. Points b1 to b12 represent the twelve distinct C–C bonds: b11 has C2v local symmetry; and bn (n = 2, 3, 5, 6, 8, 9, and 10) have C1 local symmetry. r61 to r64 denote the four types of six-member rings: r61 and r63 have Cs local symmetry; r64 has C2v local symmetry. r51 and r52 represent the two types of five-member rings with Cs local symmetry. When 12 elements of the D3h group are operated on the patch, the patch will encompass the entire surface of the polyhedron. 3.2.2. The interaction between Ba/Sr and C74 The interaction energy between Ba or Sr and C74 (D3h) were calculated by the relativistic density functional theory. Firstly, the C74 (D3h) cage was fixed, and then the Ba and Sr atoms were allowed to approach the 27 key points along the radial directions, which pass through the center of cage and the key points. The calculated potential energy curves as a function of the distance between the Ba or Sr atom and the key points are shown in Fig. 3. From Fig. 3, there is a minimum energy point in each potential energy curve. These energy minima are located between 1.2 and 1.5 Å from the center of cage which is in agreement with Andreas’s results [12]. Three minimum energy lines are C7, b11 and r52, which are all located in the rh plane. To clarify the lowest energy pathway of dynamic motion for Ba and Sr in C74 (D3h) cage, the rh plane should be investigated in detail. Using the energy scan, the PES of the rh plane (±2 Å off the center) was obtained and the results are shown in Fig. 4. There are three equivalent local minima in the rh plane along the C2 axis, denoted by A, that are about 1.21.5 Å off-center. The transition states, denoted by B, are about 1.11.2 Å off-center, which are located in the opposite
Fig. 3. Calculated potential energy curves of Sr atom approaching to the 27 key points of the C74 cage.
Fig. 2. Optimized geometry of C74-D3h (a) and the representative patch of C74(D3h) (b).
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Fig. 4. Calculated PES of Sr atom (a) and Ba atom (b) in the rh plane of the C74 (D3h) cage, and probable trajectory of the Sr or Ba atom in the cage (c).
Table 2 The 13C NMR spectrum parameters of Ba@C74 and Sr@C74. d(Ba@C74, ppm)
d(Sr@C74, ppm)
Degeneracy
C atoms
131.60 133.69 134.16 138.12 138.79 139.38 144.23 145.72 148.54
131.29 132.13 133.35 138.49 138.18 139.43 144.77 147.06 147.78
2 12 6 12 6 12 12 6 6
C1 C8 C9 C6 C5 C3 C4 C7 C2
to the representative patch of C74 (D3h), and their arithmetic average chemical shifts were obtained. The calculated chemical shieldings (d(Ci)) were referenced to those of C60 to obtain the calculated NMR chemical shifts using the following formula [38].
dðCiÞ ¼ dðC 60 Þ þ rðC 60 Þ rðCiÞ
ð1Þ
where d(C60) is taken to be 143.15 ppm [39], r(C60) is the calculated chemical shielding of C60 (28.30 ppm), and (Ci) is the carbon atom under consideration. The 13C NMR spectrum parameters of Ba@C74 and Sr@C74 are shown in Table 2. 3.3. Raman frequency analysis
position with A along the C2 axis. Ba and Sr need to overcome the potential barriers of respective 7.88 and 8.30 kcal mol1 when they hop between the three off-center stable minima while passing through saddle points. The minimum energy pathway is in the rh plane and it is proposed that the motion of M (M = Ba and Sr) forms a ring, which is shown in Fig. 4c. 3.2.3. Calculation of 13C NMR spectrum Using the trajectory of M (M = Ba and Sr) in the C74 (D3h) cage, the 13C NMR spectrum of Ba@C74 and Sr@C74 can be predicted. First, we qualitatively analyzed the 13C NMR of Ba@C74 and Sr@C74. According to the symmetry, there should be nine lines that correspond to the 9 types of carbon atoms in the C74 (D3h) cage as shown in Fig. 2. The intensity of lines was predicted as follows: C1 has C3v local symmetry, so it should give 1/6 intensity signals; C2, C5, C7, C9 have Cs local symmetry and should give half intensity signals; C3, C4, C6, C8 have C1 local symmetry with full intensity signals. Thus the 74 C atoms are divided into nine groups according
For the D3h symmetry, there are the 216 normal modes of empty C74 as follows:
C ¼ 21A01 ðRamanÞ þ 16A02 ðRamanÞ þ 37E0 ðIR; RamanÞ þ 16A001 ðIRÞ þ 19A002 ðIRÞ þ 35E00 ðRamanÞ While for the C2v point group, there are 219 normal modes of M@C74 (M = Ba and Sr):
C ¼ 59A1 ðIR; RamanÞ þ 51A2 ðIR; RamanÞ þ 55B1 ðIR; RamanÞ þ 54B2 ðIR; RamanÞ Among all the 219 vibrational modes, 216 normal modes is the vibration of hollow C74 cage and 3 normal modes is attributed to the vibration of M-C74 (M = Ba, Sr). Kuran et al. [5] studied the Raman spectra of Eu@C74 and pointed out that the observed vibrational modes can be roughly distinguished as internal cage modes between 200 cm1 and 1600 cm1 and a special (Eu–C74) mode at 123 cm1. Only one
Fig. 5. Three kinds of vibration modes less than 200 cm1: (a) vibration mode for 136 cm1, (b) vibration mode for 50 cm1 and (c) vibration mode for 40 cm1.
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Fig. 6. Low-wavenumber region of the Raman spectra of C2 74 (top) and Sr@C74 (lower).
mode in the low frequency range (<200 cm1) is attributed to the metal vs. cage mode, and there is no change for the other 216 normal modes of the hollow C74 cage. By the relativistic density functional calculations, we obtained 3 vibration frequencies of Sr@C74 lower than 200 cm1, which are assigned to the A1 mode (136 cm1), the B1 mode (40 cm1) and the B2 mode (50 cm1). Vibration mode analysis shows that the A1 mode is along a C2 axis on the rh plane as shown in Fig. 5a; the B1 mode is perpendicular to a C2 axis on the rh plane (Fig. 5b) and the B2 mode is perpendicular to the rh plane (Fig. 5c). There is only one peak in Raman spectra of endohedral metallofullerenes from 100 to 200 cm1 [4,5]. Since this peak is only found in endohedral metallofullerenes and relates to the motion of encapsulated metal ions in cages, it has been taken as the fingerprint vibration of endohedral metallofullerenes. Three vibration frequencies of 123 cm1 (Eu@C74) [4,5], 134 cm1 (Sr@C74) [4] and 120 cm1 (Ba@C74) [5] were observed experimentally. The present calculated peak of 136 cm1, which may correspond to 134 cm1 in the Raman experiment [4], is assigned as the metal vs. cage mode. Within the low-frequency (200–250 cm1) of the C2 74 , there are three vibration modes as follows: E0 and E0 0 are two-dimensional vibration mode and A01 is one-dimensional. However, all of the five vibration modes of Sr@C74 are one-dimensional. When the Ba or Sr atom is encapsulated into the cage with the most stable configuration (C2v), the system symmetry changes from D3h to C2v, splitting the two-dimensional vibration into one-dimensional vibration as follows (in Fig. 6).
E0 ! A1 þ B2 E00 ! A2 þ B1 A01 ! A1 Due to the changes of the system symmetry of M@C74 (M = Ba, Sr) from D3h to C2v, blue shift in the calculated Raman vibration mode within 100–200 cm1 of M@C74 (M = Ba, Sr) occurs. The splitting peak in low-frequency of M@C74 (M = Ba, Sr) needs to be confirmed by higher resolution spectral experiments. Vibration spectra have often been regarded as molecular fingerprints, being characteristic but very hard to interpret. The present study demonstrates that computational works combined with experimental electronic, infrared and Raman spectra can help to interpret spectroscopic data and to assign structures. 4. Conclusions In summary, the interaction between M(M = Ba,Sr) and C74(D3h) cage has been investigated by relativistic density function theory. The lowest energy structure of M@C74 (M = Ba,Sr) was obtained and the TS was searched. Both configurations of the lowest energy structure and the TS have C2v symmetry. The energy barriers are respective 8.30 and 7.88 kcal mol1 for Ba and Sr hopping from one stable site to another. The lowest energy pathway is in the rh plane, and the trajectory was predicted to be a ring with D3h symmetry for M@C74 (M = Ba, Sr). On the basis of the trajectory,
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the dynamic 13C NMR spectra of M@C74 (M = Ba,Sr) was predicted. By calculating the Raman spectra of M@C74 (M = Ba, Sr) and the empty cage of C2 74 , the system symmetry of M@C74 (M = Ba, Sr) change from D3h to C2v was found when the M (M = Ba, Sr) atom was encapsulated into the C74 cage. In addition, the blue shift in the calculated Raman vibrational mode within 100–200 cm1 of M@C74 (M = Ba, Sr) occurs. The splitting peak in low-frequency of M@C74 (M = Ba, Sr) needs to be tested by higher resolutions spectral experiments. The present study demonstrates that computational works combined with experimental electronic, infrared and Raman spectra can help to interpret spectroscopic data and to assign structures. Acknowledgments Tian would like to thank the National Natural Science Foundation of China (21001019) and the Fundamental Research Funds for the Central Universities (DUT12LK26). Hao thanks the National Natural Science Foundation of China (Grant Nos. 21036006 and 21137001). The results were obtained on the ScGrid of Supercomputing Center, Computer Network Information Center of Chinese Academy of Sciences. References [1] J.R. Heath, S.C. O’Brien, Q. Zhang, Y. Liu, R.F. Curl, F.K. Tittel, R.E. Smalley, Lanthanum complexes of spheroidal carbon shells, J. Am. Chem. Soc. 107 (1985) 7779–7780. [2] J.X. Xu, T. Tsuchiya, C. Hao, Z.J. Shi, T. Wakahara, W.H. Mi, Z.N. Gu, T. Akasaka, Structure determination of a missing-caged metallofullerene: Yb@C74 (II) and the dynamic motion of the encaged ytterbium ion, Chem. Phys. Lett. 419 (2006) 44–47. [3] H. Oliver, A. Reich, C. MoÈSchel, M. Jansen Prof, Dr, preparation, isolation, and characterization of Ba@C74 Z Anorg, Allg. Chem. 627 (2001) 23–27. [4] H. Oliver, H. Martin, G. Arthur, M. Michael, D.P.J. Martin, Isolation and spectroscopic characterization of new endohedral fullerenes in the size gap of C74 to C76, Z. Anorg. Allg. Chem. 631 (2005) 126–130. [5] P. Kuran, M. Krause, A. Bartl, L. Dunsch, Preparation, isolation and characterisation of Eu@C74: the first isolated europium endohedral fullerene, Chem. Phys. Lett. 292 (1998) 580–586. [6] T. Okazaki, Y. Lian, Z. Gu, K. Suenaga, S. Hisanori, Isolation and spectroscopic characterization of Sm-containing metallofullerenes, Chem. Phys. Lett. 320 (2000) 435–440. [7] T. Okazaki, K. Suenaga, Y. Lian, Z. Gu, H. Shinohara, Intrafullerene electron transfers in Sm-containing metallofullerenes: Sm@C2n (74 6 2n 6 84), J. Mol. Graph. Model. 19 (2001) 244–251. [8] T. Okazaki, K. Suenaga, Y.F. Lian, Z.N. Gu, H. Shinohara, Direct EELS observation of the oxidation states of Sm atoms in Sm@C-2n metallofullerenes (74 <= 2n <= 84), J. Chem. Phys. 113 (2000) 9593–9597. [9] R.S. Ruoff, K.M. Kadish, Fullerenes: recent advances in the chemistry and physics of fullerenes and related materials, in: K.M. Kadish, R.S. Ruoff, (Eds.), The Electrochemical Society Inc., Pennington, vol. 4, 1997, p. 490. [10] T.S.M. Wan, H.W. Zhang, T. Nakane, Z. Xu, M. Inakuma, H. Shinohara, K. Kobayashi, S. Nagase, Production, isolation, and electronic properties of missing fullerenes: Ca@C72 and Ca@C74, J. Am. Chem. Soc. 120 (1998) 6806–6807. [11] J.X. Xu, X. Lu, X.H. Zhou, X.R. He, Z.J. Shi, Z.N. Gu, Synthesis, isolation, and spectroscopic characterization of ytterbium-containing metallofullerenes, Chem. Mater. 16 (2004) 2959–2964. [12] R. Andreas, P. Martin, M. Hartwig, W. Ulrich, J. Martin, The structure of Ba@C74, J. Am. Chem. Soc. 126 (2004) 14428–14434. [13] Z. Slanina, S. Nagase, Stability computations for Ba@C74 isomers, Chem. Phys. Lett. 422 (2006) 133–136. [14] Z. Slanina, F. Uhlı, K.S. Nagase, Computational evaluation of the relative production yields in the X@C74 series (X = Ca, Sr, Ba), Chem. Phys. Lett. 440 (2007) 259–262. [15] Z. Slanina, F. Uhlı´k, Shyi-Long Lee, Ludwik Adamowicz, Shigeru Nagase, Computational screening of metallofullerenes for nanoscience. Sr@C74, Mol. Simulat. 34 (2008) 17–21.
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A relativistic DFT study on the structure and property of M(M = Ba, Sr) @ C74 (D3h) Dongxu Tian ⇑, Wei Zheng, Suzheng Ren, Ce Hao ⇑ State Key Laboratory of Fine Chemicals, Dalian University of Technology, Dalian 116024, People’s Republic of China
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Article history: Received 20 March 2013 Received in revised form 17 July 2013 Accepted 17 July 2013 Available online 26 July 2013 Keywords: M@C74 Relativistic DFT Energy potential surface Dynamic NMR Raman
a b s t r a c t The interaction between M (M = Ba, Sr) and C74 (D3h) was investigated by the relativistic DFT. With the representative patch of C74 (D3h), all the possible isomers, transition states, and energy barriers were studied. Optimized structures show that there are three equivalent isomers, with Ba or Sr located about 1.7 Å off-center. According to the minimum energy pathway, the possible movement trajectory of Ba or Sr in the C74 (D3h) cage was predicted. The energy barriers for Ba and Sr hopping from one stable site to another are 8.30 and 7.88 kcal mol1, respectively. According to the trajectory, the NMR spectra of M@C74 (M = Ba, Sr) was predicted. When the Ba or Sr was encapsulated into the C74 cage, the symmetry of M@C74 (M = Ba, Sr) changes from D3h to C2v, and the blue shift of the Raman vibrational mode within 100–200 cm1 of M@C74 was found. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Since the first extraction of metallofullerene La@C82 [1], endohedral metallofullerenes (EMFs) have attracted considerable attention [2–11] due to their promising properties and applications in material and biological science. The C74 cage is stabilized when a divalent metal is inserted, with two electrons transferred from the metal to the C74 [2–11]. Experimentally, some divalent M2+@C74 EMFs (M = Ba [3–4], Eu [5], Sm [6–8], Ca [9,10], Sr [4], or Yb [11]) have been isolated. Andreas et al. [12] observed that the Ba atom is located at a 130–150 ppm off-center position by employing a combination of X-ray diffraction, XANES spectroscopy, and theoretical calculations. Slanina et al. [13–15] found that both of the Ba@C74 and Sr@C74 derived from the sole D3h–C74 cage by calculating the Gibbs energies. On the basis of Slanina’s work, Tang et al. [16] found that the most favorable site for a Ba atom is off-center under a [6,6] double bond along the C2 axis on the rh plane. The position and motion of the encapsulated metal atoms are important for the properties of EMFs. Experimental and theoretical works have studied the behavior of the encapsulated metal atoms [17–27]. Miyaka et al. [17] have used 45Sc solution NMR spectroscopy to study the internal motion of the Sc in Sc2@C84. The two Sc in Sc2@C84 have a D2d symmetry and rapidly change their positions with changing temperature. Nishibori et al. [18] showed that the
⇑ Corresponding authors. Tel.: +86 4113352216890; fax: +86 41184986335. E-mail addresses: [email protected] (D. Tian), [email protected] (C. Hao). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.07.020
trajectory of La atoms inside C82 cage is like a bowl at room temperature using the maximum entropy method. Similar dynamical motion of divalent metals in C74 (D3h) cages has been observed [19]. The 13C NMR spectra of Ca@C74 indicates that the Ca atom hops inside the cage [19]. Yamada et al. [20] reported the synthesis of La2@C80(CH2)2NTrt, suggesting that two La atoms can rotate freely in fullerene. Recently, 13C NMR spectroscopy suggests that two encapsulated Lu atoms rapidly rotate in Td–C76 fullerene cages [21]. The motion of metal atoms inside the fullerene cages has also been found by computational studies [22–26]. Andreoni and Curioni [22] obtained the dynamic trajectory of La inside C60 using ab initio molecular dynamics. The dynamic behavior of europium in C74 was investigated by quasi-relativistic DFT by Vietze et al. [23]. Heine et al. [24] calculated the dynamic NMR spectra of Sc3N@C80. Xu et al. [2] calculated the 13C NMR spectra of Yb@C74 and found that the motion of Yb atom is similar to Ca atom in C74 (D3h). Jin et al. [25] showed that the La atom probably undergoes boat-shaped movement at high temperatures. Recently, Zhang et al. [26] reported that the two La ions of La2@C80 form a pentagonal-dodecahedral path. And, what is the dynamic properties of the Ba and Sr in C74 (D3h) cage? In present study, the stable isomers and transition states (TS) of Ba@C74 and Sr@C74 were investigated using relativistic density function theory. With the aid of the potential energy surface (PES), we obtained the trajectory of the Ba atom and Sr atom in the C74 (D3h) cage respectively and forecasted the dynamic NMR spectra of Ba@C74 and Sr@C74. The Raman spectra of Sr@C74 and the hollow C74 cage were calculated and the vibration modes were analyzed.
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2. Computational details Using ADF program [27–36], the relativistic density functional theory calculations were carried out for Ba@C74 and Sr@C74 EMFs. The geometry optimization, Raman frequency analysis as well as the line transition (LT) [37] of the configurations was calculated by the zeroth-order regular approximation (ZORA) basis sets, in which the relativistic effects are considered. All calculations employed the Becke Perdew within the generalized gradient approximation (GGA), with the DZP basis sets used for C atoms and the TZP basis sets for Ba and Sr atoms. In addition, the frozen-core approximation up to the 1s orbital for C atoms and the 4d orbital for Ba atom while the 4p orbital for Sr atom was used. In the calculation of scanning the potential energy curves and the potential energy surface, the coordinate of the hollow C74 cage was fixed. The NMR spectra of Ba@C74 and Sr@C74 were calculated with the BLYP exchange correlation functional within generalized gradient approximation (GGA), and the TZP basis sets.
optimized geometric parameters were shown in Table 1. The point group symmetry of Ba@C74 and Sr@C74 changes from D3h to C2v upon encapsulation of the Ba or Sr atom. The Ba or Sr atom is located about 1.34 Å off-center and under a [6,6] double bond along a C2 axis on the rh plane. Three symmetrically equivalent stable sites for the Ba or Sr atom were found inside the cage along the three C2 axes on the rh plane due to the D3h symmetry of the C74 cage. Because there are three equivalent sites for Ba or Sr atom, which are linked by rotation around the threefold axis, there is a transition state (TS) between two such equivalent minima as shown in Fig. 1b. The vibrational frequencies of transition states for Ba@C74 and Sr@C74 were computed to ensure that the configurations were the saddle points. The transition state structure (Fig. 1b) shows that Ba and Sr are located about 1.10 Å off-center along the C2 axis, and are under a hexagon opposite to the C–C double bond on the rh plane. The activation energy between the minimum energy
Table 1 Geometry parameters and energies of most stable structures and transition states of Sr@C74 (C2v) and Ba@C74 (C2v).
3. Results and discussion 3.1. Geometry optimization and transition state search The hollow C74 cage with D3h symmetry was optimized, and then full geometry optimizations were carried out for Ba@C74 and Sr@C74 to find the favorable position for the metal atoms, with the most stable structures of Ba@C74 and Sr@C74 shown in Fig. 1a. The vibrational frequencies were computed and all turned out to be real, ensuring that the configuration was a true minimum. The
M2+@C2 74
Structure
Relative energies (kcal mol1)
The distance of M-Center (Å)
Number of imaginary frequencies
Sr@C74
C2v(a) C2v(b)
0 7.88
1.34 1.19
0 1
Ba@C74
C2v(a) C2v(b)
0 8.30
1.34 1.10
0 1
(a)
(b) Fig. 1. (a) Relativistic DFT optimized geometry of Sr@C74 and Ba@C74. (b) Optimized transition states.
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point and the saddle points are 7.88 and 8.30 kcal mol1 for Ba@C74 and Sr@C74, respectively. This indicates that the configurations of the energy minimum point are easy to convert from one to another. 3.2. The interaction between Ba/Sr and C74 (D3h)
3.2.1. A representative patch for C74 (D3h) C74 fullerene has only one isomer that satisfies the isolated pentagon rule with D3h symmetry. A right angle patch under a circumspherical surface was taken as a representative patch of the C74 (D3h) cage to describe the C74 (D3h) cage simply as shown in Fig. 2. The area of the patch ABC is equal to 1/12 of the total surface area. There are 27 key points on the C74(D3h) representative patch. Points C1 to C9 represent nine different types of carbon atoms: C1 has C3v local symmetry; C2, C5, C7, C9 have Cs local symmetry; and C3, C4, C6, C8 have C1 local symmetry. Points b1 to b12 represent the twelve distinct C–C bonds: b11 has C2v local symmetry; and bn (n = 2, 3, 5, 6, 8, 9, and 10) have C1 local symmetry. r61 to r64 denote the four types of six-member rings: r61 and r63 have Cs local symmetry; r64 has C2v local symmetry. r51 and r52 represent the two types of five-member rings with Cs local symmetry. When 12 elements of the D3h group are operated on the patch, the patch will encompass the entire surface of the polyhedron. 3.2.2. The interaction between Ba/Sr and C74 The interaction energy between Ba or Sr and C74 (D3h) were calculated by the relativistic density functional theory. Firstly, the C74 (D3h) cage was fixed, and then the Ba and Sr atoms were allowed to approach the 27 key points along the radial directions, which pass through the center of cage and the key points. The calculated potential energy curves as a function of the distance between the Ba or Sr atom and the key points are shown in Fig. 3. From Fig. 3, there is a minimum energy point in each potential energy curve. These energy minima are located between 1.2 and 1.5 Å from the center of cage which is in agreement with Andreas’s results [12]. Three minimum energy lines are C7, b11 and r52, which are all located in the rh plane. To clarify the lowest energy pathway of dynamic motion for Ba and Sr in C74 (D3h) cage, the rh plane should be investigated in detail. Using the energy scan, the PES of the rh plane (±2 Å off the center) was obtained and the results are shown in Fig. 4. There are three equivalent local minima in the rh plane along the C2 axis, denoted by A, that are about 1.21.5 Å off-center. The transition states, denoted by B, are about 1.11.2 Å off-center, which are located in the opposite
Fig. 3. Calculated potential energy curves of Sr atom approaching to the 27 key points of the C74 cage.
Fig. 2. Optimized geometry of C74-D3h (a) and the representative patch of C74(D3h) (b).
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Fig. 4. Calculated PES of Sr atom (a) and Ba atom (b) in the rh plane of the C74 (D3h) cage, and probable trajectory of the Sr or Ba atom in the cage (c).
Table 2 The 13C NMR spectrum parameters of Ba@C74 and Sr@C74. d(Ba@C74, ppm)
d(Sr@C74, ppm)
Degeneracy
C atoms
131.60 133.69 134.16 138.12 138.79 139.38 144.23 145.72 148.54
131.29 132.13 133.35 138.49 138.18 139.43 144.77 147.06 147.78
2 12 6 12 6 12 12 6 6
C1 C8 C9 C6 C5 C3 C4 C7 C2
to the representative patch of C74 (D3h), and their arithmetic average chemical shifts were obtained. The calculated chemical shieldings (d(Ci)) were referenced to those of C60 to obtain the calculated NMR chemical shifts using the following formula [38].
dðCiÞ ¼ dðC 60 Þ þ rðC 60 Þ rðCiÞ
ð1Þ
where d(C60) is taken to be 143.15 ppm [39], r(C60) is the calculated chemical shielding of C60 (28.30 ppm), and (Ci) is the carbon atom under consideration. The 13C NMR spectrum parameters of Ba@C74 and Sr@C74 are shown in Table 2. 3.3. Raman frequency analysis
position with A along the C2 axis. Ba and Sr need to overcome the potential barriers of respective 7.88 and 8.30 kcal mol1 when they hop between the three off-center stable minima while passing through saddle points. The minimum energy pathway is in the rh plane and it is proposed that the motion of M (M = Ba and Sr) forms a ring, which is shown in Fig. 4c. 3.2.3. Calculation of 13C NMR spectrum Using the trajectory of M (M = Ba and Sr) in the C74 (D3h) cage, the 13C NMR spectrum of Ba@C74 and Sr@C74 can be predicted. First, we qualitatively analyzed the 13C NMR of Ba@C74 and Sr@C74. According to the symmetry, there should be nine lines that correspond to the 9 types of carbon atoms in the C74 (D3h) cage as shown in Fig. 2. The intensity of lines was predicted as follows: C1 has C3v local symmetry, so it should give 1/6 intensity signals; C2, C5, C7, C9 have Cs local symmetry and should give half intensity signals; C3, C4, C6, C8 have C1 local symmetry with full intensity signals. Thus the 74 C atoms are divided into nine groups according
For the D3h symmetry, there are the 216 normal modes of empty C74 as follows:
C ¼ 21A01 ðRamanÞ þ 16A02 ðRamanÞ þ 37E0 ðIR; RamanÞ þ 16A001 ðIRÞ þ 19A002 ðIRÞ þ 35E00 ðRamanÞ While for the C2v point group, there are 219 normal modes of M@C74 (M = Ba and Sr):
C ¼ 59A1 ðIR; RamanÞ þ 51A2 ðIR; RamanÞ þ 55B1 ðIR; RamanÞ þ 54B2 ðIR; RamanÞ Among all the 219 vibrational modes, 216 normal modes is the vibration of hollow C74 cage and 3 normal modes is attributed to the vibration of M-C74 (M = Ba, Sr). Kuran et al. [5] studied the Raman spectra of Eu@C74 and pointed out that the observed vibrational modes can be roughly distinguished as internal cage modes between 200 cm1 and 1600 cm1 and a special (Eu–C74) mode at 123 cm1. Only one
Fig. 5. Three kinds of vibration modes less than 200 cm1: (a) vibration mode for 136 cm1, (b) vibration mode for 50 cm1 and (c) vibration mode for 40 cm1.
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Fig. 6. Low-wavenumber region of the Raman spectra of C2 74 (top) and Sr@C74 (lower).
mode in the low frequency range (<200 cm1) is attributed to the metal vs. cage mode, and there is no change for the other 216 normal modes of the hollow C74 cage. By the relativistic density functional calculations, we obtained 3 vibration frequencies of Sr@C74 lower than 200 cm1, which are assigned to the A1 mode (136 cm1), the B1 mode (40 cm1) and the B2 mode (50 cm1). Vibration mode analysis shows that the A1 mode is along a C2 axis on the rh plane as shown in Fig. 5a; the B1 mode is perpendicular to a C2 axis on the rh plane (Fig. 5b) and the B2 mode is perpendicular to the rh plane (Fig. 5c). There is only one peak in Raman spectra of endohedral metallofullerenes from 100 to 200 cm1 [4,5]. Since this peak is only found in endohedral metallofullerenes and relates to the motion of encapsulated metal ions in cages, it has been taken as the fingerprint vibration of endohedral metallofullerenes. Three vibration frequencies of 123 cm1 (Eu@C74) [4,5], 134 cm1 (Sr@C74) [4] and 120 cm1 (Ba@C74) [5] were observed experimentally. The present calculated peak of 136 cm1, which may correspond to 134 cm1 in the Raman experiment [4], is assigned as the metal vs. cage mode. Within the low-frequency (200–250 cm1) of the C2 74 , there are three vibration modes as follows: E0 and E0 0 are two-dimensional vibration mode and A01 is one-dimensional. However, all of the five vibration modes of Sr@C74 are one-dimensional. When the Ba or Sr atom is encapsulated into the cage with the most stable configuration (C2v), the system symmetry changes from D3h to C2v, splitting the two-dimensional vibration into one-dimensional vibration as follows (in Fig. 6).
E0 ! A1 þ B2 E00 ! A2 þ B1 A01 ! A1 Due to the changes of the system symmetry of M@C74 (M = Ba, Sr) from D3h to C2v, blue shift in the calculated Raman vibration mode within 100–200 cm1 of M@C74 (M = Ba, Sr) occurs. The splitting peak in low-frequency of M@C74 (M = Ba, Sr) needs to be confirmed by higher resolution spectral experiments. Vibration spectra have often been regarded as molecular fingerprints, being characteristic but very hard to interpret. The present study demonstrates that computational works combined with experimental electronic, infrared and Raman spectra can help to interpret spectroscopic data and to assign structures. 4. Conclusions In summary, the interaction between M(M = Ba,Sr) and C74(D3h) cage has been investigated by relativistic density function theory. The lowest energy structure of M@C74 (M = Ba,Sr) was obtained and the TS was searched. Both configurations of the lowest energy structure and the TS have C2v symmetry. The energy barriers are respective 8.30 and 7.88 kcal mol1 for Ba and Sr hopping from one stable site to another. The lowest energy pathway is in the rh plane, and the trajectory was predicted to be a ring with D3h symmetry for M@C74 (M = Ba, Sr). On the basis of the trajectory,
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the dynamic 13C NMR spectra of M@C74 (M = Ba,Sr) was predicted. By calculating the Raman spectra of M@C74 (M = Ba, Sr) and the empty cage of C2 74 , the system symmetry of M@C74 (M = Ba, Sr) change from D3h to C2v was found when the M (M = Ba, Sr) atom was encapsulated into the C74 cage. In addition, the blue shift in the calculated Raman vibrational mode within 100–200 cm1 of M@C74 (M = Ba, Sr) occurs. The splitting peak in low-frequency of M@C74 (M = Ba, Sr) needs to be tested by higher resolutions spectral experiments. The present study demonstrates that computational works combined with experimental electronic, infrared and Raman spectra can help to interpret spectroscopic data and to assign structures. Acknowledgments Tian would like to thank the National Natural Science Foundation of China (21001019) and the Fundamental Research Funds for the Central Universities (DUT12LK26). Hao thanks the National Natural Science Foundation of China (Grant Nos. 21036006 and 21137001). The results were obtained on the ScGrid of Supercomputing Center, Computer Network Information Center of Chinese Academy of Sciences. References [1] J.R. Heath, S.C. O’Brien, Q. Zhang, Y. Liu, R.F. Curl, F.K. Tittel, R.E. Smalley, Lanthanum complexes of spheroidal carbon shells, J. Am. Chem. Soc. 107 (1985) 7779–7780. [2] J.X. Xu, T. Tsuchiya, C. Hao, Z.J. Shi, T. Wakahara, W.H. Mi, Z.N. Gu, T. Akasaka, Structure determination of a missing-caged metallofullerene: Yb@C74 (II) and the dynamic motion of the encaged ytterbium ion, Chem. Phys. Lett. 419 (2006) 44–47. [3] H. Oliver, A. Reich, C. MoÈSchel, M. Jansen Prof, Dr, preparation, isolation, and characterization of Ba@C74 Z Anorg, Allg. Chem. 627 (2001) 23–27. [4] H. Oliver, H. Martin, G. Arthur, M. Michael, D.P.J. Martin, Isolation and spectroscopic characterization of new endohedral fullerenes in the size gap of C74 to C76, Z. Anorg. Allg. Chem. 631 (2005) 126–130. [5] P. Kuran, M. Krause, A. Bartl, L. Dunsch, Preparation, isolation and characterisation of Eu@C74: the first isolated europium endohedral fullerene, Chem. Phys. Lett. 292 (1998) 580–586. [6] T. Okazaki, Y. Lian, Z. Gu, K. Suenaga, S. Hisanori, Isolation and spectroscopic characterization of Sm-containing metallofullerenes, Chem. Phys. Lett. 320 (2000) 435–440. [7] T. Okazaki, K. Suenaga, Y. Lian, Z. Gu, H. Shinohara, Intrafullerene electron transfers in Sm-containing metallofullerenes: Sm@C2n (74 6 2n 6 84), J. Mol. Graph. Model. 19 (2001) 244–251. [8] T. Okazaki, K. Suenaga, Y.F. Lian, Z.N. Gu, H. Shinohara, Direct EELS observation of the oxidation states of Sm atoms in Sm@C-2n metallofullerenes (74 <= 2n <= 84), J. Chem. Phys. 113 (2000) 9593–9597. [9] R.S. Ruoff, K.M. Kadish, Fullerenes: recent advances in the chemistry and physics of fullerenes and related materials, in: K.M. Kadish, R.S. Ruoff, (Eds.), The Electrochemical Society Inc., Pennington, vol. 4, 1997, p. 490. [10] T.S.M. Wan, H.W. Zhang, T. Nakane, Z. Xu, M. Inakuma, H. Shinohara, K. Kobayashi, S. Nagase, Production, isolation, and electronic properties of missing fullerenes: Ca@C72 and Ca@C74, J. Am. Chem. Soc. 120 (1998) 6806–6807. [11] J.X. Xu, X. Lu, X.H. Zhou, X.R. He, Z.J. Shi, Z.N. Gu, Synthesis, isolation, and spectroscopic characterization of ytterbium-containing metallofullerenes, Chem. Mater. 16 (2004) 2959–2964. [12] R. Andreas, P. Martin, M. Hartwig, W. Ulrich, J. Martin, The structure of Ba@C74, J. Am. Chem. Soc. 126 (2004) 14428–14434. [13] Z. Slanina, S. Nagase, Stability computations for Ba@C74 isomers, Chem. Phys. Lett. 422 (2006) 133–136. [14] Z. Slanina, F. Uhlı, K.S. Nagase, Computational evaluation of the relative production yields in the X@C74 series (X = Ca, Sr, Ba), Chem. Phys. Lett. 440 (2007) 259–262. [15] Z. Slanina, F. Uhlı´k, Shyi-Long Lee, Ludwik Adamowicz, Shigeru Nagase, Computational screening of metallofullerenes for nanoscience. Sr@C74, Mol. Simulat. 34 (2008) 17–21.
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