Quantum Chemical Insight into Metallofullerenes M2C98: M2C2@C96

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Quantum Chemical Insight into Metallofullerenes M2C98: M2C2@C96 or M2@C98, Which Will Survive? Hong Zheng,† Xiang Zhao,*,† Wei-Wei Wang,† Jing-Shuang Dang,† and Shigeru Nagase‡ †

Institute for Chemical Physics & Department of Chemistry, State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China ‡ Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan S Supporting Information *

ABSTRACT: Systematic studies on M2C98 (M = Sc, Y, La, Gd, Lu) series by means of density functional theory (DFT) methods disclose that having large concentrations within the temperature interval of fullerene formation, the metal−carbide endohedral fullerenes M2C2@C96 are found to be more stable than the dimetallofullerenes M2@C98. When encapsulating M2C2 clusters, three types of C96 cages will present excellent thermodynamic stabilities and become the largest metal−carbide endohedral fullerenes so far. The dynamic mechanisms of the internal C2 moieties in the most important M2C2@C96 species have been discussed, which provide profound understanding of metal−carbide endohedral fullerenes. Moreover, 13C NMR and IR spectra have been simulated to aid further experimental identification and characterization.

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atoms or metalloclusters.15−19 On the other hand, in the case of M2C2n fullerenes, there always are disputations on M2C2@C2n−2 vs. M2@C2n, which have been persisted for a long time.20−28 Many middle-size M2C2n EMFs tend to take M2C2@C2n−2 model,20,23−29 but there are also reports on the stable M2@C2n EMFs which have been discovered in experimental or theoretical works such as Sc2@C70,22 Sc2@C80,30 La2@C72,31 Td2@C76,32 Dy2@C100,18 etc. Consequently, cautious studies on M2C2n EMFs including the non-IPR isomers indicate that the competition between M2C2@C2n−2 and M2@C2n should be taken into consideration. As for Gd2C98 EMF which was discovered in 200833 by Balch et al., one recent theoretical study has pointed out that a nonIPR isomer (Gd2@C1(168785)-C98) with one pentagon adjacency (PA) should be the most proper product in experiment.19 Nevertheless, it should be noted that the authors did not discuss the relative stabilities of Gd2C2@C96 isomers as comparison. The real structures of such high-spin EMFs, which determine their properties and further applications, should be discussed based on more comprehensive theoretical computations. Besides, Sc2C98 and Y2C98 have been synthesized even earlier in 1994 without isolation.34 One common character among these three kinds of rare earth metal elements (Sc, Y, Gd) is that they have similar valence electron structures as nd1(n + 1)s2. Moreover, as another two types of popular endohedral metal atoms in EMFs, La and Lu also have the same valence electron structures as Gd. Which kind of M2C98

INTRODUCTION Ever since the first endohedral fullerene La@C82 was discovered in 1991,1 endohedral metallofullerenes (EMFs) have attracted wide interests during the past few decades for their unique structural, electronic, and magnetic properties and are expected to be applied in many fields such as electronics, photovoltaics, and biomedicine.2−8 The charge transfer from encapsulated metal atoms or metalloclusters to fullerene cages in the EMFs will stabilize many fullerene isomers which cannot exist in neutral hollow state. Particularly, some fullerene cages violating the well-known isolated-pentagon rule (IPR),9,10 designated non-IPR fullerenes, can become more stable than IPR fullerenes when accept some metal atoms or metalloclusters.8,11−15 Therefore, theoretical study on the stability of EMFs should take both IPR and non-IPR isomers into consideration. As for the large size EMFs, many dimetallofullerenes and trimetallic nitride endohedral fullerenes with carbon cages ≥C90 have been synthesized without structural qualitative analysis. Since many large-scale EMFs can hardly be isolated and characterized in experiments, deep insights into their geometry structures and other significant properties can only be supplied by theoretical methods. However, detailed theoretical studies about the large-scale EMFs is still lacking, and previous works always neglected some important aspects when discussing their relative stabilities. On one hand, recent theoretical reports have better stabilities than the IPR ones when encapsulating certain metal atoms or metalloclusters.15−19 Recent theoretical reports have revealed that the stabilities of some non-IPR structures may surpass most IPR structures, although not always can become the most stable ones, when encapsulating certain metal © 2013 American Chemical Society

Received: October 6, 2013 Revised: October 28, 2013 Published: October 28, 2013 25195

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Figure 1. Relative concentrations of low-energy M2C98 (M = Sc, Y, La, Gd, Lu) isomers.

C96 cages has been probed to supply much deeper understanding of M2C2@C96 EMFs. In addition, the simulated NMR and IR spectra of most stable M2C98 isomers have been calculated to aid further experimental characterization.

structure should be the most stable isomer, and what are the similarities and differences among these five M2C98 (M = Sc, Y, La, Gd, Lu) series? Only more systematic studies could figure out these questions and disclose some important properties of M2C98 EMFs which would be necessary and interesting. In this paper, comprehensive analysis on M2C98 (M = Sc, Y, La, Gd, Lu) series have been carried out with DFT methods based on full screening of 17941 C98 isomers and 12840 C96 isomers (PA ≤ 2). In conjunction with statistical mechanics calculations, the studies on relative stabilities reveal that M2C2@C96 isomers have optimal stabilities in all M2C98 series. Size effects of cages and metal atoms have been discussed in detail. The nanoscale parameters of various M2C2 clusters and the interaction between metalloclusters and C96 cages which have a crucial influence on the macroscopic properties of materials have been presented. Further analysis on electronic structures discloses electron transfer between the metal atoms and C98 cages. The dynamic behavior of the M2C2 clusters in

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EXPERIMENTAL SECTION Since each of the encapsulated metal atoms would donate three electrons in the M2@C98 isomers and the M2C2 clusters always keep a +4 valence state in the fullerene cages, the energetics for all those 17 941 C98 isomers and 12 840 C96 isomers with no more than two PA fragments were first screened at the AM135 level on hexa- and tetraanion states, respectively. Then certain most stable isomers (including IPR and non-IPR isomers) were reoptimized at the hybrid density functional theory B3LYP36−38 level with 6-31G* basis set. The results of C986− series are from the previous report (ref 19). Geometry optimizations of M2@ C98 and M2C2@C96 series with five kinds of rare earth atoms were performed at the B3LYP/3-21G-CEP level (3-21G basis 25196

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development of relative concentrations of M2C98 series within a broad temperature region is presented in Figure 1. The relative concentrations of Gd2C98 series present outstanding stability of Gd2C2@C2(191809)-C96 in a wide temperature interval (Figure 1d). Obviously, Gd2C2@C2(191809)-C96 always shares the largest relative concentration until the temperature reaches around 4200 K, meaning it will possess the best thermodynamic stability among all the isomers in the temperature interval for metallofullerene formation (below 3000 K).46 b. Relative Stabilities of M2C98 (M = Sc, Y, La, Lu) Series. The energy sequences of the rest of M2C98 series are presented in Table S2b−e, also taking the comparison of two probable structural patterns into consideration. Specially, the relative energies of M2@C98 (M = Sc, Y, La, Lu) series are introduced in Table S3 determining the lowest-energy structures of each M2@C98 series. Sc2@C2(230924)-C98, Y2@C1(168785)-C98, La2@C1(168785)-C98, and Lu2@C2(230979)-C98 are the lowest-energy isomers of the four M2@C98 series. Being similar to the Gd2C98 series, Sc2C2@C2(191809)-C96 is predicted as the lowest-energy structure of Sc2C98 series, and Sc2@C2(230924)-C98, the most stable Sc2@C98 isomer as shown in Table S3, has a large relative energy of 19.70 kcal/mol (Table S2b). A non-IPR isomer Sc2C2@Cs(189891)-C96 with one PA fragment has the second lowest energy. Reoptimizations at the B3LYP/6-31G*-CEP level show good accordance to the B3LYP/3-21G-CEP results in both energy sequences and HOMO−LUMO gaps. C2(191809)-C96 is also the carrier cage of the lowest-energy isomer of the Y2C98 series when accepting a Y2C2 cluster (Table S2c), followed by Y2C2@ D2(191838)-C96 with a large relative energy of 10.65 kcal/mol. However, in La2C98 series, La2C2@C2(191809)-C96 loses the energy advantage since it is 4.76 kcal/mol higher than La2@ C1(168785)-C98. The energy sequence of Lu2C98 series is much similar to that of Y2C98 series, which supports Lu2C2@ C2(191809)-C96 as the lowest-energy isomer. Statistical thermodynamic analyses of Sc2C98 series (Figure 1a) show contribution interchanges at around 3000−3200 K, where isomer Sc2C2@C2(191809)-C96 is surpassed by Sc2C2@ D 2 (191838)-C 96 and Sc 2 C 2 @C 1 (191812)-C 96 . Sc 2 C 2 @ C2(191809)-C96 shares the largest contributions in the temperature interval for metallofullerene formation, and so it should be the most important thermodynamic stability isomer. That Sc2C2@D2(191838)-C96 and Sc2C2@C1(191812)-C96 show notable fractions at high temperature indicates that both isomers could also be synthesized experimentally with smaller yields. The lowest-energy Sc2@C98 isomer Sc2@ C2(230924)-C98 is extremely disfavored by the entropy effect. For Y2C98 series, Y2C2@C2(191809)-C96 has the largest contributions below 2600 K (Figure 1b), and then, very surprisingly, it is surpassed by another isomer Y2C2@ D2d(191815)-C96 which has a large relative energy of 14.43 kcal/mol. Thus, the composition of Y2C98 should be mainly composed of Y2C2@C2(191809)-C96 and Y2C2@D2d(191815)C96. Although La2@C1(168785)-C98 is predicted as the lowestenergy isomer of La2C98 series, it is obviously disfavored by the entropy effect since its contribution quickly descends after 200 K and is surpassed by La2C2@C2(191809)-C96 at 580 K. The La2C2@C2(191809)-C96 structure is completely dominant in the temperature interval for metallofullerene formation, while La2C2@D2(191838)-C96 shows notable fractions over 30% at high temperatures as subordinate isomer. Like the case of Y2C98 fullerenes, in the Lu2C98 series, the contribution of the lowestenergy isomer Lu2C2@C2(191809)-C96 is surpassed by Lu2C2@

set for C atoms and CEP-31G basis set with the corresponding pseudopotential for metal atoms), just as the reported Gd2@ C98 series in ref 19. Specially, for the first three lowest-energy isomers of Sc2C98 series, reoptimizations with a larger basis set 6-31G* for C atoms has been carried out, and the results are introduced in Table S2b. Rotational−vibrational partition functions were supplied by the computed structural and vibrational data at the B3LYP/3-21G-CEP level of theory. The simulations of NMR spectra for M2C98 isomers using the gauge-independent atomic orbital (GIAO) method39 are performed at the B3LYP/6-311G-CEP level. The GIAO method has been proven to be very sufficiently accurate at simulating 13C NMR chemical shifts of both fullerenes and metallofullerenes.24,40−42 All computational works above were carried out with the Gaussian03 program package.43

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RESULTS AND DISCUSSION As depicted in Table S1, the D2(191838)-C964− cage is predicted as the most stable C964− anions, followed by another IPR isomer D2d(191815)-C964− with a small relative energy and a much larger HOMO−LUMO gap (1.60 eV). The smallest relative energy of non-IPR cages lies 16.6 kcal/mol above D2(191838)-C964−, indicating poor stabilities of non-IPR C964− anions. Relative Stabilities of M2C98 (M = Sc, Y, La, Gd, Lu) Series. a. Relative Stabilities of Gd2C98. As the most arrestive M2C98 EMFs which has been discussed before, the Gd2C98 series including both Gd2C2@C96 and Gd2@C98 structural patterns have shown rather surprising differences comparing to previous report according to our new results. The potential energy of Gd2C2@C2(191809)-C96 is 5.72 kcal/mol lower than that of the Gd2@C2(230924)-C98 which was predicted as the lowest-energy structure19 (Table S2a) and becomes the lowest energy isomer with a large HOMO−LUMO gap of 1.72 eV. The second lowest-energy isomer Gd2C2@D2(191838)-C96 is 9.26 kcal/mol higher than Gd2C2@C2(191809)-C96. Such a sequence reversal of EMF energy in comparison with the charged series of pristine fullerenes could be found in many theoretical studies on EMF systems.15−17,44 Usually discussion on the charged cages just deals with the possible charge transfer to empty cages. However, in an EMF system the charge transfer (from metallocluster to carbon cage) is not the only factor influencing its thermodynamic stability, steric strain of the whole EMF molecule (due to limited space of fullerene cage), and bonding between metal atom and carbon cage could also profoundly affect the thermodynamic stability of the EMF system.15,22 Therefore, it is reasonable that sometimes the energy sequence of EMF isomers may present some difference to that of the charged cages. Since stability interchanges induced by the enthalpy−entropy interplay always occur in EMFs systems, the relative stabilities of M2C98 series at high temperatures cannot be predicted by only the separation energy itself. Thus, to gain deep insight into the thermodynamic stability of the M2C98 fullerenes, we have investigated the entropy effect and evaluated the relative concentrations based on equilibrium statistical thermodynamic analysis.45 Such thermodynamic investigations have successfully depicted relative stability panoramas for various EMF series.14−16,18,19 Here, the isomers with lower energy gaps (1800 cm−1) in most of the M2C2@C96 isomers, which corresponds to C−C stretching of the internal C2 moieties.

concentrations. Having evident relative energies, the M2C2@ D2d(191815)-C96 (M = Y, Lu) structures are favored by the entropy effect with even larger concentrations than M2C2@ C2(191809)-C96 (M = Y, Lu) structures. As a consequence, the M2C2@C96 species present outstanding thermodynamical stabilities, and they are the largest metal−carbide endohedral fullerenes which are theoretically discovered heretofore. Observations on the geometry structures of M2C2@C96 isomers recover their evident dependence on the size of metal atoms. The analysis of electronic structures for M2C2@C96 isomers discloses that their electronic properties are mainly related to that of the carrier cages, but independent of the geometric structures of M2C2 clusters and the types of metal element. Interestingly, oscillation and rotation mechanisms of the internal C2 moieties in the most important M2C2@C96 species (excepting La2C2@D2(191838)-C96) with rather small barriers have been discovered, suggesting that these EMFs should maintain the same symmetries as their carrier cages. The predicted 13C NMR spectra of various M2C2@C96 species expected to aid future experiment reflect that the chemical shift of the internal C2 moiety may have a strong dependence on the compression and C−C distance of M2C2 clusters in the C96 cages. In addition, the IR spectra of the most significant M2C2@C96 isomers are theoretically predicted to recover the vibration characteristics which would be helpful for future experimental identification. To sum up, our work not only provides a profound understanding of thermodynamic stabilities and electronic/geometric peculiarities of M2C98 metallofullerenes but also assists further experimental research on these large size endohedral fullerenes containing rare earth metal atoms.

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ASSOCIATED CONTENT

* Supporting Information S

Relative energies and HOMO−LUMO gaps of partial C964− isomers and M2C98 series, energetics comparison between two kinds of M2C24+ cations, simulated IR spectra of M2C2@C98 isomers, complete author lists of refs 34, 43, and 47, and coordinates of main M2C2@C98 isomers. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax +86 29 8266 8559; Tel +86 29 8266 5671; e-mail xzhao@ mail.xjtu.edu.cn (X.Z.).

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Notes

CONCLUSIONS Detailed studies on M2C98 (M = Sc, Y, La, Gd, Lu) series by means of DFT calculations in conjunction with statistical thermodynamic analysis reveal that unlike the reported Gd2@ C98 series, the most stable isomers prefer to be metal−carbide endohedral fullerenes. The M2C2@C2(191809)-C96 structures become the lowest-energy isomers in most of the M2C98 series, except in the La2C98 series a La2@C98 structure is lower than isomer La2C2@C2(191809)-C96. Further studies by means of statistical thermodynamic analysis disclose that the most thermodynamically important isomers in all series should choose M2C2@C96 form rather than M2@C98 form. The M2C2@C2(191809)-C96 (M = La, Gd) structures should be the main product in electric arc since they share the largest concentrations within the temperature interval of fullerene formation. The M2C2@D2(191838)-C 96 (M = Sc, La) structures can also be synthesized due to their comparable

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the National Natural Science Foundation of China (21171138), National Key Basic Research Program of China (2012CB720904), and China Postdoctoral Science Foundation (2013M532038).

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The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp409915t | J. Phys. Chem. C 2013, 117, 25195−25204