Article pubs.acs.org/IC
Theoretical Insight into Sc2C76: Carbide Clusterfullerene Sc2C2@C74 versus Dimetallofullerene Sc2@C76 Pei Zhao,† Xiang Zhao,*,† and Masahiro Ehara‡ †
Institute for Chemical Physics & Department of Chemistry, State Key Laboratory of Electrical Insulation and Power Equipment, School of Science, Xi’an Jiaotong University, Xi’an 710049, China ‡ Institute for Molecular Science, Okazaki 444-8585, Japan S Supporting Information *
ABSTRACT: In terms of density functional theory in combination with a statistical thermodynamic method, we have investigated the Sc2C76 species including dimetallofullerenes Sc2@C76 and carbide clusterfullerenes Sc2C2@C74. Two dimetallofullerenes, Sc2@Cs(17490)C76 and Sc2@Td(19151)-C76, possess the lowest relative energies but exhibit poor thermodynamic stability within the fullerene-formation region (500−3000 K). In contrast, four carbide clusterfullerene isomers, Sc2C2@D3h(14246)-C74, Sc2C2@C2v(14239)-C74, Sc2C2@C2(13333)C74, and Sc2C2@C1(13334)-C74, have excellent thermodynamic stability when considering the temperature effect. The Sc2C2@D3h(14246)-C74 isomer, which satisfies the isolated-pentagon rule (IPR), was characterized by its crystallographic structure; however, the other three non-IPR structures with two pairs of pentagon adjacencies are predicted for the first time. In particular, Sc2C2@C2(13333)-C74 and Sc2C2@C1(13334)-C74 are linked by a single Stone−Wales transformation. Meanwhile, bonding critical points and Mayer bond orders in the four isomers were analyzed to disclose the unique interactions between the inner clusters and cages. Additionally, the structural characteristics, 13C and 45Sc NMR chemical shifts, and IR spectra of the four stable isomers are introduced to assist experimental identification and characterization in the future.
1. INTRODUCTION Endohedral metallofullerenes (EMFs) have attracted significant attention because of their unique structures and novel properties; thus, potential applications in many fields, including electronics, magnetism, medicine, and materials science, have been proposed.1−5 Trapping various metallic species in fullerene cages provides different kinds of EMFs, including mono-EMFs, di-EMFs, and cluster-EMFs. In particular, since the discovery of Sc3N@C80 in 1999,6 lots of cluster-EMFs, which encapsulate metallic clusters of nitride, carbide, oxide, cyanide, and sulfide, have been obtained.7 For the family of carbide cluster metallofullerenes (CCMFs), ever since the first example of CCEMFs, Sc2C2@D2d(23)-C84, was isolated in 2001,8 tremendous conventional di-EMFs Mx@ C2n+2 have been determined as MxC2@C2n by means of X-ray crystallographic studies or theoretical calculations. Most of these species are scandium-containing compounds such as Sc 2C2 @Cs-C72 ,9 Sc 3C2 @Ih (7)-C 80,10 Sc 2C 2@C2v (5)-C80,11 Sc2C2@Cs(6)-C82, Sc2C2@C2v(9)-C82,12,13 and Sc2C2@C3v(8)C82.14−16 Recently, a nonclassical Sc2C2@Cs(hept)-C88 fullerene with a heptagonal ring was even isolated and characterized by single-crystal X-ray diffraction.17 Additional examples of CCMFs cover Ti2C2@D3h(5)-C78,18 Y2C2@C3v(8)C82, Y2C2@Cs(6)-C82,19 Y2C2@C1(51383)-C84,20,21 Y2C2@ D3(85)-C92,20 and Lu3C2@D2(35)-C88.22 Consequently, for © XXXX American Chemical Society
EMFs with M2C2n compositions, two structures including Mx@ C2n+2 and MxC2@C2n should be considered simultaneously. In 2002, Wang et al. synthesized and isolated the Sc2C76 fullerene, and then they pointed out that Sc2C76 is a mixture of Sc2@ C76(D2−x) and Sc2@C76(D2−y) after considering two C76 isolated-pentagon rule (IPR) isomers in conjunction with the 13 C NMR spectrum (38 × 2).23 Later, Popov et al. proposed that Sc2C76 should possess a non-IPR Cs(17490)-C76 cage because of the high stability of the corresponding C76 isomer in the hexaanionic state.24 However, because of the valence electron structure of 3d14s2 for Sc atom, Sc atoms in the C cages may present as Sc2+ or Sc3+.25 The C76 isomers in the tetraanionic state should be taken into account. Very recently, the IPR structure of Sc2C2@D3h(14246)-C74 was determined by a single-crystal X-ray crystallographic study.26 Meanwhile, on the basis of the UV−vis−near-IR spectra, the previously reported Sc2@C76 is actually Sc2C2@D3h(14246)-C74. Nevertheless, is it possible to obtain the Sc2@C76 isomer for the Sc2C76 series? Is there any other missing isomer for the Sc2C2@ C74 fullerene? Herein, a systematic theoretical investigation was performed on the Sc2C76 series. The Sc2@C76 and Sc2C2@C74 structures Received: March 28, 2017
A
DOI: 10.1021/acs.inorgchem.7b00760 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Table 1. Relative Energies (ΔE, in kcal·mol−1) and HOMO−LUMO (for Closed Shell) or SOMO−LUMO (for Open Shell) Gaps (in eV) of the Sc2C76 Series ωB97XD/6-31G*∼Lanl2dz
M06-2X/6-31G*∼Lanl2dz
B3LYP/6-31G*∼Lanl2dz
isomer
PA
ground state
ΔE
gap
ground state
ΔE
gap
ground state
ΔE
gap
Sc2@Cs(17490)-C76 Sc2@Td(19151)-C76 Sc2C2@C2(13333)-C74 Sc2@C2v(19138)-C76 Sc2C2@C2v(14239)-C74 Sc2@C2(17512)-C76 Sc2C2@C1(13334)-C74 Sc2@C1(17465)-C76 Sc2C2@C2(13290)-C74 Sc2C2@D3h(14246)-C74
2 0 2 1 2 2 2 2 2 0
singlet triplet singlet singlet singlet singlet singlet singlet singlet singlet
0.0 2.7 5.0 12.1 14.6 14.6 16.1 18.1 21.3 22.0
4.55 3.47 4.28 4.14 3.99 4.50 4.43 4.11 4.15 3.67
triplet triplet singlet singlet singlet singlet singlet singlet singlet singlet
6.8 0.0 11.1 23.0 22.0 27.2 21.9 28.9 27.1 28.1
2.58 1.93 2.96 2.09 2.59 2.40 3.09 2.12 2.81 2.34
singlet triplet singlet singlet singlet singlet singlet singlet singlet singlet
0.4 0.0 20.4 11.3 32.2 14.1 32.0 16.8 35.8 31.8
1.55 1.45 1.67 0.99 1.23 1.74 1.77 1.20 1.53 1.16
relative energy. In the case of C76 anions, Td(19151)-C76 is the most stable isomer for the tetraanions and Cs(17490)-C76 is the most stable isomer for the hexaanions. Table 1 presents the relative energies and highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) (for closed shell) or singly occupied molecular orbital (SOMO)−LUMO (for open shell) gaps of 10 Sc2C76 isomers at three different methods. The potential energy of Sc2@ Cs(17490)-C76 is 2.7 kcal·mol−1 lower than that of Sc2@ Td(19151)-C76 for the ωB97XD method, which is predicted as the lowest-energy structure. The relative energy of Sc2@ Cs(17490)-C76 is only 0.4 kcal·mol−1 higher than that of Sc2@ Td(19151)-C76 for the B3LYP method; thus, they are almost isoenergetic. However, compared to Sc2@Td(19151)-C76, Sc2@ Cs(17490)-C76 possesses a higher energy (6.8 kcal·mol−1) for the M06-2X method. Interestingly, the ground state of Sc2@ Cs(17490)-C76 is a triplet for the M06-2X method but a singlet for the other two methods. Sc2@Td(19151)-C76 has the triplet ground state for the three aforementioned methods. The relative energy of Sc2C2@C2(13333)-C74 is 5.0 and 11.1 kcal· mol−1 respectively for the ωB97XD and M06-2X methods, which can be considered to be the third most stable isomer. Nevertheless, Sc2C2@C2(13333)-C74 has a higher relative energy of 20.4 kcal·mol−1 for the B3LYP method, which is less stable than the five considered Sc2@C76 isomers. For the CCMF isomers, the relative energies derived from the B3LYP method are 9.8−17.6 kcal·mol−1 higher than those from the ωB97XD method and 3.7−10.2 kcal·mol−1 higher than those from the M06-2X method. The overestimated energies of Sc2C2@C74 for the B3LYP method are similar to those in the previous report. 31 Sc 2 C 2 @C 2v (14239)-C 74 and Sc 2 @ C2(17512)-C76 exhibit the same relative energy of 14.6 kcal· mol−1 for the ωB97XD method. It should be noted that the Sc2C2@D3h(14246)-C74 isomer characterized by the crystallographic study possesses a high relative energy (22.0, 28.1, and 31.8 kcal·mol−1 for the three different methods). Consequently, the entropy effect at high temperatures may play an important role in the thermodynamic stability of Sc2C2@D3h(14246)-C74. Especially, compared to the original cages, the calculations at the three methods reveal that the HOMO−LUMO gaps of CCMFs have increased, indicating that encapsulation of the inner clusters is helpful to improving the chemical stability of a fullerene cage. According to the relative energies at the level of ωB97XD/631G*∼Lanl2dz, the temperature-relative concentrations of the Sc2C76 series based on equilibrium statistical thermodynamic analysis are depicted in Figure 1. The results derived from the
were studied on the basis of full-screen classic C76 and C74 cages with no more than two pentagon adjacencies (PAs). The thermodynamic stability of the isomers was further determined by a statistical thermodynamic method. It was found that the Sc2C76 species prefer to be the carbide cluster structures rather than the dimetal ones.
2. COMPUTATIONAL DETAILS The C cage formally accepts four electrons by encapsulating the Sc2C2 cluster, while the transfer of four or six electrons from the Sc2 cluster may happen. Consequently, evaluations for C744−, C764−, and C766− anions with less than three PAs (476 isomers for C74 and 807 isomers for C76) were screened with the AM1 method,27 and some of the stable isomers were reoptimized at the level of B3LYP/6-31G*.28−30 A recent study pointed out that the B3LYP method as well as other DFT methods without long-range corrections tends to overestimate the energies of CCMFs, whereas the energies of di-EMFs are relatively accurate.31 Consequently, the corresponding Sc2@C76 and Sc2C2@C74 isomers were optimized at three DFT methods of ωB97XD,32 M06-2X,33 and B3LYP with 6-31G*∼Lanl2dz basis sets (the 6-31G* basis set for C atoms and the Lanl2dz34 basis set for Sc atoms). Meanwhile, C744−, C764−, and C766− anions were also optimized by M06-2X and ωB97XD methods. Frequency analyses of the Sc2@C76 and Sc2C2@C74 isomers were performed on the optimized structures at the same level of theory. According to the frequency analyses, rotational− vibrational partition functions were obtained to evaluate the molar fractions of the Sc2C76 series at elevated temperatures. Previous studies have demonstrated that the entropy effect plays a critical role in the stabilization of endohedral fullerene isomers.35−37 On the basis of the geometries derived from ωB97XD/6-31G*∼Lanl2dz, the 13C and 45Sc NMR chemical shifts were computed at the ωB97XD/6-311G(d,p)∼Lanl2dz level. The calculated 13C and 45Sc NMR chemical shifts were referenced to those of C60 and Sc3N@C80, respectively.36,38,39 The IR spectra were obtained by harmonic vibrational analyses at the level of ωB97XD/6-31G*∼Lanl2dz. All computational works above were performed by the Gaussian09 program package.40 3. RESULTS AND DISCUSSION Relative Energy and Thermodynamic Stability. The energy sequences of C74 and C76 anions at the B3LYP method show good accordance with the results of the other two methods (see Tables S1−S3 in the Supporting Information). For the tetraanions C74, C2(13333)-C74 possesses the lowest B
DOI: 10.1021/acs.inorgchem.7b00760 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 1. Relative concentrations of the Sc2C76 series at the ωB97XD/6-31G*∼Lanl2dz level of theory.
Figure 2. Optimized structures of Sc2C2@D3h(14246)-C74, Sc2C2@C2v(14239)-C74, Sc2C2@C2(13333)-C74, and Sc2C2@C1(13334)-C74. The Sc and C atoms are shown in pink and white, respectively. The PAs are highlighted in green, and the filled areas in parts c and d represent the fragments where Stone−Wales transformation occurs.
after 2800 K, which has a trend similar to that of Sc2C2@ C2v(14239)-C74. Sc2@Td(19151)-C76 reaches its peak of 12.0% at 700 K and then decreases to almost 0.0% at 3000 K. The relative concentrations of other isomers can be negligent. Consequently, among the isomeric Sc2C76 system, except for Sc2C2@D3h(14246)-C74, it is possible to obtain the three CCMFs [Sc2C2@C2v(14239)-C74, Sc2C2@C2(13333)-C74, and Sc2C2@C1(13334)-C74] in experiments. Geometry and Bonding Nature of Four Sc2C2@C74 Isomers. The structures of Sc2C2@D3h(14246)-C74, Sc2C2@ C 2v (14239)-C 74 , Sc 2 C 2 @C 2 (13333)-C 74 , and Sc 2 C 2 @
other two methods are shown in Figures S1 and S2 in the Supporting Information. Sc2@Cs(17490)-C76 with the lowest relative energy dominates below 600 K but decreases dramatically as the temperature increases. Meanwhile, Sc2C2@C2(13333)-C74 increases dramatically and reaches its peak fraction of 67.7% at 1000 K. The increasing Sc2C2@ C2v(14239)-C74 surpasses Sc2C2@C2(13333)-C74 at 2400 K with a molar fraction of 27.5%. For the Sc2C2@D3h(14246)-C74 isomer, its molar fraction keeps rising from 1000 K and keeps the largest relative concentrations after 2800 K. Sc2C2@ C1(13334)-C74 exhibits the third largest relative concentrations C
DOI: 10.1021/acs.inorgchem.7b00760 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 3. Structures of the Sc2C2 clusters and C atoms adjacent to Sc atoms in each isomer.
Figure 4. BCPs and BCP paths in Sc2C2@D3h(14246)-C74, Sc2C2@C2v(14239)-C74, Sc2C2@C2(13333)-C74, and Sc2C2@C1(13334)-C74. Yellow balls represent BCPs, and green sticks stand for BCP paths. Blue and pink balls represent the C and Sc atoms. The PAs are filled with green.
C 1 (13334)-C 74 optimized at the level of ωB97XD/631G*∼Lanl2dz are presented in Figure 2. It is apparent that Sc2C2@D3h(14246)-C74 is the only IPR isomer, and the other three IPR-violating isomers contain two pairs of PAs. Especially, Sc2C2@C2(13333)-C74 and Sc2C2@C1(13334)-C74 are linked by a single Stone−Wales transformation. After encapsulation of the Sc2C2 cluster, the Sc2C2@C2v(14239)-C74 isomer still keep the symmetry of the original cage. Various shapes of the Sc2C2 clusters can be found in the four different structures. To gain a further insight into these shapes, the structures of the Sc2C2 clusters and C atoms adjacent to Sc atoms are shown in Figure 3, and some of their structural parameters are summarized in Table S5 in the Supporting Information. For the four Sc2C2 clusters, the C−C separations are quite similar (1.25−1.26 Å) and are typical for endohedral
fullerene carbides.7,41 The Sc2C2 cluster in Sc2C2@D3h(14246)C74 has a bent butterfly structure with a dihedral angle of 123.1°, which is similar to the value of the crystal structure (120.8°).25 The Sc−Sc distance is 3.812 Å, which also coincides with the experimental values (3.888−4.474 Å).25 Each Sc atom locates beside a hexagon, and the distance between the Sc atoms and the cage is around 2.19 Å. In the case of Sc2C2@ C2v(14239)-C74, the interior cluster still exhibits a butterfly structure but with a larger dihedral angle of 138.1°, which should be attributed to elongation of the Sc−Sc distance. Each Sc atom in the cage is nearest to the pentagon/pentagon (5/5) edge in the PA areas. For the Sc2C2@C2(13333)-C74 structure, the dihedral angle of the inner Sc2C2 cluster is 179.8°, which results in a nearly planar and zigzag structure. Sc75 and Sc76 are closest to C31 and C20 of the 5/5 edges, respectively. The D
DOI: 10.1021/acs.inorgchem.7b00760 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 5. Simulated 13C NMR spectra of Sc2C2@D3h(14246)-C74, Sc2C2@C2v(14239)-C74, Sc2C2@C2(13333)-C74, and Sc2C2@C1(13334)-C74.
metals can be characterized by (1) small values of ρBCP and ▽2ρBCP, (2) negative HBCP values, and (3) the ratio of the kinetic energy density GBCP to ρBCP, which is smaller than 1.44 These Sc−C BCPs exhibit negative HBCP values and small GBCP/ρBCP ratios ( 0.2 au) at these BCPs is large, and its density Laplacian (▽2ρBCP) is large and negative. The total energy density HBCP is negative, and the |VBCP|/GBCP ratio is greater than 2. Overall, these features reveal obvious covalent interactions between two C atoms for the Sc2C2 cluster. In addition, large MBO values (1.867−1.945) further indicate that these C−C bonds may have the characteristics of a double bond. The bonding of each Sc atom to the whole C2 unit with a T-shaped graph can be found in Sc2C2@C2v(14239)-C74, while each C atom of the C2 unit is bonding to one Sc atom for the other three isomers. A similar metal−C2 bonding was also discovered in Sc2C2@C82, Sc2C2@C84, and Y2C2@C82,24 in which the C2 unit is perpendicular to the metal−metal axis. These BCPs exhibit small ρBCP values (
