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. 2022 Nov 16;7(47):42883–42889. doi: 10.1021/acsomega.2c04978

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

Wenxin Zhang †, Mengyang Li ‡, Jun He †, Xiang Zhao †,*
PMCID: PMC9713898  PMID: 36467948

Abstract

graphic file with name ao2c04978_0006.jpg

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 LaC60, 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 Sc3N@C2n (2n = 68–70 and 78–82),8−16 Sc2C2@C2n (2n = 68, 72–74, and 80–84),17−22 Sc2S@C2n (2n = 70 and 82),23−25 YCN@C82,26 Sc3CH@C80,27 Sc3NC@C2n (2n = 78–80),28,29 and Sc2O@C2n (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 Sc2O@C2n, Ho2O@C74,37 Ho2O@C84,38 Dy2O@C80,39 etc., have been widely studied. In particular, Sc2O@C2n 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 M2O 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@C82, for the first time in 2018.43 The mass spectra showed the existence of ScGdO@C80, and Sc2O@C8032 was prepared previously. Clearly, ScGdO@C80 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@C80. Then, the metal–nonmetal interaction in M2O@C2v(31922)-C80 (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 study44 showed the relative stability of anion C804–, wherein seven lowest-energy tetra-anionic cages (less than ∼40 kcal·mol–1) were selected to encase ScGdO. Then, the optimizations of ScGdO@C80 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 theoretically32,44,49 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 single-point 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@C80 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@C80, Sc2O@C80, and Gd2O@C80 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 program54 to study the interactions between metal and nonmetal atoms.

Results and Discussion

According to the ionic model of EMFs, the seven low-lying C804– anions were selected to encage ScGdO cluster.44 After the encapsulations, IPR ScGdO@C2v(31922)-C80 possesses the lowest potential energy, followed by IPR ScGdO@Ih(31924)-C80 and ScGdO@D5h(31923)-C80 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@C80 isomers (Figure S1) decreased after the encapsulation compared with those of the C804– anions.44 The energies of the single-point calculations at the ωB97X-D level of theory also indicate that ScGdO@C2v(31922)-C80 has the lowest relative energy (Table S1). As shown in Figure 1, the statistical thermodynamic analysis of ScGdO@C80 isomers, including the enthalpy–entropy effects, confirmed the highest concentration of ScGdO@C2v(31922)-C80 in the whole temperature region, followed by ScGdO@Ih(31924)-C80 and ScGdO@D5h(31923)-C80 with highest concentrations of no more than 24.1% and 10%, respectively, below about 2500 K; this showed that ScGdO@C2v(31922)-C80 had the highest thermodynamic stability. The accuracy of this theoretical method has been confirmed in many experiments, such as those for Sc2O@Td(19151)-C76, Sc2O@C2v(5)-C80, Sc2O@Cs(6)-C82, and Sc2O@C3v(8)-C82.32−34,55

Figure 1.

Figure 1

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Relative concentrations of several low-lying isomers of ScGdO@C80 at the BP86/6-31G(d)∼CEP-4G level of theory.

Besides, Sc2O@C2v(5)-C80 has been isolated32 with the same carbon cage as optimal ScGdO@C2v(31922)-C80. To elucidate the effect of inner metal atoms on M2O@C2n (M = Sc and Gd), including the metal–nonmetal interactions, crystallized Sc2O@C2v(31922)-C80 and the Gd2O@C2v(31922)-C80 model were optimized at the same theoretical level used for the optimization of ScGdO@C2v(31922)-C80. The interaction energies (E) in ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80 between inner metal oxides and C2v(31922)-C80 are −167.9, −172.3, and −178.2 kcal·mol–1, respectively, indicating the thermodynamically maintained present configurations; the interaction energy was calculated using E = EEMF – Ecarbon-cage – Ecluster. The energies of EMFs (EEMF) were obtained by the optimization of EMFs, and the energies of the singlet-ground-state carbon cage (Ecarbon-cage) and the inner cluster (Ecluster, octet-ground state ScGdO, singlet-ground-state Sc2O, and 15-et-ground-state Gd2O) were obtained from the single-point calculations of the carbon cage and the inner cluster from the corresponding optimized EMFs, respectively. ScGdO@C2v(31922)-C80 has the largest interaction energy, indicating its lower thermodynamically stability; thus, it is a bit difficult to isolate and crystallize ScGdO@C2v(31922)-C80, likely because of its asymmetric geometry.

As shown in Figures 2 and S2, the Sc–O bond length in ScGdO@C2v(31922)-C80 is 1.889 Å, which is shorter than the length of the Gd–O bond (2.113 Å). The greater electronegativity of Sc possibly leads to this result. Surprisingly, both distances are slightly larger than those (1.859 and 2.056 Å for Sc–O and Gd–O bonds, respectively) in ScGdO@C3v(8)-C8243 with larger fullerene cages, which is derived from the orientation of the inner ScGdO cluster along the short axis of C3v(8)-C82.

Figure 2.

Figure 2

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Geometry structures of ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80 optimized at the BP86/6-31G(d)∼CEP-4G level of theory. Oxygen, scandium, and gadolinium atoms are colored in red, pink, and orange, respectively.

Additionally, the Sc–O and Gd–O bond lengths are 1.924 and 2.053 Å in Sc2O@C2v(31922)-C80 and 1.960 and 2.067 Å in Gd2O@C2v(31922)-C80, respectively. The Sc–O–Gd angle (163.0°) is larger than the Sc–O–Sc angle (161.7°) and the Gd–O–Gd angle (139.9°) in Sc2O@C2v(31922)-C80 and Gd2O@C2v(31922)-C80, respectively. These results show the more serious effect of the Sc metal atom on the geometries of metal oxide fullerenes compared to the Gd metal atom, which further illustrates the influence of the electronegativity of the Sc atom.

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 (3d14s2) and Gd (4f75d16s2) atoms and the spin electronic population of ScGdO@C2v(31922)-C80 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 Sc2O@C2v(31922)-C80 and 15-et-ground-state Gd2O@C2v(31922)-C80 are also III. The spin ground state of Sc2O@C2v(31922)-C80 was calculated previously,32 and we inferred the spin state of Gd2O@C2v(31922)-C80 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@C2v(31922)-C80, 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, Sc2O, and Gd2O) to C2v(31922)-C80.

Table 1. Natural Electron Configuration Populations of O, Sc, and Gd atoms in ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80 at the BP86/6-31G(d)∼CEP-4G Level of Theory.

isomer atom NBO charge population
ScGdO@C2v(31922)-C80 O81 –1.091 2s1.792p5.30
  Sc82 1.436 3d0.684s0.074p0.36
  Gd83 1.863 4f7.025d0.886s0.076p0.20
Sc2O@C2v(31922)-C80 O81 –1.204 2s1.822p5.37
  Sc82 1.891 3d0.634s0.014p0.36
  Sc83 1.898 3d0.644s0.014p0.35
Gd2O@C2v(31922)-C80 O81 –1.463 2s1.932p5.52
  Gd82 2.368 4f7.035d0.536s0.036p0.07
  Gd83 2.375 4f7.035d0.536s0.026p0.07
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Figure 3.

Figure 3

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TDOS and PDOS of ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80.

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 indicators between Sc(Gd) and carbon atoms have similar values. The density of electrons (ρBCP) is small, and the Laplacian of electron density (▽2ρBCP) is positive, in line with the previous results on EMFs.56,57 Low ρBCP values, positive ▽2ρBCP values, energy density (HBCP) close to zero, and low Mayer bond orders (MBOs) show the ionic interaction between metal and nonmetal atoms. The larger than 1 ratio between the absolute value of the potential energy density and the kinetic energy density (|VBCP |/GBCP) indicates the interaction consists of an ionic interaction and a covalent interaction, and the negative HBCP value is the symbol of the covalent interaction. Therefore, the metal–nonmetal interaction inside M2O@C2v(31922)-C80 (M = Sc or Gd) is mainly an ionic interaction with some covalent character. Because of larger ρBCP, more negative HBCP, larger |VBCP |/GBCP, larger MBO, and shorter atom distance, the Sc–O and Sc–C interactions are stronger than the Gd–O and Gd–C interactons in ScGdO@C2v(31922)-C80, which may be attributed to the higher electronegativity of the Sc atom. Compared with Sc2O@C2v(31922)-C80, Table 2 shows that the Sc–O interaction in ScGdO@C2v(31922)-C80 is stronger according to the BCP indicators. In contrast, the Gd–O interaction in ScGdO@C2v(31922)-C80 is weaker than that in Gd2O@C2v(31922)-C80. This phenomenon is likely related to (1) the difference in electronegativity determining the electron-withdrawing ability, (2) the atomic orbital energy level determining the degree of effective overlap between bonding atoms, and (3) the size of the atomic radius. Additionally, close to zero bond ellipticity values between Sc or Gd and O atoms indicate single bonds, confirming the four-electron transfer phenomenon. Replacing the Sc atom with the Gd atom in Sc2O@C2v(31922)-C80 makes the Sc–C interaction (Sc82–C51 and Sc82–C52) stronger; interestingly, however, substituting the Sc atom for the Gd atom in Gd2O@ C2v(31922)-C80 makes the Gd–C (Gd82–C71 and Gd82–C72) interaction weaker.

Figure 4.

Figure 4

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BCPs in ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80. BCPs are represented in orange, and BCP paths are represented as brown sticks. BCPs between metal atoms and the carbon cage are highlighted in red, and those between metal atoms and O atoms are circled in blue.

Table 2. BCP Parameters of Clusters and Cluster–Cage Interactions in ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80a.

bond d (Å) ρBCP ▽2ρBCP HBCP |VBCP |/GBCP ε MBO
ScGdO@C2v(31922)-C80
Sc82–C51 2.304 0.054 0.202 –0.004 1.080 1.158 0.242
Sc82–C52 2.305 0.054 0.202 –0.004 1.079 1.240 0.242
Sc82–O81 1.889 0.122 0.623 –0.020 1.113 0.009 1.194
Gd83–C71 2.524 0.048 0.163 –0.004 1.090 0.748 0.169
Gd83–C72 2.525 0.048 0.162 –0.004 1.090 0.789 0.169
Gd83–O81 2.113 0.098 0.434 –0.012 1.101 0.001 0.685
Sc2O@C2v(31922)-C80
Sc82–C51 2.345 0.050 0.187 –0.003 1.061 1.534 0.208
Sc82–C52 2.344 0.050 0.187 –0.003 1.062 1.489 0.209
Sc82–O81 1.924 0.111 0.575 –0.014 1.088 0.006 1.009
Sc83–C71 2.316 0.053 0.195 –0.004 1.081 1.188 0.229
Sc83–C72 2.321 0.053 0.194 –0.004 1.078 1.362 0.229
Sc83–O81 1.960 0.100 0.525 –0.008 1.059 0.016 0.922
Gd2O@C2v(31922)-C80
Gd82–C71 2.497 0.050 0.172 –0.005 1.103 0.737 0.170
Gd82–C72 2.496 0.050 0.173 –0.005 1.103 0.715 0.170
Gd82–O81 2.067 0.110 0.488 –0.019 1.136 0.015 0.886
Gd83–C47 2.581 0.042 0.146 –0.002 1.054 2.142 0.162
Gd83–C44 2.582 0.042 0.146 –0.002 1.054 2.192 0.162
Gd83–C52 2.557 0.045 0.156 –0.003 1.074 1.190 0.153
Gd83–C51 2.556 0.045 0.156 –0.003 1.074 1.159 0.153
Gd83–O81 2.053 0.114 0.498 –0.022 1.150 0.013 0.917
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a

The units of all the BCP parameters are Å and a.u.

To give some useful structural information to distinguish similar molecules of ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80 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.

Figure 5.

Figure 5

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Infrared spectra of thermodynamically stable ScGdO@C2v(31922)-C80, Sc2O@C2v(31922)-C80, and Gd2O@C2v(31922)-C80 at the BP86/6-31G(d)∼CEP-4G level of theory.

Conclusion

Using density functional theory and statistical thermodynamic analysis, ScGdO@C2v(31922)-C80 was found to be the most likely isomer isolated in the experiment. The comparative study on Sc2O@C2v(31922)-C80 and Gd2O@C2v(31922)-C80 shows that ScGdO@C2v(31922)-C80 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.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (21773181 and 21573172). X.Z. would like to acknowledge the financial support from the Nanotechnology Platform Program (Molecule and Material Synthesis) of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.2c04978.

  • Relative energies, single-point energies, relative concentrations, spin density maps, structures for BCPs, BCP parameters, TDOS and PDOS, SOMO- and HOMO–LUMO gaps and maps, and Cartesian coordinates of M2O@C80 (M = Sc or Gd) (PDF)

Author Contributions

W.X.Z. and M.Y.L. contributed equally to this work.

The authors declare no competing financial interest.

Supplementary Material

ao2c04978_si_001.pdf (520.2KB, pdf)

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