Theoretical Insights into the Metal–Nonmetal Interaction Inside M2O@C2v(31922)-C80 (M = Sc or Gd)

The metal–nonmetal interaction is complicated but significant in organometallic chemistry and metallic catalysis and is susceptible to the coordination surroundings. Endohedral metallofullerene is considered to be an excellent model for studying metal–nonmetal interactions with the shielding effect of fullerenes. Herein, with the detection of ScGdO@C80 in a previous mass spectrum, we studied the effects of metal atoms (Sc and Gd) on the metal–nonmetal interactions of the thermodynamically stable molecules M2O@C2v(31922)-C80 (M = Sc and Gd), where metal atoms M can be the same or different, using density functional theory calculations. The inner metal atom and the fullerene cage show mainly ionic interactions with some covalent character. The Sc atom with higher electronegativity plays a greater important role in the metal–nonmetal interactions than the Gd atom. This study would be useful for the further study of the metal–nonmetal interaction.


■ INTRODUCTION
Endohedral metallofullerene (EMF) is a unique carbon nanomaterial in which metal ions, metal atoms, or metal clusters are embedded in fullerene carbon cages. Since the discovery of LaC 60 , the prototype of EMFs, in 1985, 1 EMFs have attracted much attention because of their unique core− shell structure and promising applications in biomedicine, solar cells, and materials science. 2−7 Additionally, more and more EMFs have been reported, such as Sc 3 N@C 2n (2n = 68−70 and 78−82), 8−16 Sc 2 C 2 @C 2n (2n = 68, 72−74, and 80− 84), 17−22 Sc 2 S@C 2n (2n = 70 and 82), 23−25 YCN@C 82 , 26 Sc 3 CH@C 80 , 27 Sc 3 NC@C 2n (2n = 78−80), 28,29 and Sc 2 O@ C 2n (n = 35−47). 30−35 According to the types of inner clusters, clusterfullerenes can be classified into nitride clusterfullerene, carbide clusterfullerene, sulfide clusterfullerene, cyanide clusterfullerene, metal hydrocarbon clusterfullerene, metal carbonitride clusterfullerene, and oxide clusterfullerene (OCF). 36 OCFs, including Sc 2 O@C 2n , Ho 2 O@C 74 , 37 Ho 2 O@C 84 , 38 Dy 2 O@C 80 , 39 etc., have been widely studied. In particular, Sc 2 O@C 2n has attracted much attention since 2010 due to their successful preparation and characterization. The molecular orbital energy levels and internal cluster dynamics of OCFs rely on both the cluster and the carbon cages. 36 In general, with the increase in of the size of the carbon cage, the angle of Sc−O−Sc clusters gradually increases and the M 2 O clusters become more disordered. This may be attributed to the strong metal−carbon interaction and the spatial limitation of fullerene cages. 31 Clusterfullerene is an ideal model for studying the interaction between metals and nonmetals (C, N, and O atoms), which is of great significance for the reasonable design of metal−organic frameworks and metal catalysts that show promising and excellent applications in dealing with global warming and the energy crisis. In addition, the study of the metal−nonmetal interaction in EMFs is very important to reveal the reaction selectivity and predict the molecular structure and reactivity of EMFs. 40−42 To date, there have been many studies on the metal−nonmetal interaction in the model of clusterfullerenes, but only a few studies on the effect of different metals on the metal−nonmetal interaction in the same fullerene cage. Luckily, Chen et al. isolated a mixed metal oxide cluster fullerene (MMOCF), ScGdO@C 82 , for the first time in 2018. 43 The mass spectra showed the existence of ScGdO@C 80 , and Sc 2 O@C 80 32 was prepared previously. Clearly, ScGdO@C 80 is an excellent prototype to understand the effect of Gd and Sc on the metal−nonmetal interaction. Here, a theoretical study was first carried out on the thermodynamic stability, geometry, and electronic structure of ScGdO@C 80 . Then, the metal−nonmetal interaction in M 2 O@C 2v (31922)-C 80 (M = Sc and Gd), where metal atoms M can be the same or different, was studied and compared in detail using density functional theory (DFT) calculations and wave functional analyses. Note that the name of the fullerene cage in references has not been changed with respect to the original authors, and in this work we use the spiral number to name the fullerene cages.

■ COMPUTATIONAL DETAILS
The previous study 44 showed the relative stability of anion C 80 4− , wherein seven lowest-energy tetra-anionic cages (less than ∼40 kcal·mol −1 ) were selected to encase ScGdO. Then, the optimizations of ScGdO@C 80 were performed at the BP86/6-31G(d)∼CEP-4G level of theory, 45−48 where the basis set 6-31G(d) was used for C and O atoms and CEP-4G, including the pseudopotential function, was used for Sc and Gd atoms. The BP86 function has been used to study many EMFs theoretically 32,44,49 with negligible spin contamination. The core electron of the heavy metal atom will not affect the electronic features of metal-based complexes, and the CEP-4G basis function including a pseudopotential can accurately describe the electronic features of Gd. The vibration frequency analysis was carried out at the same theoretical level to confirm that all the stationary points were minimums and free from an imaginary frequency. Furthermore, the results of the singlepoint calculations at the ωB97X-D/6-31G(d)∼CEP-4G level of theory confirm the optimization results at the BP86/6-31G(d)∼CEP-4G level of theory, indicating the rationality of the theoretical levels in the present work. Based on the structure and vibration data, the relative concentration of ScGdO@C 80 and the enthalpy−entropy effect were calculated, which is a reliable method of evaluating the thermodynamic stability of EMFs in the fullerene-formation temperature region. 50−52 The interaction energies of ScGdO@C 80 , Sc 2 O@C 80 , and Gd 2 O@C 80 were also calculated to elucidate their relative stabilities. Their electronic structures were studied by natural population analysis, and infrared (IR) spectra were also simulated to give more information to help characterize the structures experimentally. All the above DFT calculations in this work were performed with the Gaussian 16 program. 53 The Mayer bond order analysis, the DOS, and the BCP analysis were based on the results of the geometric optimization and frequency calculation at the BP86/6-31G(d)∼CEP-4G level of theory and were carried out the with Multifwn program 54 to study the interactions between metal and nonmetal atoms.

■ RESULTS AND DISCUSSION
According to the ionic model of EMFs, the seven low-lying C 80 4− anions were selected to encage ScGdO cluster. 44 After the encapsulations, IPR ScGdO@C 2v (31922)-C 80 possesses the lowest potential energy, followed by IPR ScGdO@ I h (31924)-C 80 and ScGdO@D 5h (31923)-C 80 with higher relative energies of 2.4 and 6.0 kcal·mol −1 , respectively, as shown in Table S1. Additionally, because of the electron transfer, the energy gaps between the singly occupied molecular orbital (SOMO) and the lowest unoccupied molecular orbital (LUMO) of the ScGdO@C 80 isomers ( Figure S1) decreased after the encapsulation compared with those of the C 80 4− anions. 44 The energies of the single-point calculations at the ωB97X-D level of theory also indicate that ScGdO@C 2v (31922)-C 80 has the lowest relative energy (Table  S1). As shown in Figure 1, the statistical thermodynamic analysis of ScGdO@C 80 isomers, including the enthalpy− entropy effects, confirmed the highest concentration of ScGdO@C 2v (31922)-C 80 in the whole temperature region, followed by ScGdO@I h (31924)-C 80 and ScGdO@ D 5h (31923)-C 80 with highest concentrations of no more than 24.1% and 10%, respectively, below about 2500 K; this showed that ScGdO@C 2v (31922)-C 80 had the highest thermodynamic stability. The accuracy of this theoretical method has been confirmed in many experiments, such as those for Sc 2 O@ T d (19151)-C 76 , Sc 2 O@C 2v (5)-C 80 , Sc 2 O@C s (6)-C 82 , and Sc 2 O@C 3v (8)-C 82 . [32][33][34]55 Besides, Sc 2 O@C 2v (5)-C 80 has been isolated 32 with the same carbon cage as optimal ScGdO@C 2v (31922)-C 80 . To elucidate the effect of inner metal atoms on M 2 O@C 2n (M = Sc and Gd), including the metal−nonmetal interactions, crystallized Sc 2 O@C 2v (31922)-C 80 and the Gd 2 O@C 2v (31922)-C 80 model were optimized at the same theoretical level used for the optimization of ScGdO@C 2v (31922)-C 80 . The interaction energies (E) in ScGdO@C 2v (31922)-C 80 , Sc 2 O@C 2v (31922)-C 80 , and Gd 2 O@C 2v (31922)-C 80 between inner metal oxides     To further understand the effect of the metal atom on electronic structures, natural bond orbital (NBO) calculations were performed (Table 1). Based on the ground-state electronic configurations of the Sc (3d 1 4s 2 ) and Gd (4f 7 5d 1 6s 2 ) atoms and the spin electronic population of ScGdO@C 2v (31922)-C 80 in the octet ground state ( Figure S3 and Table S2), the formal oxidation states of inner Sc and Gd atoms are III. In the similar way, the formal oxidation states of Sc and Gd in singlet-ground-state Sc 2 O@C 2v (31922)-C 80 and 15-et-ground-state Gd 2 O@C 2v (31922)-C 80 are also III. The spin ground state of Sc 2 O@C 2v (31922)-C 80 was calculated previously, 32 and we inferred the spin state of Gd 2 O@ C 2v (31922)-C 80 from the other two isomers. The NBO charge is negative for the O atom and positive for the metal atom, which shows there is electron transfer from metal atoms to the O atom. In ScGdO@C 2v (31922)-C 80 , the NBO charge of the O atom is less negative and the two metals are quite different.
Because of the f orbital, the Gd atoms seem to lose electrons more easily. The partial charge in outer s, p, and d orbitals is derived from back-donation from the O atom and the fullerene cage, indicating the covalent features between metal and nonmetal atoms; these features were also confirmed by the density of states (Figure 3). The large difference in atomic charge between Sc and Gd is attributed to their electronegativity. According to the eight-electron rule of the O atom, the formal four-electron transfer occurs from the inner cluster (ScGdO, Sc 2 O, and Gd 2 O) to C 2v (31922)-C 80 .
Bonding critical point (BCP) indicators based on the quantum theory of atoms in molecules (QTAIM, a mature quantum theory for analyzing the topology of the electron density) were studied (Figure 4) to further determine the metal−nonmetal interactions. As shown in Table 2, the BCP   To give some useful structural information to distinguish similar molecules of ScGdO@C 2v (31922)-C 80 , Sc 2 O@ C 2v (31922)-C 80 , and Gd 2 O@C 2v (31922)-C 80 in future experiments, their infrared spectra were simulated, as shown in Figure 5. These three kinds of EMFs have very similar absorption peaks. The absorption peak between 200 and 800 cm −1 is the vibration of the fullerene frame. The absorption peaks above 1000 cm −1 come from the stretching vibration of the C−C bond. For higher numbers of Gd atoms, the strongest absorption peak is slightly red shifted, which is meaningful for their experimental characterization.

■ CONCLUSION
Using density functional theory and statistical thermodynamic analysis, ScGdO@C 2v (31922)-C 80 was found to be the most likely isomer isolated in the experiment. The comparative study on Sc 2 O@C 2v (31922)-C 80 and Gd 2 O@C 2v (31922)-C 80 shows that ScGdO@C 2v (31922)-C 80 has the largest bond angle because of its stronger interaction between metal and carbon atoms, and the Sc atom with higher electronegativity plays a much more important role in the metal−nonmetal interactions than the Gd atom. The interactions of Sc−O and Sc−C are larger than those of Gd−C and Gd−O, which is likely related to the higher electronegativity of the Sc atoms and the much closer orbital energy levels. Finally, IR spectra of three isomers were simulated to help future experimental research.