Theoretical Insights into Monometallofullerene Th@C76: Strong

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Theoretical Insights into Monometallofullerene Th@C76: Strong Covalent Interaction between Thorium and the Carbon Cage Pei Zhao,† Xiang Zhao,*,† and Masahiro Ehara‡ †

Institute for Chemical Physics & Department of Chemistry, School of Science, 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 S Supporting Information *

that Th@C76 is the third most abundant species according to the mass spectrum. There are a total of 19151 classical fullerene isomers of C76, and only two of them (labeled as 19151 and 19150) satisfy the isolated pentagon rule (IPR).34 For M@C76 (M = Yb, Ca, Sr, and Ba), computational results revealed that two non-IPR structures, C1(17459) and C2v(19138), are the best candidates because the metal atom donates two electrons.28,29 Later, Sm@C2v(19138)-C76,35 TbNC@C2v(19138)-C76, and YNC@C2v(19138)-C7636 were characterized by single-crystal X-ray diffraction, indicating a preference for C2v(19138)-C76 when two or three electrons transfer to C cages. When the transfer of four electrons from the inner cluster to the cage occurs, Td(19151)-C76, C2v(19138)-C76, and C1(17459)-C76 have been viewed as possible isomers to encapsulate the Sc2S cluster by theoretical calculations.37 Later, Sc2O@Td(19151)C76 was characterized by single-crystal X-ray diffraction, in which the C cage obtains four valence electrons from the metallic cluster.38 For such a special mono-EMF, Th@C76, which cage will be the best candidate? Consequently, a systematic investigation on Th@C76 has been performed by density functional theory (DFT) combined with statistical thermodynamic studies. Optimizations on the tetraanions of C76 including two IPR isomers, 12 isomers with one pentagon adjacency (PA) fragment, and the five most stable isomers with a triple sequentially fused pentagon (according to the results at the AM1 method from ref 37) were carried out at hybrid DFT B3LYP39−41 with a splitvalence d-polarized 6-31G* basis set (the results are shown in Table S1). All of the corresponding Th@C76 species were optimized at B3LYP with the basis sets of 3-21G (for C) and SDD (for Th)42−44 (the results are shown in Table S2). The SDD basis set was chosen because it has been demonstrated to provide an accurate estimation on the geometrical and electronic features of EMFs involving lanthanide and actinide.45,46 Reoptimizations on 14 isomers with relative energies of less than 30 kcal·mol−1 were carried out at the B3LYP/631G*∼SDD level, and stationary points were verified as minima by vibrational frequency analyses at the B3LYP/6-31G*∼SDD level. All quantum-chemical calculations were carried out using the Gaussian 09 program.47 As listed in Table S3, the IPR structure, Th@Td(19151)-C76, was determined to possess the lowest energy, followed by a nonIPR isomer, [Th@C1(17418)-C76], with a relative energy of 8.3

ABSTRACT: Th@C76 has been studied by density functional theory combined with statistical mechanics calculations. The results reveal that Th@Td(19151)-C76 satisfying the isolated pentagon rule possesses the lowest energy. Nevertheless, considering the enthalpy−entropy interplay, Th@C1(17418)-C76 with one pair of adjacent pentagons is thermodynamically favorable at elevated temperatures, which is reported for the first time. The bonding critical points in both isomers were analyzed to disclose covalent interactions between the inner Th and cages. In addition, the Wiberg bond orders of M−C bonding in different endohedral metallofullerenes (EMFs) were investigated to prove stronger covalent interactions of Th−C in Th-based EMFs.

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ntrapping metal atoms or metal-containing clusters in fullerene cages results in the formation of endohedral metallofullerenes (EMFs).1,2 The encapsulated species significantly influence the electronic and magnetic properties of these hybrid molecules.3,4 Recently, maximum pentagon separation and aromaticity rules were proposed to interpret the preferred encapsulation cage for EMF formation.5−9 The former pointed out that the negative charge in the EMFs mainly accumulated in the pentagons and preferred the cages with the largest separation among the 12 pentagons. The latter indicates that maximizing the total aromaticity is the main stabilizing force for highly charged fullerenes or EMFs. Monometallofullerenes (mono-EMFs) are the simplest prototypes of EMFs, in which only one single metal atom is incarcerated in the C cages.10,11 Generally, two or three valence electrons could be transferred from the metal to the cage, generating an ionic structure, Mx+@(C2n) x−. For those containing Sc, Y, La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, and Lu, three electrons are transferred from the metal to the cage.12−25 In the case of mono-EMFs involving Sm, Eu, Tm, Yb, and alkalineearth atoms, two electrons are transferred to the cage.26−30 Nevertheless, recent studies reveal that actinide mono-EMFs exhibit special features of charge transfer. The transfer of three or four electrons can be found in uranium mono-EMFs,31 while four electrons can be transferred from the metal to the cage in Th@ C2n (n = 82, 84).32,33 It is reasonable to speculate that novel C cages can be discovered because of unique charge transfer from actinide to C cages. The family of Th@C2n (n = 37−48) has been synthesized by a modified arc-discharge method. It was found © XXXX American Chemical Society

Received: December 11, 2017

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DOI: 10.1021/acs.inorgchem.7b03114 Inorg. Chem. XXXX, XXX, XXX−XXX

Communication

Inorganic Chemistry kcal·mol−1. It should be noted that the tetraanion of C1(17418)C76 possesses a high energy (33.3 kcal·mol−1). As far as we know, this is the first time that the novel C1(17418)-C76 cage was stabilized by encapsulating a single metal atom. Two different DFT methods of M06-2X48,49and PBE050 were further applied to the 10 most stable isomers, and the energy orders are the same. In addition, seven isomers were calculated at the BP86/defSVP∼Th-ECP level of theory,39,44,51 which also exhibits the same energy order (Table S4). It was found that the highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gap of Th@C 1 (17418)-C 76 has been significantly increased by 0.81 eV after encapsulation, which is the largest value (1.85 eV) among all of the considered isomers, indicating its high kinetic stability. After trapping of a single Th atom, four C76 isomers, including C2v(19138), C1(17750), C1(17894), and C1(17459), possess similar relative energies in the range of 13.2−17.3 kcal·mol−1. Other isomers possess higher relative energies. Meanwhile, HOMA-based aromaticity calculations of 14 Th@C76 isomers based on the geometries of B3LYP/6-31G*∼SDD were performed. As shown in Table S3, the most stable complex, Th@Td(19151)-C76, exhibits the largest aromaticity. However, the aromaticity of Th@C1(17418)C76 is slightly smaller than that of Th@C2v(19138)-C76. The separation energy itself cannot predict the relative stabilities in an isomeric system at high temperatures; therefore, it is necessary to take enthalpy−entropy interplay into consideration.52,53 On the basis of frequency analyses, rotational−vibrational partition functions were obtained to evaluate the molar fractions of each Th@C76 isomer at elevated temperatures (method details are presented in the Supporting Information). As shown in Figure 1, even though Th@

temperatures. The contributions of other isomers can be neglected. The geometry structures of Th@Td(19151)-C76 and Th@ C1(17418)-C76 are shown in Figure 2. The Th atom in Th@

Figure 2. Optimized molecular structures of Th@Td(19151)-C76 and Th@C1(17418)-C76 (left, side view; right, top view).

Td(19151)-C76 coordinates with a sumanene-type hexagon with Th−C distances of 2.488−2.489 Å (Table S6), indicating the location of the Th atom near the center of the hexagon. The same coordination between Th and a hexagon with similar Th−C separation (2.5 Å) was also identified in Th@C84-Cs(10).33 However, the major Th site in Th@C3v(8)-C82 situates at the intersection of three hexagons with a short Th−C distance of 2.340(14) Å. The Th atom in Th@C1(17418)-C76 resides under the adjacent pentagons, in which the two nearest Th−C separations are 2.497 and 2.508 Å for Th−C72 and Th−C70, respectively, indicating a slight elongation of the Th−C distances compared to that in Th@Td(19151)-C76. Natural electron configuration analyses on both isomers reveal that electron transfer from the inner metal to C76 cages are mainly from the 7s and 6d orbitals of the Th atoms by four electrons, which is consistent with the previous report (Table S5).32,33 In order to gain further insight into the interaction between the inner metal atom and C cages, the bonding critical point (BCP) indicators based on the quantum theory of atoms in molecules of Th−C in both isomers were obtained to investigate their bonding nature, which were examined with the MULTIWFN 3.3.7 program.54 In the case of Th@Td(19151)C76, each Th−C bond coordinating with the hexagon generates one BCP with almost the same parameters (Table S6), which further indicates the same Th−C bonding nature. The electron density (ρBCP) and density Laplacian (∇2ρBCP) at these BCPs are positive and small. Their total energy density (HBCP) are negative, and the ratios of the kinetic energy density GBCP to ρBCP are smaller than 1. These features of Th−C bonds are consistent with that of covalent interactions involving transition metals summarized by Macchi and Sironi.55 As for Th@C1(17418)-C76, except for Th−C75, other Th−C bonds coordinating with the

Figure 1. Relative concentrations of Th@C76 isomers at the B3LYP/631G*∼SDD level.

Td(19151)-C76 is overwhelming at low temperatures, the relative concentration of Th@C1(17418)-C76 increases rapidly as the temperature rises. Th@C 1 (17418)-C 76 surpasses Th@ Td(19151)-C76 with a relative concentration of 47.0% at 1200 K and reaches its maximum with 53.6% at 1600 K. Even when the temperature increases up to 4500 K, Th@C1(17418)-C76 still has the highest relative concentration, which should be the most favorable product in the experiments. Further analyses reveal that both the rotational and vibrational partition functions of Th@ C1(17418)-C76 are larger than those of Th@Td(19151)-C76 in the considered temperature range. Meanwhile, Th@C1(17750)C76, Th@C1(17894)-C76, and Th@C1(17459)-C76 exhibit quite similar trends at high temperatures, which keep rising from 1000 K and get to around 16% at 4500 K. Therefore, it is reasonable to predict that the three isomers may be obtained at high B

DOI: 10.1021/acs.inorgchem.7b03114 Inorg. Chem. XXXX, XXX, XXX−XXX

Communication

Inorganic Chemistry PA are observed with one BCP. Those Th−C BCPs exhibit similar characteristics for the above parameters, indicating their covalent interactions. It should be noticed that the total energy density HBCP of Th−C74 is more positive (−0.009 au) than that of other Th−C bonds (−0.013 to −0.018 au), which may reveal its weaker covalent interaction. In addition, Wiberg bond order (WBO) analyses on M−C in different EMFs were calculated to evaluate interactions between metal and C cages (Tables S6 and S8). The values of WBOs for Th−C bonds in Th@Td(19151)-C76 fall into the interval of 0.642−0.643, and that in Th@C1(17418)-C76 is in the range of 0.511−0.636. Thus, for C cages with the same size, stronger interaction of Th−C bonds can be figured out under the hexagon instead of the PA. As mentioned above, the Th atom also resides under a hexagon in Th@Cs(10)-C84; however, the WBO values of Th−C are slightly smaller (0.557−0.624) than those in Th@ Td(19151)-C76, which may be attributed to the larger size of C84. As for Th@C3v(8)-C82, the largest value of the WBO can be found between the Th and C atoms at the junction of three hexagons (0.709), further indicating their strong covalent interaction. Obviously, the positions of Th and the sizes of the cages have an effect on the Th−C interactions. When a La atom replaces the position of Th in Th@Td(19151)-C76, La−C exhibits a slight elongation and smaller WBO values, indicating a weaker interaction of La−C than Th−C. For the smaller EMF of Sc2C2@D3h(14246)-C74, the shortest separations between Sc and the cage are around 2.2 Å, and a previous report disclosed covalent interaction between them.56 Interestingly, the WBO values of Sc−C are larger than that in La@Td(19151)-C76 but smaller than that in Th-EMFs, further indicating strong covalent interaction of Th−C. Furthermore, simulated 13C NMR and UV−vis−near-IR spectra of Th@Td(19151)-C76 and Th@ C1(17418)-C76 were also carried out (Figures S6 and S7). In summary, a systematic study on Th@C76 has been performed by means of DFT calculations and statistical thermodynamic analyses. An IPR structure, Th@Td(19151)C76, is confirmed to possess the lowest energy, followed by one non-IPR isomer, Th@C1(17418)-C76, with one adjacent pentagon pair. When considering entropy effects, Th@ C1(17418)-C76 is predicted as the most favorable product in experiments because of the predominant molar fraction at elevated temperatures. BCPs and WBOs in both isomers were analyzed to disclose the strong covalent interaction between the Th atom and cages. Overall, the present work may provide further understanding for the physical and chemical properties of thorium-based EMFs.

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orbitals of both isomers, WBOs and distances of M−C in different EMFs, simulated 13NMR and UV−vis−nearNIR spectra of both isomers, and Cartesian coordinates of both isomers PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86-29-82665671. Fax: +86-29-82668559. ORCID

Xiang Zhao: 0000-0003-3982-4763 Masahiro Ehara: 0000-0002-2185-0077 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been financially supported by the National Natural Science Foundation of China (Grants 21573172, 21773181, and 21503159) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP No. 20130201110033). The authors also acknowledge financial support from the Nanotechnology Platform Program (Molecule and Material Synthesis) of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b03114. Relative energies and HOMO−LUMO gaps of C764− and Th@C76 isomers, different positions of the Th atom in IPR isomers, HOMA-based aromaticity of Th@C76 isomers, relative concentrations of Th@C76 isomers at the M06-2X/6-31G*∼SDD level, natural electron configuration populations of Th atoms in Th@Td(19151)-C76 and Th@C1(17418)-C76, bond lengths, Wiberg bond orders, and BCP parameters of the Th−C bonds in both isomers, vertical/adiabatic electron affinity and vertical/ adiabatic ionization potential values, main molecular C

DOI: 10.1021/acs.inorgchem.7b03114 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.7b03114 Inorg. Chem. XXXX, XXX, XXX−XXX