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Deciphering the Role of Long-Range Interaction in Endohedral Metallofullerenes: A Revisit to ScC 2

70

Rui-Sheng Zhao, Kun Yuan, Sheng-Dun Zhao, Masahiro Ehara, Shigeru Nagase, Josep M. Poblet, and Xiang Zhao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06111 • Publication Date (Web): 23 Aug 2017 Downloaded from http://pubs.acs.org on August 23, 2017

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The Journal of Physical Chemistry

Deciphering the Role of Long-Range Interaction in Endohedral Metallofullerenes: A Revisit to Sc2C70 Ruisheng Zhao,†‡ Kun Yuan,†Shengdun Zhao,† Masahiro Ehara,*‡ Shigeru Nagase,§Josep M. Poblet,# and Xiang Zhao*†‡ †

Institute for Chemical Physics & School of Mechanical Engineering 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 # Department de QuÍmicaFÍsicaiInorgànica, UniversitatRovira I Virgili, Tarragona, 43007, Spain ‡

ABSTRACT:Structure elucidation is a vital step to study endohedral metallofullerene (EMF), and theoretical investigation is a useful complementary way to elucidate structures of EMFs, but our recent work exposed that density functional theory(DFT) methods without long-range corrections are prone to overestimate energies of Sc2C2@C72 isomers. In this work, the role of long-range interaction in energy estimation of EMFs was rigorously investigated by comparing energies and interaction energies of Sc2C70 and La2C96 series with wB97XD, M06-2X, B3LYP and PBE0 methods, and it was disclosed that long-range interaction is ubiquitously imperative for metal cluster fullerenes and conventional metallofullerenes whose cages are absent of adjacent pentagon pair(s). Meanwhile, thermodynamic stabilities of the controversial Sc2C70 series were thoroughly investigated, and Sc2C2@C2v(6073)-C68 with the highest abundance on the temperature range of EMF formation instead of Sc2@C2v(7854)-C70 was confirmed to be the experimentally isolated Sc2C70 isomer by DFT calculations combined with statistical mechanics and simulated UV-vis-NIR spectra.This work could provide instructive guidelines on structure elucidation of EMFs and investigation of reactivity of EMFs.

■INTRODUCTION Fullerenes, which are spherical molecules usually consisting of pentagonal and hexagonal carbon rings, were discovered in 1985.1Large hollow cavities enable fullerenes to encapsulate metal atoms, metallic clusters, and small molecules, such as H2, CO, CH4, NH3, and H2O, and these fullerene derivatives are called endohedral fullerenes (EFs).2,3 Endohedral metallofullerene (EMF) is a unique kind of fullerene derivative and has attracted lots of interest since its first species, i.e. La@C60, was discovered in 1985.4 To date, over 200 kinds of EMFs have been synthesized, isolated and characterized, covering monometal, dimetal, metal carbide, metal nitride, metal oxide, metal sulfide, metal hydrocarbon, and metal carbonitridefullerenes.2 The significant electron transfer from inner metal atoms (or metal clusters) to carbon cages endows EMF with some extraordinary properties which can be used in many fields.5 Structural elucidation is the prerequisite for mining potential values and applications of EMFs, because properties are dictated by structures. Single-crystal X-ray diffraction is the only way to definitively determine structures of EMFs up to now.6,713C NMR spectroscopy,8 mass spectrometry,9 UV-visNIR absorption spectroscopy10 can also provide some important but not precise information of structures of EMFs, such as symmetries of EMF molecules and molecular formulas of EMFs. It is noteworthy that X-ray powder diffraction can-

not correctly determine structures of EMFs,sometimes. For instance, Sc2@C66was initially interpreted to possess the C2v(4348)-C66 cage by 13C NMR spectroscopy and maximumentropy method/Rietveld analysis with synchrotron X-ray powder diffraction,11 but the recent single-crystal X-ray diffraction study demonstrated that the Sc2@C66 is of the C2v(4059)-C66 cage, which contains two sets of unsaturated linear triquinanes.12 Unfortunately, in many cases, single-crystal X-ray diffraction studies were hampered by low availability of EMFs and rotational disorder of EMF crystals.2 Theoretical studies, which can give reliable information of structures of EMFs, are complementary to single-crystal X-ray diffraction studies. On the basis of potential energies and orbital gaps, thermodynamic and kinetic stabilities of different isomers of a EMF series can be roughly appraised; nevertheless this method is not precise enough sometimes because the energies and gaps can only appraise the stabilities at absolute zero but EMFs are usually produced at elevated temperature about 500−3500 K.13-15 A more precise method is to calculate relative concentration (abundance) of each isomer within a wide temperature range by means of statistical mechanics.16,17 Our recent work exposed that density functional theory (DFT) methods without long-range corrections tend to overestimate energies and underestimate abundance of Sc2C2@C72, which can lead to erroneous structure elucidation, but the underlying causes for this still remain a puzzle.18

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Table 1. Relative Energies (in kcal/mol) and HOMO−LUMO (for Closed Shell) or SOMO−LUMO (for Open Shell) Gaps (in eV) of Sc2C70Seriesa wB97XD/M06-2Xb Sc2@C2v(7854)-C70

B3LYP

PA

Multiplicity

∆E

gap

∆E

gap

|∆(∆E)|c

3

singlet

0.0

4.51

2.6

1.42

2.6

d

Sc2@C2(7892)-C70

2

singlet

0.2

3.93

0.0

1.16

0.2

Sc2@C2(7957)-C70

2

singlet

2.0

4.23

3.3

1.50

1.3

Sc2C2@C2v(6073)-C68

2

singlet

15.1

4.29

33.2

1.55

18.1

Sc2C2@C2(6146)-C68

2

singlet

27.6

3.98

44.2

1.25

16.6

Sc2C2@C1(6148)-C68

2

singlet

36.3

3.78

52.6

1.07

16.3

La2@D2(191838)-C96

0

triplet

0.0

2.17

0.0

0.97

0.0

La2@D2(191853)-C96

0

triplet

4.8

1.91

3.3

1.32

1.5

La2@C2(191809)-C96

0

triplet

6.2

2.02

4.6

1.28

1.6

La2C2@Cs(153479)-C94

0

singlet

32.3

2.88

32.3

1.63

0.0

La2C2@C2(153476)-C94

0

singlet

32.6

2.65

31.0

1.31

1.6

La2C2@C1(153491)-C94

0

singlet

40.5

2.59

37.9

1.35

2.6

a

The basis set is 6-31G*~Lanl2DZ for both wB97XD and B3LYP methods.

b

The energies of Sc2C70 and La2C96 were calculated by wB97XD and M06-2X method respectively

c

The |∆(∆E)| which is defined to reflect inconsistency of relative energies of the two methods equals the absolute value of difference between relative energies with the two method. d

The ground state of Sc2@C2(7892)-C70 isomer of B3LYP method is triplet, different from the result of wB97XD method.

Inthe present work, we investigated a controversial EMF series, namely Sc2C70 series, by means of DFT methods with and without long-range corrections combined with statistical mechanics.Shi et al. first isolated the Sc2C70 isomer, and determined the isomer as Sc2C2@C2v(6073)-C68 by means of timeof-flight mass spectrum, UV-vis-NIR absorption spectrum, and13CNMRspectrum,19 whereas Zheng et al. theoretically demonstrated that Sc2@C2v(7854)-C70 is the most thermodynamically stable isomer within the temperature region of EMF formation.20 In Shi's work, there were 21 distinct lines between δ = 135 and 158 ppm in the 13C NMR spectrum of theisolated Sc2C70 isomer, indicating that the Sc2C70 isomer possesses at least 21 unique C atoms, and only eleven isomersincluding seven Sc2@C70 and four Sc2C2@C68isomers can satisfy this criterion. On the basis of energies and orbital gaps, Shi et al. narrowed down the eleven candidates to Sc2C2@C2v(6073)C68. Oppositely, Zheng et al. performed a complete investigation of Sc2C70 series, including all the Sc2C2@C68 and Sc2@C70 isomers, by B3LYP and PBE0 methods combined with statistical mechanics, and the calculated results indicated that Sc2@C2v(7854)-C70 is the most thermodynamically stable isomer at the temperature of EMF formation (Note that neither B3LYP nor PBE0 contains long-range corrections). Recently, Zheng's work was queried, and in particular, the minimum bond resonance energy of C2v(7854)-C704- is too small, indicating that Sc2@C2v(7854)-C70 is not kinetically stable (The electronic structure of Sc2@C2v(7854)-C70 is reckoned to be (Sc2+)2@C2v(7854)-C704-).21 In present work, the controversial Sc2C70 series were investigated with DFT methods with and without long-rang corrections, and moreover, the puzzle what

role of long-range interactions plays in stabilization EMFs were thoroughly deciphered.

■COMPUTATIONAL SECTION Since each Sc atom of Sc2@C70 and Sc2C2 cluster of Sc2C2@C68 denote three and four electrons to carbon cage respectively, 69 tetra- C68 and 146 hexa- C70 carbon cage anions with 0−3 adjacent pentagon pairs (PA) were first screened at the semiempirical AM1 level.22 Then, the cage anions whose relative energies were no more than 30 kcal/mol were selected and reoptimized at B3LYP/6-31G* level,23 and those cage anions with relative energies less than 20 kcal/mol were chosen as candidates to encapsulated scandium atoms or scandium carbide clusters. Sc2@C70 and Sc2C2@C68 isomers were optimized by two long-range corrected DFT methods, i.e. wB97XD24 and M06-2X,25 and two DFT methods without long-range corrections, i.e., B3LYP,23 and PBE0 (PBE1PBE),26 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 role of long-range interaction in energy estimation of dimetallofullerenes and metal carbide fullerenes, six isomers of another EMF series, La2C96,27 were also investigated by thesimilar methods except wB97XD (wB97XD method is not available for lanthanum, since this method has no van der Waals radius for lanthanum) to those of Sc2C70 series as a comparison, and interaction between inner moieties and carbon cages was calculated including basis set superposition error (BSSE) corrections using the counterpoise method.28,29 Vibrational frequency analyses were carried out on the


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Figure 1. Binding energies (in kcal/mol) of Sc2C70 (1, Sc2C2@C2v(6073)-C68; 2, Sc2C2@C2(6146)-C68; 3, Sc2C2@C1(6148)-C68; 4, Sc2@C2(7892)-C70; 5, Sc2@C2(7957)-C70; 6, Sc2@C2v(7854)-C70), Sc2C74 (1, Sc2C2@Cs(10528)-C72; 2, Sc2C2@Cs(10616)-C72; 3, Sc2C2@D2(10611)-C72; 4, Sc2@C2(13295)-C74; 5, Sc2@C2(13333)-C74; 6, Sc2@D3h(14246)-C74), and La2C96(1, La2C2@C2(153476)-C94; 2, La2C2@Cs(153479)-C94; 3, La2C2@C1(153491)-C94; 4, La2@C2(191809)-C96; 5, La2@D2(191835)-C96; 6, La2@D2(191838)-C96) series calculated with B3LYP (blue), wB97XD (red), and M06-2X (green) methods

optimized structures at the same level of theory to verify the stationary points as minima and also to produce necessary data for rotational−vibrational partition functions which were calculated on the basis of the structural and vibrational data (only the rigid rotator and harmonic oscillator quality though, and without frequency scaling). The relative concentration (mole fraction) wi of the isomer i among all the m isomers was calculated by eq 1, expressed by partition functions of isomer i, i.e. qi and enthalpy at absolute zero ∆, equal to the potential energy∆, , ∆, /

∑

! ∆, /

(1)

where R and T are gas constant and absolute temperature.16,17 UV-vis-NIR spectra were simulated by time-dependent (TD) DFT calculations in carbon disulfide CS2 using the polarized continuum model (PCM)30 at B3LYP/6-31G*~Lanl2DZ level, since B3LYP gives more accurate results in respect of TDDFT calculations.31 All these calculations were implemented with Gaussian 09 program.32

■RESULTS AND DISCUSSION Relative energies of tetra-anions C684- and hexa-anions C706- of AM1 and B3LYP methods are collected in Tables S1−S4 of the Supporting Information. Both the semiempiricism and DFT results indicate that C2v(6073)-C684- and C2v(7854)-C706are the most stable anions of C684- and C706- anions, respectively. Relative energies and HOMO−LUMO (for closed shell) or HOMO−SOMO (for open shell) gaps of DFT methods are collected in Tables 1 and S5 of the Supporting Information (Table S5 gives the energies and gaps of more Sc2C70 isomers, as well as the results of M06-2X and PBE0 methods). The results of wB97XD method show that Sc2@C2v(7854)-C70 is the most stable isomer of Sc2C70 series, and Sc2@C2(7892)-C70 and Sc2@C2(7957)-C70 are less stable byonly 0.2 and 2.0 kcal/mol respectively, and Sc2C2@C2v(6073)-C68 with a relative energy of 15.1 kcal/mol is the most stable isomer of Sc2C2@C68 subseries. As for B3LYP method, Sc2@C2(7892)C70 instead of Sc2@C2v(7854)-C70 is the most stable isomer of Sc2C70 series, even though Sc2@C2v(7854)-C70 is also of very

high stability (it relative energy is only 2.6 kcal/mol), and these results are different from the previous work which reported that Sc2@C2(7892)-C70 isomer was lessstable than Sc2@C2v(7854)-C70 by 2.07 kcal/mol at the same level of theory, and thisinconstancy can be ascribed to that singlet was erroneously reckoned as the ground state of Sc2@C2(7892)C70isomer in the previous work.20 These energy variances for wB97XD and B3LYP methods are rational and can be attributed to the fact that the two DFT methods utilize integrals of different functions of the density and the density gradient to compute exchange and correlation functional.23-26 Sc2C2@C2v(6073)-C68 is also the most stable isomer of Sc2C2@C68 subseries for B3LYP method, but its relative energy is as high as 33.2 kcal/mol (18.1 kcal/mol higher than that of wB97XD method). Not only for Sc2C2@C2v(6073)-C68 but also for all the Sc2C2@C68 isomers, the relative energies of B3LYP (as well as PBE0) method are much higher than those of wB97XD (and M06-2X) method while for Sc2@C70 subseries, the relative energies of different DFT methods with and without long-range corrections are quite consistent as shown in Tables 1 and S5 of the Supporting Information. The absolute value of the difference between relative energy of a particular isomer of B3LYP and wB97XD methods is denoted as |∆(∆E)| and listed in Table 1, and the value of |∆(∆E)| can reflect the magnitude of consistency of relative energies obtained with different DFT methods. For the Sc2C2@C68 subseries, the relative energies of B3LYP methodare much higher than those of wB97XD method (the |∆(∆E)|s are more than 15.0 kcal/mol), while for Sc2@C70 subseries, the relative energies of the two DFT methods are quite similar (the |∆(∆E)|s are only about 5.5 kcal/mol). As is the case of Sc2C74 series in which relative energies of Sc2C2@C72 subseries are severely overestimated by the DFT methods without long-range corrections, including B3LYP, BLYP, B3PW91, BP86, PBE, and PBE0 methods,18 the B3LYP and PBE0 methods overestimate relative energies of Sc2C2@C68 subseries again, but give relatively accurate results for the conventional dimetallofullerene Sc2@C70 subseries (the results of PBE0 and M06-2X are collected in Table S5 of the Supporting Information). Do the conventional DFT methods without long-range corrections, such as B3LYP and PBE0, tend to overestimate energies of all the metal carbide fullerenes, M2C2@C2n-2? We



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also investigated six isomers of another EMF series,La2C96 as a comparison. Definitely contrary to the cases of Sc2C70 and Sc2C74series,18 the DFT methods with and without long-range corrections (M06-2X, B3LYP and PBE0 methods) give similar energies for both La2C2@C94 and La2@C96 subseries (Table 1). To shed light on the role of long-range interaction in energy estimations of the EMFs, interaction energies (IEs) between inner moieties and carbon cages were calculated utilizing the counterpoise method including BSSE corrections and illustrated in Figure 1 and listed in Table S6 of the Supporting Information.

Figure 2. Structures of (a) Sc2@C2v(7854)-C70, (b) Sc2C2@C2v(6073)-C68, (c) Sc2@C2(13295)-C74, (d) Sc2C2@Cs(10528)-C72 optimized with wB97XD method, (e) La2@D2(191838)-C96, and (f) La2C2@C1(153491)-C94 optimized at M06-2X method (pentalene motifs are highlighted in red and Sc-C and La-C distances are in Å).

In general, IEs of M2@C2n isomers are larger than those of M2C2@C2n-2 isomers (M=Sc and La; 2n=70, 74, and 96). Moreover, for Sc2C70 and Sc2C74 series, IEs of Sc2C2@C68 and Sc2C2@C70 subseries of wB97XD and M06-2X methods are larger than those of B3LYP and PBE0 methods, but IEs of Sc2@C70 and Sc2@C74 subseries of the four methods are much more consistent. These results indicate that long-range interaction plays a more important role in carbide Sc2C2@C68 and Sc2C2@C72 subseries than in dimetal Sc2@C70 and Sc2@C74 subseries. This can be interpreted from difference between the structures of metal carbide subseries, Sc2C2@C68 and

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Sc2C2@C72, and dimetal subseries, Sc2@C70, and Sc2@C74, shown in Figures 2a-2f and S1 of the Supporting Information. The distances denoted as dM-cage and Mayer bond orders between metal atoms (M=Sc, La) and vicinal cage carbon atoms are collected in Tables S7 and S8 of the Supporting Information respectively. The dM-cage values and Mayer bond orders of carbide Sc2C2@C68 and Sc2C2@C72 isomers are ~0.1 Å larger and ~0.1 smaller than those of dimetal Sc2@C70 and Sc2@C74 isomers for both wB97XD and B3LYP methods respectively, indicating that the coordination between inner moieties and carbon cages ofSc2C2@C68 andSc2C2@C72 subseries are weaker than those of Sc2@C70 and Sc2@C74 subseries. These structural differences should be due to the fact that Sc atoms of Sc2@C70 and Sc2@C74 subseries can be effectively coordinated by pentalene motifs of carbon cages while forSc2C2@C68 andSc2C2@C72 subseries, this coordination is constrained to some extent by the shapes of Sc2C2 clusters. The weaker coordination of Sc2C2@C68 and Sc2C2@C70 subseries results in that long-range interaction plays a more important role in estimation of interaction between inner Sc2C2 clusters and carbon cages than in that of dimetal Sc2@C70 and Sc2@C74 counterparts. As the interaction between inner moieties and carbon cages is the paramount ingredient to stabilize EMFs,33 conventional DFT methods devoid of long-range corrections are prone to severely overestimate energies of Sc2C2@C68 and Sc2C2@C72 series. Contrary to the cases of Sc2C70 and Sc2C74 series, IEs of M06-2X are larger than those of B3LYP and PBE0 methods for both the carbide La2C2@C94 and dimetal La2@C96 subseries, indicating that long-range interaction is a crucial part of the interaction between inner moieties (La2C2and La2) and carbon cages (C94 and C96) for both the two subseries. The dMcage values and Mayer bond orders of La2C2@C94 subseries are as large as those of La2@C96 subseries, suggesting the coordination of the two subseries are comparative, which is different from the situations of Sc2C70 and Sc2C74 series. Unlike the cases of Sc2C70 or Sc2C74 series18 in which most of the stable isomers adopt the non-IPR cages (the cages violating the wellknow isolated pentagon rule34), the stable isomers of La2C96 series (both La2C2@C94 and La2@C96 subseries) prefer to adoptIPR cages (no pentalene motif), resulting in that the inner moieties, i.e. La2 and La2C2, cannot be effectively coordinated by cages, and this is also the reason why long-range interaction is innegligible for La2@C96 subseries but negligible for Sc2@C70 and Sc2@C74 subseries. Therefore, conventional DFT methods without long-range corrections are prone to underestimate the interaction for both the two subseries of La2C96. However, why B3LYP, PBE0, and M06-2X methods give similar energies for both La2C2@C94 and La2@C96 subseries? It is not a profound mystery. When the thermodynamic stabilities of a particular EMF series are investigated,attentions are usually focused on relative energies ratherthan absolute energies. The isomer with the lowest energy is taken as the reference benchmark,and its energy is artificially set to be zero. If the absolute energies of reference benchmark and other isomers are erroneously estimated to the similar extent, accurate relative energies will be obtained though. Oppositely, if the


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Figure 3. The profile of difference between binding energy of DFT methods with and without long-range corrections (a, Sc-C8H6 model, b, Sc2C2-(C8H6)2 model).

absolute energies of the isomers are misestimated to different degree or if only some of the isomers are misestimated, the calculated relative energies must be inaccurate. In fact, the B3LYP as well as PBE0 method overestimates absolute energies of the La2C2@C94 and La2@C96 isomers to the similardegree but overestimates those of Sc2C2@C68 (and Sc2C2@C72) and Sc2@C70 (and Sc2@C74 isomers) to the different degree, which can be corroborated by almost identical difference between absolute energies (AEs) of different DFT methods, and the similar dM-cage values and Mayer bond orders of La2C2@C94 and La2@C96 subseries can also support this point (the absolute energies of Sc2C70, Sc2C74, and La2C96 series are collected in Table S9 of the Supporting Information). To ascertain the relationship between magnitude of the deviation stemming from long-range interaction and structures, ∆IE which is the difference between interaction energies of B3LYP and wB97XD (this index can reflect the magnitude of long-range interaction) profiles along distance between metal and cage were computed and depicted in Figures 3a and 3b. Pentalene C8H6 was utilized to model carbon cage on basis of the fact that metal atoms strongly interact with abut pentagon motifsfor the EMFs with non-IPR cages, and this model was proposed by Popov and co-workers,35 and an index X in range of 1.7−2.5 Å which is the distance between Sc atoms and middle points of C-C bonds shared by two pentagon was defined to describe the Sc-cage distance, and the 1.7−2.5 Å range can cover almostall the situations of the EMFs with non-IPR cages. The IEs of wB97XD are larger than those of B3LYP method for both the two models. The ∆IEs of Sc-C8H6 increase with the increase of X, while the ∆IEs of Sc2C2-(C8H6)2 decrease with the increase of X. The magnitude of long-range interactions is negligible on a large X range for Sc-C8H6 (modeling Sc2@C2n) but important for Sc2C2-(C8H6)2 (modeling Sc2C2@C2n-2). These results suggest that long-range interaction is not exclusively important for the EMF series discussed in present work. As for the large dimetallofullerenes M2C2n (C2n≥ 90), since these EMFs usually adopt IPR cages,2 the inner metals cannot be effectively coordinated, leading to that long-range

interaction is imperative for both M2@C2n and M2@C2n-2 subseries especially for the isomers with spherical cages (ellipsoidal IPR-cages coordinate inner moieties a little stronger than spherical IPR-ones. For instance, the La-cage distances of ellipsoidal La2C2@D5(450)-C100 are smaller those of spherical La2C2@C2(41)-C90, La2C2@D3(85)-C92, La2C2@C1(132)-C94, La2C2@C2(157)-C96, and La2C2@C1(175)-C98).27,36 For the cases of clusterfullerenes including carbide, nitride, oxide, methano, and cyanoclusterfullerenes, long-range interactions are vital for all the isomers regardless of whether the cages are IPR-ones or not, due to the constraint of clusters. Therefore, DFT methods without long-range corrections may give the seemly right relative energies for EMFs with IPR cages clusterfullerenes except carbide clusterfullerenes which usually rival with conventional dimetal or trimetal fullerenes, since all the isomers may be overestimated to the nearly same degree. One case is that the B3LYP method gives similar relative energies of Sc3N@C82 series compared to M06-2X, and wB97XD methods.37 However, it is still dangerous to utilize the methods without long-range corrections to investigate the reactivity and regioselectivity of the clusterfullerenes and conventional EMFs (Mx@C2n) with IPR cages, because the interaction between inner moieties and carbon cages has a big influence on the reactivity and regioselectivity.38 The thermodynamic stabilities of Sc2C70 series at high temperature were investigated on the basis of potential energies combined with statistical mechanics calculations. The concentration-temperature curves of Sc2C70 series of wB97XD and B3LYPmethods are illustrated in Figures 4a and 4b, respectively. For wB97XD method, at the absolute zero, Sc2@C2v(7854)-C70 is the most abundant isomer, and its concentration decreases with the increase of temperature, while the concentration of Sc2C2@C2v(6073)-C68 (as well asSc2C2@C2(6146)-C68) increases, and surpasses that of Sc2@C2v(7854)-C70at ~2400 K. For B3LYP method, Sc2@C2(7892)-C70 is the richest isomer within a wide range of temperature, and Sc2C2@C2v(6073)-C68 turns the overwhelming isomer at very high temperature (over 4000 K). The



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Figure 4. Relative concentrations of Sc2C70 series calculated by wB97XD (a) and B3LYP (b) methods within temperature range from 0 to 6000 K. (the curves of those isomers with low relative concentrations are omitted for clarity).

concentration-temperature curve of B3LYP produces misleading structure elucidation that Sc2@C2(7892)-C70 is the most thermodynamically stable isomer on the temperature range of EMF formation and the most likely one to be synthesized and isolated. This erroneous elucidation of B3LYP method stems from that long-range interaction between inner Sc2C2 clusterand C68 cage is disregarded. As depicted in eq 1, the energy deviations were further exponentially magnified when relative concentrations were calculated. The UV-vis-NIR spectrum of the experimentally isolated Sc2C70 isomer19 and the stimulated ones of Sc2@C2v(7854)-C70 and Sc2C2@C2v(6073)-C68 are shown in Figures 5a, 5b, and 5c respectively. It can be determined that the isolated Sc2C70 isomer is Sc2C2@C2v(6073)-C68 rather than Sc2@C2v(7854)-C70 by comparing the UV-vis-NIR spectrum of isolated Sc2C70 isomer with the simulated ones of the two controversial isomers. There are three absorption peaks located at 570, 841, and 1126 nm in the spectrum of the isolated Sc2C70 isomer. The simulated one of Sc2@C2v(7854)-C70 possesses six peaks at 268.4, 321.6, 488.8, 647.2, 708.8 and 737.6 nm, and the information that the two peaks at 488.8 and 647.2 nm exhibit similar strength and that there is no peak around 1126 nm is definitely inconsistent from that of the isolated Sc2C70 isomer, i.e., Figure 5a. On the other hand, there are five peaks at 270.7,295.0, 495.0, 730.0, and 980.0 nm in the simulated UVvis-NIR spectrum of Sc2C2@C2v(6073)-C68, and the peaks at 495.0, 730.0, and 980.0 nm can be related to the peaks at 570, 841,and 1126 nm of the isolated isomer respectively.

■ CONCLUSIONS

Figure 5. UV-vis-NIR spectrum of the experimentally isolated Sc2C70 isomer (a), and simulated ones of Sc2@C2v(7854)-C70(b) and Sc2C2@C2v(6073)-C68(c), where (a) was reproduced with permission from ref 19. Copyright 2006 WILEY-VCH VerlagGmbh&Co.KGaA, Weinheim.

The thermodynamic stabilities of Sc2C70 series were investigated by four DFT methods, i.e., wB97XD, M06-2X, B3LYP, and PBE0, combined with statistical mechanics. The calculated results show that Sc2C2@C2v(6073)-C68 is the most thermodynamically stable isomer of Sc2C70 series within the temperature of EMF formation. The DFT methods without long-range corrections, such as B3LYP and PBE0, tend to underestimate stabilities of Sc2C2@C68 subseries, analogous to the case of Sc2C2@C72 subseries. On the contrary, the B3LYP and PBE0 methods give nearly identical relative energies of La2C2@C94 subseries to M06-2X method. The interaction energies dis-


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closethat long-rang interaction plays an important role in Sc2C2@C68, Sc2C2@C72, La2C2@C94, and La2@C96 subseries, but a minor role in Sc2@C70 and Sc2@C74 subseries. This can be attributed to the structure difference between the two groups of EMFs. For the former group, i.e., Sc2C2@C68, Sc2C2@C72, La2C2@C94 and La2@C96subseries, the inner moieties cannot be effectively coordinated by cages due to constraint of the shapes of inner clusters (Sc2C2@C68, Sc2C2@C72, and La2C2@C94) or lack of pentalene motifs of the cages (La2C2@C94 and La2@C96). The rule can be further expanded other EMFs, and in other words, long-range interaction is imperative for clusterfullerenes and conventional fullerenes with IPR cages. It is noteworthy that the DFT methods without long-range corrections may give seemly correct relative energies for some EMF series, because all the isomers may be systemically overestimated to the same degree, but it is dangerous to use these methods to investigate reactivity and regioselectivity of these EMFs. The simulated UV-vis-NIR spectra of Sc2@C2v(7854)-C70 and Sc2C2@C2v(6073)-C68 also confirm that the experimentally isolated Sc2C70 isomer should be Sc2C2@C2v(6073)-C68 rather than Sc2@C2v(7854)-C70.

■ ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Relative energies of C684-, C706-, and Sc2C70 isomers structures of the most stable isomers of Sc2C70, Sc2C74, and La2C96 series, interaction energies, metal-cage distances, Mayer bond orders, absolute energies of Sc2C70, Sc2C74, and La2C96 series (PDF), and coordinates of EMF isomers (ZIP).

■ AUTHOR INFORMATION Corresponding Author *[email protected]. *[email protected].

Notes The authors declare no competing financial interests.

■ACKNOWLEDGMENT This work was financially supported by the National Natural Science Foundation of China (Nos. 21573172, 21773181, and 21663024) and the China Postdoctoral Science Foundation (2017M613125). One of authors (X. Zhao) appreciates JSPS for an Invited Professorship (Short-term) for Academic Research in Japan (S17037). The financial support from the Nanotechnology Platform Program (Molecule and Material Synthesis) of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan is also acknowledged.

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