Warning to Theoretical Structure Elucidation of Endohedral

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Warning to Theoretical Structure Elucidation of Endohedral Metallofullerenes Rui-Sheng Zhao, Yi-Jun Guo, Pei Zhao, Masahiro Ehara, Shigeru Nagase, and Xiang Zhao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b09403 • Publication Date (Web): 24 Dec 2015 Downloaded from http://pubs.acs.org on December 25, 2015

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The Journal of Physical Chemistry

Warning to Theoretical Structure Elucidation of Endohedral Metallofullerenes Ruisheng Zhao,†, ‡ Yijun Guo,†, ‡ Pei Zhao,†, ‡ Masahiro Ehara,§ Shigeru Nagase# and Xiang Zhao,*,†, ‡ †

Institute for Chemical Physics & Department of Chemistry, MOE Key Laboratory for Non-equilibrium Condensed Matter and Quantum Engineering, School of Science, Xi’an Jiaotong University, Xi’an 710049, China ‡ State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China § Institute for Molecular Science, Okazaki 444-8585, Japan # Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan ABSTRACT: Endohedral scandium fullerenes have attracted substantial interests since they were synthesized and isolated in 1992. Sc2C74 series including both Sc2@C74 and Sc2C2@C72 forms were thoroughly investigated with density functional theory methods including B3LYP, CAM-B3LYP, M06-2X, wB97XD and some other DFT methods combined with statistical mechanics in the present work. Among all the Sc2C74 isomers, Sc2C2@Cs(10528)-C72 is the most thermodynamically stable one , and it is overwhelming at the temperature region of fullerene formation, which is well consistent with experiment. A deviation that B3LYP method as well as other DFT methods without long range corrections tends to overestimate energies of Sc2C2@C72 series was exposed for the first time to our best knowledge, and this deviation may not only be restricted to Sc2C2@C72 series but also apply to other scandium carbide fullerenes Sc2C2@C2n (2n≠72) and even other metal carbide fullerenes. Misleading conclusions will be drawn on the basis of inaccurate energies calculated with B3LYP method and other DFT methods without long range corrections. As B3LYP, BP86, PBE, etc. are fairly widely-used methods in theoretical studies of endohedral metallofullerenes, our work is an instructive warning to these studies. KEYWORDS: endohedral metallofullerene, thermodynamic stability, density functional theory, energy overestimation, long range correction

■ INTRODUCTION Endohedral metallofullerenes (EMF) emerged when fullerene science was still in its infancy.1,2 In 1985, the first EMF, La@C60 was synthesized by Heath and co-wokers.1 Since then a huge number of EMFs have been synthesized3 and EMFs have attracted wide interest due to their extraordinary electronic and structural features and wide potential applications in superconductors,4-6 metallofullerene laser,4 ferroelectric material,7,8 nanomemory device,4 quantum computer9-11 and biomedical field.12-14 It was reported that blending Dy@C82 in Langmuir-Blodgett film of poly(3-hexylthiophene) could dramatically improve the performance of photo-electrochemistry cells.15,16 In biomedical field, Gd@C82(OH)22 nanoparticles were discovered to possess great antitumor activity and low toxicity, which recommends Cd@C82(OH)22 to be an ideal anticancer drug.17 Up to now, more than 200 EMFs have been isolated, and the encapsulated metal involves alkali metals, alkaline-earth metals, rare earth metals and other transition metals, and the carbon cages vary from C60 to C104.3,18 EMFs can be divided into monometallofullerenes, dimetallofullerenes, trimetallofullenenes and clustrefullerenes according to

the form of encapsulated metal(s) or metal cluster. In general, there is only one form for monometallofullerene M@C2n that the sole encapsulated metal is incarcerated by a carbon cage, and when the number of encapsulated metals is above three, these metals together with nonmetallic element form a metallic cluster and are jailed by a carbon cage, and in the intermediate zone (the number of encapsulated metals is two), the M2C2n series usually have two possible forms, i.e. dimetallofullerene form M2@C2n and metal carbide form [email protected],19,20 Structure elucidation is vital to gain deep insights into EMFs and to mine potential values of EMFs. Single-crystal Xray diffraction is the most direct and effective way to determine structures of EMFs.21-23 13C NMR spectroscopy,24 UVvis-NIR absorption spectroscopy25 and mass spectrometry26 can also give potent structure information of EMFs. However, for many EMFs, experimental structure elucidations are hampered by low yields and other reasons. Theoretical investigation is an effective complementary way to determine structures of EMFs.27-31 Moreover, theoretical investigations can also provide useful rules to estimate stability and reactivity of EMFs, prediction of chemical and physical properties of EMFs, and guidelines on applications of EMFs.32 However,

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Table 1. Relative Energies (in kcal/mol) and HOMO-LUMO (for closed shell) and SOMO-LUMO (for open shell) gaps (eV) of Sc2C74 series B3LYP/631G*~Lanl2DZ

CAM-B3LYP/631G*~Lanl2DZ

M06-2X/631G*~Lanl2DZ gap

wB97XD/631G*~Lanl2DZ

PA

Ground state

∆E

gap

∆E

gap

∆E

Cs(10528)-C72

2

Singlet

21.0

1.86

14.4

3.56

2.2

3.20

3.8

4.55

18.8

Cs(10616)-C72

2

Singlet

34.2

1.78

29.4

3.58

17.1

3.21

19.1

4.59

17.1

∆E

Gap

∆(∆E)maxa

D2(10611)-C72

2

Singlet

40.8

0.92

38.2

2.58

25.7

2.23

28.0

3.58

15.1

C1(10610)-C72

2

Singlet

44.0

1.38

40.9

3.07

27.6

2.69

30.6

4.06

16.4

C2v(11188)-C72

1

Singlet

45.6

1.10

43.4

2.77

31.5

2.40

33.0

3.77

14.1

C2(10626)-C72

2

Singlet

47.0

1.40

43.0

3.18

29.9

2.81

32.3

4.21

17.1

C2(13333)-C74

2

Singlet

0.0

1.24

0.0

2.92

5.4

1.69

0.3

4.12

5.4

C2(13295)-C74

2

Singlet

0.7

1.78

0.4

3.52

4.5

2.54

0.0

4.60

4.5

D3h(14246)-C74

0

Triplet

6.6

1.14

8.5

2.67

0.0

2.26

12.3

3.36

12.3

C2(13290)-C74

2

Singlet

7.1

1.56

7.1

3.25

11.7

2.17

7.0

4.23

4.7

C1(13408)-C74

2

Singlet

7.4

1.58

7.9

3.34

11.5

2.36

7.9

4.47

4.1

C2(13291)-C74

2

Singlet

9.4

1.56

10.3

3.30

13.5

2.34

10.3

4.36

4.1

C2v(14239)-C74

2

Triplet

13.1

1.24

12.4

3.02

3.9

1.99

15.6

4.02

11.7

C2(13292)-C74

2

Singlet

15.2

1.48

16.1

3.19

19.4

2.23

16.2

4.20

4.2

C1(13391)-C74

2

Singlet

16.7

1.51

18.4

3.26

20.1

2.55

18.6

4.28

3.4

C1(13384)-C74

2

Singlet

21.8

1.05

23.4

0.10

25.0

2.19

23.2

3.73

3.2

Cs(13336)-C74

2

Singlet

22.7

1.13

24.5

2.90

24.6

2.34

24.9

3.96

2.2

a

The ∆(∆E)max equals to the difference between the highest relative energies of the four DFT methods and the lowest one, and it is defined to reflect the inconsistency of the relative energies of the four DFT methods.

the influence of methodology was usually neglected in the past. In the present work, we used some density function theory (DFT) methods, B3LYP, CAM-B3LYP, M06-2X wB97XD and some other DFT methods, such as BLYP, B3PW91, BP86, PBE and PBE0, combined with statistical mechanics to investigate one series of endohedral scandium fullerenes, Sc2C74 series, aiming to study the influence of methodology on thermodynamic stabilities of Sc2C74 series. Endohedral scandium fullerenes are of lots of interests and have attracted substantial attentions. A large number of endohedral scandium fullerenes have been synthesized, and scandium monomer, dimer, trimer, and scandium-based clusters including scandium carbide, scandium nitride, scandium oxide, scandium sulfide and scandium-based mixed-metal nitride cluster have been encapsulated into different carbon cages C2n (n=33-42).3 The endohedral scandium fullerenes were firstly synthesized by Shinohara’s and Costantino’s groups, and Sc2C74, Sc3C82, Sc2C84, Sc2C82, ScC82, ScC84 and ScC86, were isolated.33,34 Sc2C66, Sc2C70, Sc2C80, Sc2C86 and Sc2C76 were synthesized and isolated in the following years.35,36 Most Sc2C2n series were regarded as dimetallofullerenes Sc2@C2n in that time. However, many Sc2C2n series were corroborated to be metal carbide fullerenes Sc2C2@C2n-2 in recent years such as Sc2C2@C72 and Sc2C2@C84 series.37,38 Interestingly, as for the two isolated isomers of Sc2C82 series, one isomer was proved to adopt the metal carbide form Sc2C2@C2v(5)-C80 form,39 while the other one was suggested to adopt the dimetallofullerene form Sc2@C3v(8)-C82.40 It is ambiguous for

Sc2C70 series that the isomer with a Sc2C2@C68 form was obtained experimentally while a theoretical investigation indicated that Sc2@C2v(7854)-C70 is the most thermodynamically stable one among all the isomers of Sc2C70 series.41,42 The endohedral discandium fullerene, Sc2C74, were firstly synthesized in 1993, but the structure of Sc2C74 was unclear at that time.36 Previous theoretical work only focusing on Sc2@C74 forms suggested that Sc2@C2(13295)-C74 and Sc2@C2(13333)C74 are of the highest thermodynamic stabilities among all the isomers of Sc2@C74 series,43 and an isomer with Sc2C2@C72 form, i.e. Sc2C2@Cs(10528)-C72, was isolated and characterized in the following year.37 Therefore a complete theoretical investigation in which both Sc2C2@C72 and Sc2@C74 form should be considered is also needed to uncover those puzzles, such as, whether Sc2C2@Cs(10528)-C72 is the most thermodynamically stable isomer, and whether other isomers can be isolated in the future.

■ COMPUTATIONAL SECTION Endohedral metal(s) or metal cluster prefer to resides on the pentalene motifs in those EMFs whose carbon cages violate the well-known isolated pentagon rule (IPR).3,20 As for dimetallofullerene, it is reasonable to choose those C72 and C74 carbon cages which have no more than three adjacent pentagon pairs, namely PA=0-3 (the number of adjacent pentagon pairs was denoted as PA). Moreover, it was reported that each Sc atom can transfer two or three electrons to carbon cage.24 Therefore, both tetra- and hexa- C72 and C74 carbon cage ani-


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ons whose PA was less than three (269 isomers for C72 and 476 isomers for C74) were firstly optimized at semi-empirical AM1 level,44 and those cage anions with low relative energies (within 30 kcal/mol) were selected and re-optimized at B3LYP/6-31G* level,45 and those re-optimized cage anions with low relative energies (within 20 kcal/mol) were selected as candidates to incarcerate scandium atoms or carbide cluster. Sc2@C74 and Sc2C2@C72 isomers were optimized at DFT methods B3LYP,45 CAM-B3LYP,46 M06-2X47 and wB97XD48 with 6-31G*~Lanl2DZ basis set (6-31G* basis set for C atoms and Lanl2DZ basis set with corresponding effective core potential for Sc atoms). To study the influences of long range corrections, six Sc2C74 isomers, i.e. Sc2C2@Cs(10528)-C72, Sc2C2@Cs(10616)-C72, Sc2C2@D2(10611)-C72, Sc2@C2(13295)-C74, Sc2@C2(13333)-C74 and Sc2@D3h(14246)-C74 were further investigated by five other DFT methods without long range corrections, namely, BLYP49-51, B3PW9152, BP8653, PBE54 and PBE055 with 631G*~Lanl2DZ basis set. Vibrational frequency analyses were also performed on the optimized structures at the same level of theory to check whether the stationary points are minima and to obtain necessary data for rotational-vibrational partition functions. Rotational-vibrational partition functions were established from the calculated structural and vibrational data of the four DFT methods (only the rigid rotator and harmonic oscillator quality, though, and without frequency scaling). The relative concentrations (mole fractions) wi of the isomer i among based on all the m isomers can be computed by the equation (1), which is expressed by partition functions of iso mer i, qi and its enthalpy at absolute zero , , i.e. the ground-state energies , , [, /()]

= ∑!

(1)

"#$ [, /()]

where R is the gas constant and T is the absolute temperature.56,57 To gain natural charges and the simulated Infrared spectrum of Sc2C2@Cs(10528)-C72 isomer, natural bond orbital (NBO)58,59 and vibrational frequency analyses at wB97XD/6-31G*~Lanl2DZ level were implemented on the structure optimized at the same level, respectively. All these calculations above were carried out with Gaussian 09 program.60 Mayer bond order analyses were performed with MUTIWFN 3.2 program on the basis of the wave-function of wB97XD method.61-63

■ RESULTS AND DISCUSSION Relative energies of Sc2C74 series. Relative energies of C72 and C74 anions (including tetra and hexa anions) are collected in Table S1 to S8 of supporting information. The DFT results indicated that the Cs(10528)-C72 and D2(10611)-C72 are the most stable cages for tetra-C72 and hexa-C72 anions, respectively and that C2(13333)-C74 and C2(13295)-C74 are the most stable cages for tetra-C74 and hexa-C74 anions, respectively. Relative energies and HOMO-LUMO gaps (for closed shell) or SOMO-LUMO gaps (for open shell) of Sc2@C74 and Sc2C2@C72 series at B3LYP/6-31G*~Lanl2DZ, CAMB3LYP/6-31G*~Lanl2DZ, M06-2X/6-31G*~Lanl2DZ and wB97XD/6-31G*~Lanl2DZ are listed in table 1. Sc2@C2(13333)-C74 is the most stable isomer for B3LYP and CAM-B3LYP method. For M06-2X and wB97XD method,

although the Sc2@C2(13333)-C74 is not the most stable isomer, its relative energies are very close to zero (only 5.4 and 0.3 kcal/mol for M06-2X and wB97XD method, respectively), and these subtle energy discrepancies are reasonable because different DFT methods use integrals of different function of the density and possibly the density gradient to calculate exchange and correlation functional.45-48,56 For Sc2C2@C72 series only, the Sc2C2@Cs(10528)-C72 is the most stable isomer for the four DFT methods. Moreover, for Sc2C2@C72 series, there are huge discrepancies between the relative energies of B3LYP method and those of the other three DFT methods. The relative energies of B3LYP method are much higher than those of M06-2X and wB97XD, and still a little higher even compared with those of CAM-B3LYP. However, for Sc2@C74 series, these discrepancies are pretty subtle. Herein, an index, ∆(∆E)max, was defined to reflect the consistency of the relative energies calculated with different DFT methods of each Sc2C74 isomer, and the ∆(∆E)max equals to the difference between the highest relative energy and the lowest one. For all the Sc2C2@C72 isomers, the ∆(∆E)max values are relatively large and ~15 kcal/mol, while, for Sc2@C74 isomers, these values are quite small and only ~5 kcal/kcal (except Sc2@D3h(14246)-C74 and Sc2@C2v(14239)C74). The consistencies of relative energies of Sc2@C74 series and inconsistencies of Sc2C2@C72 series should be due to that long range interaction plays an important role in calculating the energies of Sc2C2@C72 isomers while it is not that important in the cases of Sc2@C74 series. Traditional DFT methods without long range corrections are not suitable for some systems, because the non-Coulomb part of exchange functional decays rapidly and turns inaccurate at large distance.64,65 It is known that interactions between encapsulated metals (or metal clusters) and carbon cages are important to stabilization of EFMs. The distances between Sc atoms and vicinal atoms of carbon cages are much longer for Sc2C2@C72 series, compared with those of Sc2@C74 series. The electron-electron interactions between electrons of encapsulated Sc atoms and those of vicinal atoms of carbon cages may be inaccurately estimated by DFT methods without long range corrections, which may lead to energy overestimations of Sc2@C72 series. Note that CAMB3LYP, M06-2X and wB97XD include the long range corrections but B3LYP does not. Therefore, as for B3LYP method, the energies of Sc2C2@C72 series are vastly overestimated, but the energies of Sc2@C74 series are relatively accurate. (The energies of Sc2C2@C72 series calculated with CAM-B3LYP method should also be overestimated, maybe because the long range corrections of this method are not suitable for Sc2C2@C72 series.) To further demonstrate that relative energies of Sc2C2@C72 series were overestimated by DFT method without long range corrections, six Sc2C74 isomers including Sc2C2@Cs(10528)-C72, Sc2C2@Cs(10616)-C72, Sc2C2@D2(10611)-C72, Sc2@C2(13295)-C74, Sc2@C2(13333)C74, and Sc2@D3h(14246)-C74 were investigated by five other DFT methods without the corrections, i.e. BLYP, B3PW91, BP86, PBE and PBE0 methods, and the results are collected in table S9 of supporting information. Like the situation of B3LYP, relative energies of the three Sc2C2@C72 isomers were also highly overestimated whereas those of Sc2@C74 were also relatively accurate. These results revealed that not only B3LYP method but also other DFT methods without long



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Figure 1.Concentration-temperature curves of Sc2C74 series calculated with (a) wB97XD, (b) M06-2X, (c) CAM-B3LYP and (d) B3LYP methods. (e) Concentration-temperature curve of Sc2C70 series (“wi%” in Figure 1a-1d and “X%” in Figure 1e are concentrations, i.e. mole fractions, of Sc2C74 and Sc2C70 isomers, respectively. Figure 1a-1d covers only six low-lying Sc2C74 isomers, and concentrationtemperature curves covering more isomers are given in Figure S1. Figure 1e was reproduced with permission from ref 42. Copyright 2012 American Institute of Physics)

range corrections, such as BLYP, B3PW91, BP86, PBE and PBE0, tend to overestimate energies of Sc2C2@C72 isomers. Herein, we propose that B3LYP method as well as other DFT methods without long range correction tends to overestimate energies of Sc2C2@C72 series, and this overestimation may

hold for other scandium carbide fullerenes (Sc2C2@C2n, 2n ≠ 72) and even other metal carbide fullerenes for the first time. This deviation is an instructive warning to theoretical elucidation of endohedral metallofullerenes which involve metal carbide forms.


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Table 2. Natural charges (e) and Natural Electron Configurations of wB97XD method of Sc2C2 clusters

Sc2C2@Cs(10528)-C72

4+

Sc2C2 tetra-cation

a

Sc2C26+ hexa-cationa

Sc2C2 neutral cluster

a

charges

populations

C73

-0.738

2s1.192p3.533p0.01

C74

-0.035

2s1.262p2.743p0.023d0.01

Sc75

1.002

4s0.163d1.184p0.314d0.265p0.11

Sc76

1.000

4s0.163d1.184p0.314d0.265p0.11

C73

-1.183

2s1.462p3.693s0.013p0.023d0.01

C74

0.180

2s1.592p2.223d0.01

Sc75

2.501

4s0.033d0.454p0.024d0.01

Sc76

2.501

4s0.033d0.454p0.024d0.01

C73

-0.652

2s1.512p3.133p0.013d0.01

C74

0.964

2s1.102p1.923p0.013d0.01

Sc75

2.844

3d0.144p0.014d0.01

Sc76

2.844

3d0.144p0.014d0.01

C73

-1.084

2s1.372p3.683s0.013p0.02

C74

-0.316

2s1.472p2.833p0.013d0.01

Sc75

0.700

4s1.163d1.024p0.124d0.01

Sc76

0.700

4s1.163d1.024p0.124d0.01

a

The geometries of Sc2C2 tetra- and hexa-cations and neutral cluster came from optimized Sc2C2@Cs(10528)-C72.

Thermodynamic stability of Sc2C74 series. The thermodynamic stability of Sc2C74 isomers at elevated temperatures, especially the fullerene formation region, (about 500-3000 K), were investigated on the basis of equilibrium statistical thermodynamics containing enthalpy and entropy effects.66-68 The temperature-relative concentrations of Sc2C74 series based on the results calculated with wB97XD method was evaluated and illustrated in Figure 1a. At absolute zero, Sc2@C2(13295)C74 is of the highest abundance among all the isomers of Sc2C74 series, but with increase of temperature, its population decreases rapidly. On the contrary, the population of Sc2C2@Cs(10528)-C72 is pretty low at absolute zero, but its population grows promptly with increase of temperature due to entropy effect (more detailed discussion are given in section SIII of supporting information), and at 330 K ， Sc2C2@Cs(10528)-C72 and Sc2@C2(13295)-C74 posses the same mole fractions, and exceeding this temperature point (we name this temperature point as temperature threshold in the present work), Sc2C2@Cs(10528)-C72 turns the prevailing isomer. Sc2C2@Cs(10528)-C72 is the sole overwhelming isomer in a very wide temperature interval, i.e., about 330-9000 K. Sc2@C2(13333)-C74 is of some abundance in the temperature range about from 50 to 400 K which are not within the temperature region of fullerene formation, though. As the mole fraction wi% of Sc2C2@Cs(10528)-C72 is as high as 50-90% in the temperature range of fullerene formation, this isomer is most likely to be synthesized and isolated, and moreover, others Sc2C74 isomers are very hard to be synthesized and isolated. In fact, Sc2C2@Cs(10528)-C72 is the sole isolated isomer of Sc2C74 series up to now. The concentration-temperature curve of M06 method shown in Figure 1b is generally analogous to that of wB97XD. Beyond the temperature threshold 149 K, Sc2C2@Cs(10528)-C72 becomes the overwhelming isomer, and its mole fraction is 80-95% within temperature range of fuller-

ene formation. Interestingly, for Sc2S@C72, the isolated and characterized isomer also adopts the Cs(10528)-C72 cage, and Cs(10528)-C72 may be an ideal cage to encapsulated metal cluster.69 The concentration-temperature curves of CAMB3LYP and B3LYP methods are illustrated in Figure 1c and 1d, respectively. For these two curves, although at high temperature interval Sc2C2@Cs(10528)-C72 is still the overwhelming isomer, its mole fractions are much lower compared with those of wB97XD and M06-2X methods, though, due to the overestimation of energies of Sc2C2@C72 isomers. (The maximum of mole fractions of Sc2C2@Cs(10528)-C72 within temperature region of fullerene formation are ~60 and ~35% for CAM-B3LYP and B3LYP method, respectively.) Furthermore, for CAM-B3LYP and B3LYP method, the temperature thresholds are delayed compared with those of wB97XD and M06-2X, also because of the overestimation of energies. (The temperature thresholds are 1594 and 2340 K, for CAMB3LYP and B3LYP method, respectively.) Such an erroneous conclusion that Sc2C2@Cs(10528)-C72, Sc2@C2(13333)-C74 and Sc2@C2(13295)-C74 are thermodynamically stable and these three isomers all can be synthesized and isolated experimentally might be drawn if only the results of B3LYP method were taken into account. More worse, if the energies of Sc2C2@C72 isomers were overestimated more seriously, the temperature threshold would exceed temperature region of fullerene formation and a completely wrong conclusion that Sc2@C2(13333)-C74 rather than Sc2C2@Cs(10528)-C72 is the most thermodynamically stable isomer would be reached. It is an instructive warning to theoretical structure elucidation of endohedral metallofullerenes involving metal carbide fullerenes that B3LYP method may tend overestimated energies of scandium carbide fullerenes, as B3LYP is a very widely-used method in this field. As mention above, there is a dispute on the structure of Sc2C70 series between experimental and theoretical works.41,42



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Shi et al. proposed that the structure of Sc2C70 should be Sc2C2@C2v(6073)-C68 while a following theoretical work disclosed that Sc2@C2v(7854)-C70 is more thermodynamically stable than Sc2C2@C2v(6073)-C68.41 In Shi’s work, the 13C NMR spectrum of isolated Sc2C70 isomer had 21 distinct lines between δ=135 and 158 ppm, indicating the Sc2C70 isomer has at least 21 unique C atoms, and on the basis of the 13C NMR result, a partial calculation covering seven Sc2@C70 and four Sc2C2@C68 isomers which have 21 unique C atoms was taken, and the calculated results indicated that Sc2C2@C2v(6073)-C68 is the most isomer taking energetic and kinetic factors into account.41 On the contrary, the other complete theoretical investigation with B3LYP method including all the C68 and C70 carbon cages irrespective of 13C NMR result indicated that Sc2@C2v(7854)-C70, which does not have 21 unique C atoms and was not considered in Shi’s work, is the most thermodynamically stable isomer within temperature region of fullerene formation, and that Sc2C2@C2v(6073)-C68 turns the overwhelming isomer only at very high temperature (exceeding 3500 K), as depicted in Figure 2e.42 Like the case of Sc2C2@C72, the energy of Sc2C2@C2v(6073)-C68 might be also overestimated, resulting in that the temperature threshold was delayed. Whether Sc2@C2v(7854)-C70 was more thermodynamically stable than Sc2C2@C2v(6073)-C68 or energy of Sc2C2@C2v(6073)-C68 was overestimated need to be checked in the future unless the single crystal X-ray diffraction of Sc2@C70 or Sc2C2@C68 is gotten. Structural and electronic properties and the simulated infrared spectrum of Sc2C2@Cs(10528)-C72. A comparison of the experimental X-ray structure of Sc2C2@Cs(10528)-C72 and the optimized geometries by the nine DFT methods was performed (Section SIV of supporting information). In general, the geometries optimized by these DFT methods with long range corrections match the X-ray structure better than those without the corrections, and the geometry of wB97XD matches the X-ray structure best, which suggests that wB97XD may be the best option to simulate Sc2C74 series of the nine tested methods. Hence, the structural properties, the Mayer bond order analyses and the simulated Infrared spectrum were carried out by wB97XD method.

a deformed-butterfly shape, and the two Sc atoms resides on pentagon adjacencies of Cs(10528)-C72 cage, and the two C atoms of Sc2C2 locates in the mirror plane of Cs(10528)-C72 cage. The bond length of C73-C74, i.e. C-C bond of Sc2C2 cluster, is only 1.26 Å. To probe electronic properties of Sc2C2@Cs(10528)-C72 isomer, natural bond orbital (NBO) analyses were performed. The natural charge and natural electron configuration of Sc2C2@Cs(10528)-C72 as well as Sc2C24+ tetra-cation, Sc2C26+ hexa-cation and Sc2C2 neutral cluster, whose structures are from the optimized Sc2C2@Cs(10528)-C72 of wB97XD method, are listed in table 2, Taking the electron configuration of Sc2C2 neutral cluster as a reference, encapsulating Sc2C2 into Cs(10528)-C72 cage decreases the 4s orbital populations of Sc atoms by 1.000 electron, whereas the populations of 3d, 4p, 4d and 5p slightly increase, which should be due to the fact that the back-donation from orbitals of C atoms to those of Sc atoms. Compared with Sc2C24+ and Sc2C26+, all the orbitals of Sc atoms of Sc2C2@Cs(10528)-C72, i.e. 4s, 3d, 4p, 4d and 5p orbital, have higher populations, which indicates that Sc2C2 cluster loses less electrons when encapsulated into the Cs(10528)C72, than when Sc2C2 neutral cluster turns Sc2C24+ or Sc2C26+ cation. The natural charges of Sc atoms of Sc2C2@Cs(10528)C72 are about 1.0 e (1.002 e for Sc75 and 1.000 e for Sc76), which are less positive than those of Sc2C24+ and Sc2C26+. The total charge of Sc2C2 cluster of Sc2C2@Cs(10528)-C72 is 1.228 e, which is far away from 4 or 6 e, and this should stem from that covalent interactions between the Sc2C2 cluster and carbon cage play an important role (vide infra). The electron configuration and natural charge population demonstrate that ionic model cannot completely describe the interactions between Sc and C atoms in Sc2C2@Cs(10528)-C72. (The charge of C73 is quite different that of C74, and this originates from the deformed (not perfect) butterfly shape. The bonds of C74-Sc75 and C74-Sc76 are much longer than those of C73-Sc75 and C73-Sc75, which may lead to that Sc atoms donate more electrons to C73. More detailed discussions are given in section SV of supporting information.) Table 3. Mayer bond orders of wB97XD method of Sc2C2 cluster of Sc2C2@Cs(10528)-C72 bond

Figure 2. (a) Front and (b) side views of Sc2C2@Cs(10528)-C72 optimized at wB97XD/6-31G*~Lanl2DZ level. (The two pentalene motifs of Cs(10528)-C72 cage are highlighted in red. Two Sc are labeled with “75” and “76” and C atoms of the encapsulated cluster are labeled with “73” and “74”)

The structure of Sc2C2@Cs(10528)-C72 of wB97XD method, which is the sole thermodynamically stable isomer at temperature region of fullerene formation, is shown in Figure 2. The Sc2C2 cluster is encapsulated into the Cs(10528)-C72 cage with

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orders

bond

orders

C73-C74

1.965

Sc76- C73

0.661

Sc76- C74

0.497

Sc75-C73

0.661

Sc75-C74 Sc76-C11 Sc76-C31 Sc76-C12 Sc76-C60 Sc75-C20 Sc75-C65 Sc75-C1 Sc75-C22

0.495 0.220 0.199 0.156 0.158 0.237 0.158 0.227 0.173

Sc76-C10 Sc-C9 Sc76-C30 Sc76-C59 Sc75-C19 Sc75-C18 Sc75-C66 Sc75-C21

0.237 0.228 0.173 0.218 0.220 0.156 0.218 0.199

Mayer bond order analyses were taken on the basis of wavefunction of wB97XD method to gain insights into bonding interactions, especially for the bonds between encapsulated cluster and carbon cage as well as the bonds within the cluster, and these results are listed in Table 3. Mayer bond order of C73-C74 (two C atoms of encapsulated cluster) is ~2.0, which


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indicates that this bond has a double-bond character. The bond length of C73 and C74 is 1.26 Å, which is shorter than common double bonds, and this should due to the fact that the Sc2C2 cluster is encapsulated into a small cage C72 and is constrained by the small cage. The bond orders between Sc atoms and C73 (including Sc75-C73 and Sc76-C73) are ~0.7, and the orders between Sc atoms and C74 are ~0.5, and even bond orders between Sc atoms and some C atoms of carbon cage, such as Sc76-C10 and Sc75-C19, are ~0.2. These Mayer bond order results suggest that Sc-C bonds of the encapsulated cluster, i.e. Sc75-C73, Sc75-C74, Sc76-C73 and Sc76-C74, have significantly covalent characters, and even covalent interactions between the encapsulated cluster and carbon cage cannot be neglected. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are depicted in Figure 3. The HOMO is mainly distributed on the carbon cage but there are significant overlaps between Sc atoms and carbon cage, which corroborates the covalent interaction between the encapsulated cluster and carbon cage once again. The LUMO is also mainly attributed to cage orbital. It can be speculated in light of populations of HOMO and LUMO that redox reactions will take place mainly on the carbon cage of Sc2C2@Cs(10528)-C72.

Figure 3.The highest occupied molecular orbital (HOMO) (-6.64 eV) and lowest unoccupied molecular orbital (LUMO) (-2.09 eV) diagram of wB97XD method of Sc2C2@Cs(10528)-C72.

The infrared (IR) spectrum was simulated with wB97XD method and is depicted in Figure 4. The IR spectrum can be divided in three regions. The first region at 0-210 cm-1 is attributed to rotating and rocking vibrations of the encapsulated Sc2C2 cluster. The low frequencies of this region are due to the large mass of Sc atoms, and the low intensities of these signals stem from the high symmetry of the Sc2C2 cluster. The second region at 210-1700 cm-1 is corresponding to the breathing and stretching vibrations of carbon cage. Interestingly, there is only one weak signal locating in the third region (> 1700 cm-1), and this signal locating at 1927.95 cm-1 is ascribed to the stretching vibration of C-C bond of the Sc2C2 cluster. This signal can act as a fingerprint signal to distinguish the metal carbide form Sc2C2@C72 from dimetallofullerenes form Sc2@C74.

■ CONCLUSIONS The Sc2C74 series including Sc2@C74 and Sc2C2@C72 series were thoroughly investigated with four DFT methods, namely, B3LYP, CAM-B3LYP, M06-2X and wB97XD, in conjunction

Figure 4. Simulated infrared (IR) spectrum of wB97XD method of Sc2C2@Cs(10528)-C72

with statistical mechanics, and some of the Sc2C74 isomers were further investigated with five other methods, i.e. BLYP, B3PW91, BP86, PBE and PBE0. Our results disclosed that Sc2C2@Cs(10528)-C72 whose cage does not obey the wellknown isolated pentagon rule and has two pairs of pentagon adjacencies possesses the best thermodynamic stability at temperature region of fullerene formation, which is well in line with experiment. A speculation that to synthesis and to isolate other Sc2C74 isomers but Sc2C2@Cs(10528)-C72 are almost impossible was drawn on the basis of the fact that other Sc2C74 isomers possess very small populations at temperature region of fullerene formation. More importantly, we found that B3LYP method as well as other DFT methods without long range corrections, such as BLYP, B3PW91, BP86, PBE and PBE0, tends to overestimate energies of Sc2C2@C72 isomers whereas energies of Sc2@C74 isomers are relatively accurate, and erroneous conclusion will be come to in light of the inaccurate energies, and this overestimation may also hold for other scandium carbide fullerenes and even other metal carbide fullerenes. It is an instructive warning to theoretical investigation on endohedral metallfullerenes that B3LYP and other DFT methods without long range corrections may overestimate energies of metal carbide fullerenes. Physical and chemical properties of Sc2C2@Cs(10528)-C72 were also investigated. Both the highest occupied and lowest unoccupied molecular orbital are mainly distributed on the carbon cage, intimating that redox reactions will occur on the carbon cage. The valence state of Sc2C2@Cs(10528)-C72 cannot be simply described as (Sc2C2)4+@C724-, because covalent interaction between Sc2C2 cluster and carbon cage plays an important role. The IR spectrum was simulated and the signal at 1972.95 cm-1 corresponding to stretching vibration of C-C bond of the Sc2C2 cluster is an important signal to distinguish metal carbide fullerenes from dimetallofullerenes.

■ ASSOCIATED CONTENT Supporting Information. Relative energies and HOMO-LUMO gaps of C724-, C726-, C744and C746- and coordinates of Sc2C2@Cs(10528)-C72, Sc2@C2(13333)-C74, Sc2@C2(13295)-C74 and Sc2@D3h(14246)C74. This material is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION


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The Journal of Physical Chemistry Corresponding Author

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* Fax +86 29 8266 8559; Tel +86 29 8266 5671; e-mail [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work has been financially supported by the National Natural Science Foundation of China (21171138, 21573172, 21503157, 21503159), the National Key Basic Research Program of China (No. 2011CB209404, 2012CB720904), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP No. 20130201110033).

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Warning to Theoretical Structure Elucidation of Endohedral

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