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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Encapsulation of Monometal Uranium into Fullerenes C2n (2n = 70−74): Important Ionic U4+C2n4− Characters and Covalent U‑Cage Bonding Interactions Yong-Xin Gu, Qiao-Zhi Li, Pei Zhao, and Xiang Zhao* 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 Downloaded via UNIV OF LOUISIANA AT LAFAYETTE on August 7, 2019 at 19:06:14 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: By using density functional theory calculations combined with statistical thermodynamic analyses, the stabilization performance of a series of fullerene cages C2n (2n = 70−74) via encapsulating monometal uranium was systematically and thoroughly investigated. Results indicate that fullerene cages D5h(8149)-C70 and D3h(14246)-C74 obeying the isolated pentagon rule and C2(10612)-C72 featured with one pentalene moiety were the most promising candidates to encage uranium. Subsequent Mulliken spin density distribution and frontier molecular orbital analyses suggest that four formal electron transfer occurs from monometal U to above the carbon cages. There also exists a high degree of covalent character between the atom U and fullerenes C2n based on Mayer bond order and quantum theory of atoms in molecule (QTAIM) analyses, indicative of the cooperative stabilization by both ionic and covalent bonding interactions. In addition, investigations on the abovementioned U@C2n isomers and other favorable candidates (U@Cs(8094)-C70, U@C1(10610)-C72, U@C1(13393)-C74, and U@C1(14049)-C74) reveal that these isomers could be closely linked via simple C2 addition and Stone−Wales transformation. These results will provide a systematic understanding on U-based endohedral metallofullerenes (EMFs) and also might be helpful for further exploration of EMF growth mechanisms.

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INTRODUCTION Endohedral metallofullerenes (EMFs) have been remarkably synthesized and characterized since the discovery of La@C82 in 1991.1 Because of their specific structures and unique electronic properties caused by the electron transfer from the encapsulated metals to the fullerene cages, EMFs have shown comprehensive applications in materials science,2,3 biomedicines,4,5 and photovoltaics.6 In the past decades, a variety of fullerene cages, which cannot be generated in hollow forms, have been successfully obtained by encaging metal atoms or metallic clusters. For example, the hollow C72 and C74 fullerenes are extremely difficult to separate because of their poor solubility in common fullerene solvents such as CS2 and their small HOMO−LUMO gaps,7,8 whereas the monometallofullerenes (mono-EMFs) based on C72 and C74 cages have been extensively isolated and reported over the years. In the case of mono-EMFs, the previous explorations were mainly focused on metal atoms in groups II, III and also the lanthanide-based EMFs for the most fullerene cages. For example, when some rare-earth metals such as Sc, La, Y, Pr, Gd, and Lu are encapsulated, three electrons can transfer from metal to carbon cages.9−17 But for alkaline-earth and other lanthanide metals such as Mg, Ca, Sr, Ba, Sm, Eu, and Yb, two electrons are transferred to fullerenes with the formal structures of M2+@C2n2−.18−27 It should be noted that reports on syntheses and characterizations of actinide mono-EMFs are © XXXX American Chemical Society

quite limited due to the complicated oxidation state and high radioactivity of the actinide elements until today. In 1992, Smalley and co-workers reported the X-ray photoelectron spectroscopy (XPS) of U@Td-C28,28 and theoretical calculations indicated that there are four electrons that could be transferred from the uranium atom to this small carbon cage, following calculations and bonding features also verified it by Alvaro Munoz-Castro and co-workers in 2017.29 Then, a series of experimental characterizations and theoretical calculations corresponding to the Th-based fullerenes have been reported, revealing that the four-electron-transfer properties should exist in these actinide EMFs.30,31 Very recently, a series of actinide endohedral metallofullerenes with non-IPR cages, U@C80, U@C76, and Th@C76, have been successfully synthesized and characterized by Chen’s group. They discussed the thermodynamic stabilities of U@C80, U@C76, and Th@C76 in detail, and the molecular orbital analysis revealed that the degree of covalency for the actinide−cage interaction is very high in them.32 Fortunately, U@C74 and U@C82 series were successfully synthesized and characterized by the single-crystal X-ray crystallographic analyses; meanwhile, the U@C82 series were systematically analyzed through theoretical computation.33 Besides the thermodynamic stabilities of the U@C74 series Received: October 31, 2018

A

DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 1. Relative Energies (kcal·mol−1) of Corresponding U@C2n (2n = 70−74) Isomers at the UBP86/6-31G(d)∼SDD Level U@C70

U@C72

U@C74

ΔE a

spiral no.

sym

PA

8149 8094 7892 7957 8144 7851 7886 7852 7854 7887 8148 7853

D5h Cs C2 C2 Cs C1 C1 C1 C2v C2 C3v C3v

0 1 2 2 2 3 3 3 3 3 3 3

b

ΔE a

triplet

quintet

spiral no.

sym

0.0 7.7 12.4 20.9 27.1 29.7 29.9 30.6 32.6 34.3 35.7 46.7

11.0 8.4 17.5 24.5 30.4 35.5 36.0 39.1 33.8 35.1 38.0 53.7

10612 11188 10528 10610 11037 10616 10611 11030 10284 9681 10518 11190 10482 11032 10958 6276

C2 C2v Cs C1 Cs Cs D2 Cs C1 C1 C1 D6d C1 C2v D2 C1

b

ΔE a

PA

triplet

quintet

spiral no.

sym

1 1 2 2 2 2 2 1 3 3 3 0 3 2 2 3

0.0 6.7 6.8 12.5 16.6 19.0 20.9 22.3 24.8 27.0 29.0 29.2 29.7 34.2 37.4 58.5

2.1 5.9 14.3 17.3 21.7 21.8 20.5 25.9 30.9 37.4 37.1 38.9 34.5 36.0 36.8 67.2

14246 13393 14049 13333 13771 13334 13384 13825 13335 13290 13408 13391 13295 14227 13479 13492

D3h C1 C1 C2 C1 C1 C1 C1 C1 C2 C1 C1 C2 C2 C1 C3

PA 0 1 1 2 2 2 2 2 2 2 2 2 2 1 3 3

b

triplet

quintet

0.0 14.0 19.3 20.1 24.5 26.0 27.4 27.4 27.4 27.6 28.1 28.8 30.6 30.6 43.2 47.3

8.7 18.9 19.5 25.2 29.3 31.2 34.7 32.7 32.2 37.1 33.2 32.0 33.4 33.9 46.5 47.3

a

Symmetry of the original hollow cages. bNumber of pentagon adjacencies.

through the formation temperature range of EMFs. Besides, theoretical calculations on U@C70 and U@C72 suggest that the isomers U@D5h(8149)-C70 and U@C2(10612)-C72 are the most stable favorable complexes with the lowest potential energy and outstanding relative abundance throughout the temperature region of fullerene formation. And there is a relative connection among those thermodynamically stable isomers by simple C2 addition and Stone−Wales transformation (SWT). Moreover, the spin density distribution and frontier molecular orbital analyses indicate that four electrons could be transferred from the uranium atom to the carbon cages C2n (2n = 70−74). Furthermore, Mayer bond order, quantum of atoms in molecule (QTAIM), and electronic absorption analyses on U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74 were performed to disclose the unique interaction between uranium atom and carbon cages.

discussed in detail by Chen and co-workers, they proved that the temperature effect plays a considerable role in the stability of actinide mono-EMFs.32 It has been well-known that not only the mono-EMFs but also other EMFs are determined via both inner moieties and fullerene isomers. For instance, the non-IPR cage C2(10612)-C72 exerts obvious dominance after encapsulating monometal La or Ca.10,18 However, in the case of the carbide cluster EMFs, the Sc2C2@Cs(10528)-C72 with two adjacent pentagon fragments is more stable than other C72-based cages.34 It is demonstrated that the inner moiety types have important effects on the stability of EMFs. Moreover, the structure of Ti@C64 has been presented in Dang et al.’s paper;35 the trapped titanium exhibits a pentagon distribution dependent electrontransfer nature. The number of electrons transferred from titanium to C64 cages is two, three, or four when titanium resides on a double fused pentagon, a triple directly fused pentagon or a triple sequentially fused pentagon fragment, respectively. It is indicated that the structures of fullerene isomers also play a significant role in the electron-transfer character of inner moieties. Moreover, Garcia-Borras and co-workers have pointed out that cage aromaticity is the most important stabilizing factor in the process of EMF formation.36,37 In fact, except for U@C74 and U@C82 series, mono-EMFs U@C70 and U@C72 were detected in experiments dating back to 1992 by Smalley and co-workers.28 The structures of U@C70 and U@ C72 were only characterized by FT-ICR mass spectral analysis but without any detailed structural characterization. Therefore, which one C70 or C72 cage would be selected to entrap the uranium atom? Does the entrapped uranium always keep a tetravalent state in C70- or C72-based EMFs just like U@C28 and U@C74?28,33 The most important misgiving is that the interaction between uranium and the C70 or C72 cage is still ambiguous. Hence, to solve related questions above, comprehensive theoretical computations on U@C2n (2n = 70−74) have been carried out through the hybrid density functional theory (DFT) method for the first time. It is demonstrated that U@ D3h(14246)-C74, the product in the experiment, is dominant

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COMPUTATIONAL DETAILS As were all known, the electron configuration of uranium atom is [Rn]5f36d17s2, meaning that the number of electrons donated from uranium atom to the fullerene cages might range from one to six. Therefore, all anionic cage isomers C2nm− (2n = 70−74, m = 1−6) with no more than four PA (pentagon adjacency) fragments were first screened at the semiempirical AM1 level.38 Then, those energetically favorable isomers were further optimized by using the hybrid density functional theory (U)B3LYP with the basis set of 6-31G for C.39−41 Subsequently, a total of 60 isomers, including 12 C70 isomers, 16 C72 isomers, and 32 C74 isomers were taken into consideration to encapsulate the uranium atom. It should be noted that the stabilization of EMFs is closely related to the different positions of uranium atom in the fullerene cage. Therefore, to obtain the lowest energy configuration, there are three to 12 different positions of uranium atom in C74 cages that have been taken into consideration. In this work, both B3LYP and BP8642,43 functions were employed to optimize the U@C74 isomers with the basis set of 3-21G∼SDD, where the 3-21G basis set was used for C and the SDD (Stuttgart/ Dresden) basis set with the corresponding effective core B

DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

potential was used for U.42−46 Since the results based on the B3LYP functional exhibit larger spin contamination than the BP86 functional in dealing with atom U, we suggest that the functional BP86 might be more suitable for U@C74. Thus, the optimization of U@C70 and U@C72 isomers were performed by using the BP86 functional with the basis set of 3-21G∼SDD. Furthermore, a larger basis set of 6-31G(d)∼SDD was used for above U@C2n (2n = 70−74), followed by the frequency calculations at the same level of BP86/6-31G(d)∼SDD to verify those stationary points were all minima. On the basis of the rotational−vibrational partition functions obtained from the structural and vibrational data, molar fractions of U@C2n (2n = 70−74) isomers at different temperatures were estimated, which is extremely essential for the stability of EMFs according to the previous studies (The theoretical details are presented in the Supporting Information.)47,48 All DFT computations in this work were carried out with the Gaussian 09 program.49

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RESULTS AND DISCUSSION Relative Stabilities of U@C2n (2n = 70−74) Series. Relative energies of carbon cages C2nm− (2n = 70−74, m = 1−6) performed at the (U)B3LYP/6-31G level are listed in Tables S1−S18 in the Supporting Information. Obviously, the number of electrons transferred from uranium atom to cages C2n (2n = 70−74) plays a critical role in the stabilization of the empty fullerene cages. Furthermore, the computational results of the corresponding U@C2n (2n = 70−74) isomers at two different theory levels, B3LYP and BP86, are presented in Figures S1 and S2 and Table 1. First of all, as shown in Figure S1 in the Supporting Information, the relative energies of U@C74 isomers optimized at different spin states (singlet, triplet, and quintet) at the (U)B3LYP/3-21G∼SDD level indicate that the relative energies calculated at the singlet state are always higher compared to those calculated at the triplet and quintet states. Therefore, the computational results performed at the singlet state would not be taken into consideration in U@C70 and U@C72 series. Then, the relative energies of U@C74 isomers and the corresponding U@C70 and U@C72 were performed at UBP86/3-21G∼SDD and UBP86/6-31G(d)∼SDD levels, as shown in Figure S2 and Table 1.Obviously, results computed at the triplet state are generally lower in energy than those at the quintet state. As shown in Table 1, the structures of U@ D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74 are predicted to be the lowest energy isomers among all U@ C2n (2n = 70−74) with the ground state of the triplet, whereas the results performed at the quintet state are generally higher

Figure 1. Relative concentrations of low-energy U@C2n (2n = 70− 74) isomers at the UBP86/6-31G(d)∼SDD level.

Figure 2. Structures of U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74. The atoms uranium and carbon are blue and white, respectively. C

DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 3. Structure of uranium and neighboring carbon fragments of U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74. Uranium and carbon atoms are blue and white, respectively.

C72; hence, both triplet and quintet states have been taken into considerations at thermodynamic analyses of the U@C72 system. For U@D5h(8149)-C70 and U@D3h(14246)-C74, both of them are the only isolated pentagon rule (IPR)-obeying isomers in C70 and C74 fullerenes. However, the isomer U@C2(10612)-C72 violates the IPR rule with one PA fragment and stands 29.2 kcal·mol−1 lower in energy than the only IPR-obeying structure U@D6d(11190)-C72. The most important thing is that the three lowest energy fullerene cages also have been experimentally generated by encapsulating alkaline-earth and lanthanide metals, as reported in La@D5h(8149)-C70,9 M@C 2 (10612)-C 72 (M = La, Ca, Yb), 1 0,18 ,25 and M@D3h(14246)-C74 (M = La, Gd, Pr).11,15,16 It is clear that the potential energy is not enough to evaluate the relative stability of all U@C2n (2n = 70−74); the enthalpy− entropy effect also should be taken into consideration. For mono-EMF, Slanina and co-workers have pointed out that the free, fluctuating, or floating encapsulated model (FEM) should be more suitable to evaluate their thermodynamic stabilities than the rigid rotator and harmonic oscillator model (RRHO), especially at high temperatures where the EMF is most likely to be produced.48 Therefore, the relative concentrations of corresponding U@C2n (2n = 70−74) by using the FEM treatment are presented in Figure 1 (all of them were computed on the basis of the triplet state results). For the U@C70 series, U@D5h(8149)-C70 remains the most abundant isomer until the temperature increases to 1800 K with the relative concentration of 45.8%. The second-lowest energy isomer, U@Cs(8094)-C70, also possesses essential concentrations with its maximum value of 51.5% at 2600 K and surpasses U@D5h(8149)-C70 at 1800 K with the concentration of 45.3%. Interestingly, these two isomers are related by a single Stone−Wales transformation; hence, these two isomers should be obtained in the experiment. For the U@C72 series, the lowest energy isomer

Figure 4. Corresponding relationship among several thermodynamically favorable isomers by C2 addition and Stone−Wales transformation (SWT).

in energy. Only in a few isomers are the quintet state energies similar to the triplet state energies, such as for U@C2v(11188)-

Figure 5. Mulliken spin density distributions (isovalue = 0.004 au) of U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74. D

DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry U@C2(10612)-C72 has the outstanding advantage throughout the full temperature region of fullerene formation. In addition, another isomer, U@C1(10610)-C72, with a large relative energy of 12.5 kcal·mol−1 has a single Stone−Wales transformation with U@C2(10612)-C72. Meanwhile, the other two isomers, U@C2v(11188)-C72 and U@Cs(10528)-C72, exhibit noticeable abundance at high temperatures, which keep rising from 1000 K and get to around 10.2% and 13.3% at 3000 K. Therefore, it is reasonable to predict that the two isomers may be obtained at high temperatures. For the U@C74 series, the IPR isomer U@D3h(14246)-C74 shares notable fractions in the temperature interval for fullerene formation. Besides, the other two isomers, U@C1(13393)-C74 and U@C1(14049)-C74, also should not be neglected at relatively higher temperatures with relative energies of 14.0 and 19.3 kcal·mol−1, respectively. As for U@C1(13393)-C74, with the temperature increasing, its relative concentration surpasses that of the most stable isomer U@D3h(14246)-C74 at 2600 K and reaches its maximum fraction of 26.0%. The relative concentration of U@ C1(14049)-C74 also increases with the temperature and reaches its largest value of 19.4% at 3600 K. It is noteworthy that the isomers U@C1(13393)-C74 and U@C1(14049)-C74 have not been reported experimentally. In order to prove that the triplets are the most stable at any temperature, the statistical thermodynamic analyses of U@C72 have been performed where both triplet state and quintet state were taken into consideration because both U@C2v(11188)-C72 and U@ D2(10611)-C72 isomers possess relatively low energies and the quintet energies are similar to triplet energies, which is illustrated in Figure S3 in the Supporting Information. It is clear that there exists a certain competitive relationship of the thermodynamic distribution between the triplet state and quintet state; the abundance of the triplet state in the whole temperature range is more dominant than that of the quintet state, even if the energies of the quintet states are relatively lower. Hence, the triplet state should be more suitable when accounting for the thermodynamic stabilities of the U@C2n series. The geometric structures of these thermodynamically most favorable isomers are listed in Figures 2 and 3 and Figure S4 in the Supporting Information. Generally, the uranium atom is located off the center of the carbon cages and is coordinated to the pyracylene fragment of all IPR structures but is close to the pentalene junctions of the non-IPR structures in all C70−C74 series. Hence, it is reasonable to believe that the same situation will occur when a single metal uranium atom is encaged in other fullerene cages. The most interesting thing is that these thermodynamically stable isomers are closely related by simple C2 addition and Stone−Wales transformation, which further proves the reliability of the thermodynamic stability of these mono-EMFs; the complete relationship between them is illustrated in Figure 4. Electronic Structures and Bonding Nature Analyses. To analyze the electronic structures of actinide mono-EMFs, the Mulliken spin density distributions and frontier molecular orbitals of U@D5h(8149)-C70, U@C2(10612)-C72, and U@ D3h(14246)-C74 are depicted in Figure 5 and Figure 6, respectively. As we can see, the unpaired electrons are mainly localized on the encaged uranium atom with the spin density around 2e for the above three isomers. This can also be demonstrated by their single occupied molecular orbital distributions, in which both singly occupied orbitals (SOMO and SOMO−1) are mainly contributed from the 5f orbital of uranium atom. This means that four electrons are transferred

Figure 6. Main frontier molecular orbital diagrams of U@D5h(8149)C70, U@C2(10612)-C72, and U@D3h(14246)-C74.

to carbon cages C2n after the encapsulation of monometal U. Considering that the electronic configuration of uranium atom is [Rn]5f36d17s2, we suggest that four formal electrons (5f16d17s2) in U are transferred to cages D5h(8149)-C70, C2(10612)-C72, and D3h(14246)-C74 with another two 5f electrons (5f2) remaining on atom U. On the basis of these results, the electronic structures of above three U-based monoEMFs could be formally described as U4+@C2n4− (2n = 70−74). Previous studies have revealed that it is incomplete to describe the EMF structures only with ionic models, and the E

DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 2. Distances of U-Cage and Mayer Bond Order (MBO) Analyses of U@D5h(8149)-C70, U@C2(10612)-C72, and U@ D3h(14246)-C74 U@D5h(8149)-C70 d (Å) MBO U@C2(10612)-C72 d (Å) MBO U@D3h(14246)-C74 d (Å) MBO

U71−C19 2.37 0.44 U73−C47 2.44 0.37 U75−C51 2.39 0.39

U71−C18 2.38 0.41 U73−C34 2.45 0.35 U75−C52 2.39 0.39

U71−C20 2.50 0.36 U73−C48 2.48 0.35 U75−C41 2.51 0.36

U71−C22 2.50 0.35 U73−C35 2.49 0.35 U75−C44 2.51 0.36

U71−C61 2.53 0.33 U73−C46 2.50 0.34 U75−C47 2.53 0.34

U71−C17 2.54 0.33 U73−C33 2.51 0.32 U75−C50 2.53 0.34

Table 3. Bonding Critical Point (BCP) Analyses of U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74 U@D5h(8149)-C70 U@C2(10612)-C72

U@D3h(14246)-C74

bond

ρBCP

∇2ρBCP

HBCP

|VBCP|/GBCP

GBCP/ρBCP

U71−C19 U71−C18 U73−C47 U73−C48 U73−C35 U73−C46 U73−C36 U73−C32 U75−C51 U75−C52

0.086 0.083 0.075 0.068 0.068 0.067 0.063 0.060 0.082 0.082

0.171 0.177 0.173 0.167 0.162 0.165 0.163 0.149 0.181 0.181

−0.028 −0.026 −0.020 −0.016 −0.016 −0.015 −0.013 −0.012 −0.025 −0.025

1.394 1.371 1.317 1.276 1.286 1.268 1.222 1.224 1.357 1.357

0.826 0.843 0.840 0.853 0.824 0.836 0.857 0.817 0.854 0.854

the electron distribution.57,58 Therefore, these values alone cannot be proper descriptors of the bonding. Moreover, the negative values of total energy density (HBCP) (−0.028 to −0.012), relatively large ratio of the absolute value of the potential energy density to kinetic energy density (|VBCP|/ GBCP), which are larger than 1 (1.222−1.394), and the relative small ratio of the kinetic energy density GBCP to ρBCP, which are smaller than 1 (0.817−0.857) in the three isomers are all evidence of the existence of covalent interactions between uranium atoms and carbon cages, as reported by Cremer, Espinosa, and Macchi groups.58−60 In summary, the covalent interactions between uranium atoms and fullerene cages should be taken into consideration. The bonding analyses of U@Cs(8094)-C70, U@C1(10610)-C72, U@C1(13393)-C74, and U@C1(14049)-C74 are illustrated in Table S22 and S24 in the Supporting Information. Furthermore, the simulated UV−vis− NIR spectra of U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74 performed at the BP86/6-31G(d)∼SDD level are listed in Figure S5 in the Supporting Information, in which several characteristic peaks of these three isomers will provide sufficient support for future experiments.

covalent interaction between hollow fullerenes and inner atoms should not be neglected.50,51 Therefore, in order to investigate the interaction between the uranium atom and C74 cages deeply, the Mayer bond order (MBO) analyses carried out by using the MUTIWFN 3.3.7 program52 and the bonding critical point (BCP) analyses utilizing the quantum theory of atoms in molecule (QTAIM)53 for three isomers U@D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74 are collected in Table 2 and Table 3, respectively. As it can be seen in Table 2, the shortest U−C distances of the three structures above are 2.37, 2.44, and 2.39 Å, respectively, which are shorter than other corresponding mono-EMFs, such as 2.50 Å for La@ D5h(8149)-C70,9 2.71 Å for Eu@C2(10612)-C72,23 2.57 Å for La@D3h(14246)-C74,12 and 2.54 Å for Yb@D3h(14246)-C74;54 therefore, this phenomenon proves that the interaction between the uranium atom and fullerenes cage is much stronger. In addition, the Mayer bond orders between the uranium atom and carbon atoms in the cage are about 0.32 to 0.44 for above three isomers, whereas, the M−C Mayer bond orders (M = Er, Sc, and Th)55,56 in the cage of D3h(14246)-C74 are obviously smaller than the U−C Mayer bond orders (see Table S23 in the Supporting Information), the Mayer bond orders between the Th atom and the D3h(14246)-C74 cage are simulated in our current work in progress, which has not been published yet. It is indicated that there exists a high degree of covalent interaction between the uranium atom and carbon cages. As shown in Table 3, the electron density (ρBCP) and Laplacian of electron density (∇2ρBCP) at BCPs between uranium and carbon atoms of U@D5h(8149)-C70, U@ C2(10612)-C72, and U@D3h(14246)-C74 are both small and positive with the range 0.060−0.086 au for ρBCP and 0.149− 0.181 au for ∇2ρBCP, respectively. Popov and co-workers have pointed out that there will exist a covalent interaction when ρBCP is large (>0.2 au) while ∇2ρBCP is large and negative. However, for transition metals, ∇2ρBCP values are usually positive and ρBCP are small because of the diffuse character of

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CONCLUSIONS In summary, the stabilization performances of a series of U-based mono-EMFs U@C2n (2n = 70−74) were theoretically investigated by density functional theory calculations in conjunction with statistical thermodynamic analyses. Three isomers U@D5h(8149)-C70, U@C2(10612)-C72, and U@ D3h(14246)-C74 with the ground state of the triplet are suggested to be the most favorable candidates in both potential energies and thermodynamic concentrations. Furthermore, U@Cs(8094)-C70, U@C1(10610)-C72, U@C1(13393)-C74, and U@C1(14049)-C74 also possess considerable abundances at higher temperatures. It is noted that these favorable isomers could be related by simple C2 addition and Stone−Wales transformation. Subsequent frontier molecular orbital analyses F

DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

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for those three most favorable isomers unambiguously suggest that four electrons (5f16d17s2) should be transferred from the uranium atom to the carbon cages D5h(8149)-C70, C2(10612)C72, and D3h(14246)-C74 (denoted as U4+@C2n4−). However, the Mayer bond order and bond critical point analyses on U@ D5h(8149)-C70, U@C2(10612)-C72, and U@D3h(14246)-C74 indicate that the encaged U atom and fullerene cages also exist with the covalent bonding interactions. This work will provide further understanding of the electronic and bonding properties in U-based EMFs.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b03079. Relative energies of C2nm− anions (2n = 70−74, m = 1−6); theoretical details of statistical thermodynamic analyses; relative energies, relative concentrations, geometry structures, bonding analyses, UV−vis−NIR absorption spectra, and Cartesian coordinates of energetically favorable U@C2n (2n = 70−74) isomers (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (X. Zhao). Fax: +86 29 8266 8559. Phone: +86 29 8266 5671. ORCID

Xiang Zhao: 0000-0003-3982-4763 Notes

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 (21573172, 21773181, 21503159). X. Z. also 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.

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REFERENCES

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DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b03079 Inorg. Chem. XXXX, XXX, XXX−XXX