Received: 1 October 2017
|
Revised: 29 November 2017
|
Accepted: 11 December 2017
DOI: 10.1002/qua.25576
FULL PAPER
Lanthanide metals in the boron cages: Computational prediction of M@Bn (M 5 Eu, Gd; n 5 38, 40) Cong Xi | Le Yang | Chang Liu | Peng You | Lanlan Li | Peng Jin School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, People’s Republic of China
Abstract Endohedral metalloborofullerenes (EMBFs) are novel boron analogues of the famous endohedral metallofullerenes (EMFs). Many EMBFs have been proposed by theoretical calculations thus far.
Correspondence Peng Jin, School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, People’s Republic of China. Email:
[email protected]
However, in sharp contrast to EMFs, which trap most of the lanthanides with f electrons inside the cages, the corresponding lanthanide-based EMBFs have never been reported. In this work, the encapsulation of Eu and Gd in the B38 and B40 fullerenes was studied by means of density functional theory calculations. Our results revealed that Gd@B38(9A), Eu@B40(8B2), and Gd@B40(7A00 ) all favor the endohedral configuration, and the electronic structures can be described as Gd31@B32 38 , 31 32 Eu21@B22 40 , and Gd @B40 with jailed f electron spins. The large binding energies and sizable
Funding information National Natural Science Foundation of China, Grant/Award Numbers: 21103224 and 21603052
HOMO–LUMO gaps suggest that they may be achieved experimentally. They feature r and p double aromaticity, and their excellent stabilities were confirmed by the Born–Oppenheimer molecular dynamics simulations. Finally, the infrared and UV/vis spectra were simulated to assist experimental characterization.
KEYWORDS
borofullerenes, density functional theory calculations, endohedral fullerenes, lanthanide element, spectra simulation
1 | INTRODUCTION Since the discovery of C60 buckyball in 1985,[1] fullerenes and their various derivatives have attracted great attention due to their beautiful structures and unique physical and chemical properties. In particular, with the presence of metal elements in the cavity, endohedral metallofullerenes (EMFs) exhibit distinctive and tunable properties that differ dramatically from those of their parent cages.[2–6] To date, most of the lanthanides and even some actinide elements have been successfully encapsulated in the fullerene cages, with much attention paid to those with f electrons.[2–7] For example, gadolinium holds a half-filled 4f subshell (4f7) with strong paramagnetic property, and the carbon cages are stable enough to prevent Gd from leakage under physiological conditions. Numerous researches have demonstrated that the Gd-based EMFs (e.g., Gd@C82), after polyhydroxylation, are highly effective and nontoxic contrasting agents for magnetic resonance imaging.[8–10] Moreover, the isolated f electron spins on the metal could serve as a nanosized qubit in quantum computers and be applied in quantum information processing.[11] Besides the carbon fullerenes, the boron clusters of certain sizes can form cage-like structures as well, as exemplified by the recent fascinating –=0
discovery of the first borofullerene, D2d-B40 (Figure 1).[12] After B40, more borofullerenes Bn in neutral or ionic forms were observed in experiments [13–29]
or predicted by theory.
Inspired by the facile preparation of EMFs, various endohedral derivatives of small borofullerenes were intensively pro-
posed by computations as well. These complexes, named as endohedral metalloborofullerenes (EMBFs)[30–32] or endohedral metalloborospher[36] enes,[33] include Fe@Bn (n 5 18, 20),[34] Mn@B2=0=1 (n 5 19, 20),[35] Ta@B2 M@B24 (M 5 Ti, Zr, Hf, Cr, Mo, W, Fe, Ru, Os),[37] W@Bn (n 5 20, n 22 , [17] [43] 24, 28, 32),[38] Zn@Bn (n 5 20, 30, 40, 50, 60),[39] Ti@B28,[40] Ca@B2 M@B38 (M 5 Ca, Sc, Y, La, Ti),[20,40,41] FLi2@B39,[42] Ca@B1 M@B40 37 , 39 ,
(M 5 Na, Ca, Sr, Ba, Sc, Y, La, Ti, Mn, Fe, Co, Ni, U, Ti2, Sc3N, Sc2C2),[33,44–50] and M@B44 (M 5 Ca, Sr, Ba).[51] Clearly, in sharp contrast to EMFs, which can trap almost all the lanthanide elements,[6] the lanthanide-containing EMBFs still remain largely unexplored with the inner metal only limited to lanthanum.[30,40,44] It is noteworthy that the lanthanide borides are important magnetic, superconducting, and thermoelectric materials.[52–54]
Int J Quantum Chem. 2018;118:e25576. https://doi.org/10.1002/qua.25576
http://q-chem.org
C 2017 Wiley Periodicals, Inc. V
|
1 of 11
2 of 11
|
XI
ET AL.
Optimized geometries of (A) D2h-B38 fullerene and its quasi-planar C1-B38 isomer and (B) D2d-B40 fullerene with hexagons and heptagons highlighted in yellow (two views)
FIGURE 1
½12
½18
In this work, for the first time, we doped the prototypical D2d-B40 and recently reported D2h-B38 fullerenes (Figure 1) with Eu and Gd either endohedrally or exohedrally. According to our density functional theory (DFT) calculations, we proposed the possible formation of three new EMBFs, namely Gd@B38, Eu@B40, and Gd@B40. Their novel electronic structures, bonding patterns, and magnetic properties were disclosed, and the excellent stabilities were confirmed. Furthermore, various spectra were simulated to assist experimental characterization.
2 | CALCULATION METHODS Full geometry optimizations were carried out using the Perdew–Burke–Ernzerhof (PBE) functional,[55] which has been confirmed more reliable than most DFT methods in predicting the energy of boron clusters.[56] The standard 6–311 1 G* basis set[57] was used for B, whereas the relativistic effective core potential and basis set developed by Cundari and Stevens (CEP-31G)[58] for Eu and Gd. Harmonic vibrational frequency analysis at the same level of theory were carried out to confirm that all the reported geometries are real minima on the potential energy surface, and also predict the infrared spectra. The electronic absorption spectra were simulated by using the time-dependent DFT (TD-DFT) method.[59] To evaluate the feasibility of realizing an EMBF, we calculated its binding energy Eb 5 E(M) 1 E(Bn) – E(M@Bn), where E(M), E(Bn), and E(M@Bn) are the total energies of the metal atom, the hollow boron cage and the endofullerene in equilibrium geometries, respectively. Therefore, a more positive Eb value means the formation of endohedral derivative is thermodynamically more favorable.
XI
|
ET AL.
3 of 11
Optimized geometries of different (A) EuB38, (B) GdB38, (C) EuB40, and (D) GdB40 isomers with molecular symmetry, electronic state, and relative energy (kcal mol21)
FIGURE 2
FIGURE 3
Spin density distributions of M@Bn with the spins (S) on the boron cages and the metals
4 of 11
|
XI
ET AL.
Difference between the electronic density of Gd@B38, Eu@B40, and Gd@B40 and the overlapping densities of metal and boron cage. Red and blue represent excess and depletion of charge density, respectively
FIGURE 4
All the above DFT computations were carried out using the Gaussian 09 software package.[60] The chemical bonding pattern was studied via topological analysis of the electron localization function (ELF)[61] and localized orbital locator (LOL)[62] as implemented in the Multiwfn software.[63] To verify the dynamic stability of these new endohedrals, Born–Oppenheimer molecular dynamics (BO-MD) simulations were carried out at the –Hoover PBE/DND level of theory as implemented in the DMol3 code.[64,65] A canonical NVT ensemble was used in the simulations, and a simple Nose thermostat was employed to set the temperatures to 300 and 800 K. For each simulation, the time step was 1.0 fs and the duration was 5 ps.
3 | RESULTS AND DISCUSSION 3.1 | Optimized geometries and relative energies The D2h-B38 cage[18] contains 56 B3 triangles and four hexagons belonging to two types (Hex 1 and Hex 2, Figure 1A). Since it is almost isoenergetic with a quasi-planar C1-B38 isomer,[18,19] both of the isomers were considered for the metal doping. The B40 cage bears a perfect D2d cage structure with 48 triangles, two hexagons and four heptagons on the surface (Figure 1B). It is 0.48 eV energetically more favorable than other B40 isomers on
FIGURE 5
Molecular orbital diagrams of M@Bn
XI
ET AL.
|
5 of 11
Plots of electron localization function (ELF) and localized orbital locator (LOL) of both r and p electron systems for Gd@B38, Eu@B40, and Gd@B40
FIGURE 6
the potential energy surface,[12] indicating that the metal doping hardly alter its extreme stability. Therefore, we only employed the B40 fullerene for the metal doping. For the endohedral doping (denoted as M@Bn), different metal positions inside the cage were considered, whereas the coordination to hexagonal and heptagonal rings were considered for the exohedral one (denoted as M&Bn) (Figure 1). The same naming scheme was applied for the quasiplanar B38 isomer to differentiate the doping forms on the concave and convex surfaces. A spin multiplicity of M 5 8 was assumed for EuBn, whereas M 5 7 and 9 for GdBn (the reasons are given below). Figure 2 depicts the optimized geometries, molecular symmetries, electronic states, and relative energies of different MBn isomers. Frequency analysis showed no imaginary frequency and confirmed their dynamical stability. Gd@B38, Eu@B40, and Gd@B40 all adopt the endohedral form as their lowest-energy structures with the corresponding exohedral ones at least 20 kcal mol21 energetically unfavorable. The septet and nonet states of each Gd@Bn are very close in energy with the difference 1.0 kcal mol21. In contrast, the larger Eu atom (atomic radii: Eu 1.85 Å vs. Gd 1.80 Å) tends to reside on the convex surface of the quasi-planar B38 isomer. We focus on the lowest-energy Gd@B38 (9A), Eu@B40 (8B2), and Gd@B40 (7A00 ) in the following sections. The Gd atom in Gd@B38 and the Eu atom in Eu@B40 reside at the cage center, whereas the Gd atom of Gd@B40 deviates from the cage center by about 0.46 Å, pointing to a hexagonal ring. The molecular symmetries of Gd@B38, Eu@B40 and Gd@B40 are C1 (very close to C2h), D2d and Cs, respectively. The shortest distance between the metal and boron cages are 2.82 Å, 3.03 Å, and 2.75 Å respectively. All these values are longer than the summation of atomic radii of metal and
6 of 11
|
FIGURE 7
XI
ET AL.
The snapshot structures of (A) Gd@B38, (B) Eu@B40, and (C) Gd@B40 after 0 fs, 2500 fs, and 5000 fs BO-MD simulations at
300 K
B atoms (Eu-B: 1.85 1 0.85 5 2.7 Å; Gd-B: 1.80 1 0.85 5 2.65 Å), suggesting the predominately ionic metal–cage interactions (see below for the bonding pattern analysis). Consistent with the interatomic distances and the ionic bonding, the calculated Wiberg bond order for the shortest M–B deviations are 0.15, 0.10, and 0.20 for Gd@B38, Eu@B40, and Gd@B40, respectively. The boron frameworks all slightly deformed on metal doping, as indicated by the calculated cage deformation energies (i.e., energy difference between the outer cage of an endofullerene and the cage in equilibrium geometry) of 10.4, 9.5, and 11.1 kcal mol21 for Gd@B38, Eu@B40, and Gd@B40, respectively. The calculated binding energies are 151.6, 96.5, and 112.6 kcal mol21 for Gd@B38, Eu@B40, and Gd@B40, respectively, suggesting that the metal encapsulation processes of these endohedrals are all rather exothermic. For comparison, the binding energies of previously ½33
reported C2v-Ca@B40 and D2d-Sr@B40 are calculated to be 64.0 kcal mol21 and 76.7 kcal mol21, respectively. The high binding energies indicate substantial metal–cage interactions and significant stabilization of these core-shell structures.
FIGURE 8
Simulated infrared spectra of pristine B38 and Gd@B38
XI
|
ET AL.
FIGURE 9
7 of 11
Simulated infrared spectra of pristine B40, Eu@B40, and Gd@B40
3.2 | Electronic structure The electronic configurations of europium and gadolinium are [Xe]4f76s2 and [Xe]4f75d16s2, respectively. We assume that the three valence electrons of Gd (5d16s2) are transferred to cage, the parallel (ferromagnetic) and antiparallel (antiferromagnetic) spin couplings between the seven parallel f spins on Gd31 and one unpaired electron on cage thus lead to spin multiplicities of M 5 9 and 7, respectively. By comparison, the two 6s valence electrons of Eu are expected to be donated to cage and have antiparallel spins, thus giving rise to M 5 8 stemming from the seven 4f electrons on the metal. Figure 3 shows that the spin densities of Gd@B38 and Gd@B40 are distributed on both the metal atom and boron cage, whereas that of Eu@B40 is mainly contributed by the internal metal. Since the spin density represents the density difference between the a and b orbital electrons, the results are in line with the spin states of Gd@B38 (9A), Eu@B40 (8B2), and Gd@B40 (7A00 ) and the scenario of a complete transfer of valence electrons from the metal to the cage. Therefore, the electronic structures of the three endofullerenes can be formally described as 21 31 22 32 Gd31@B32 38 , Eu @B40 , and Gd @B40 .
As a matter of fact, the calculated natural atomic charges of metals are much smaller than the formal ones and are 0.219 e, 0.859 e, and 0.877 e for Gd@B38, Eu@B40, and Gd@B40, respectively. The metal-to-cage charge transfer agrees with the difference in Pauling’s electronegativity: 2.04 for B and 1.2 for Eu and Gd, and is in line with the excellent electron delocalization ability of the boron cage. The natural electronic configurations of the metal cores are Gd: [Xe]6s0.144f7.045d2.006p0.66, Eu: [Xe]4f6.975d0.746p0.39, and Gd: [Xe]6s0.124f7.025d1.586p0.45 for Gd@B38, Eu@B40, and Gd@B40, respectively, indicating obvious back-donation from the boron cage to the unoccupied metal orbitals. The f orbitals have not participated in the valence bonding due to their relativistic contraction. Consistent with the above analysis, Figure 4 depicts the difference between the electronic density of Gd@B38, Eu@B40, and Gd@B40 and the overlapping densities of metal and boron cage. The figure clearly shows decreased electron density for the metal and increased density in the boron framework. Figure 5 shows the frontier molecular orbitals of the three endofullerenes. The pristine B38 and B40 fullerenes have a large energy gap of 1.11 and 1.77 eV between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), respectively, indicating their outstanding chemical stability. The metal doping slightly upshifted their orbital energy levels due to the charge transfer. The HOMO-LUMO gap energies of 0.58/0.76 eV (a/b spin orbital), 0.72/0.76 eV(a/b spin orbital) and 0.84/0.36 eV(a/b spin orbital) for Gd@B38, Eu@B40, and Gd@B40,
8 of 11
|
FIGURE 10
XI
ET AL.
Simulated UV/vis spectra of (A) Gd@B38, (B) Eu@B40, and (C) Gd@B40
respectively, are still sizable although they are smaller than that of the empty cages. For comparison, the HOMO–LUMO gaps of both Ca@B40 and Sr@B40 are calculated to be 0.76 eV. Furthermore, the HOMO and LUMO are predominately contributed by the outer cages, suggesting that these endohedrals are prone to react with both electrophilic and nucleophilic reagents.
3.3 | Bonding nature The chemical bonding patterns of Gd@B38, Eu@B40, and Gd@B40 were further analyzed using the topological analysis of the electron localization function (ELF) and localized orbital locator (LOL) and showed in Figure 6. Both the ELF and LOL maps can be partitioned in terms of ELFr and ELFp components contributed by the r and p electrons, respectively. The results show that both the r and p electron systems exhibit significant electron delocalization over the whole molecule. Apparently, Gd@B38, Eu@B40, and Gd@B40 feature double electron delocalization in both r and p orbitals, and exhibit symmetrically distributed r and p bonds in the HOMOs and LUMOs (Figure 5). The unique bonding patterns promise their remarkable stability and aromaticity. We further calculated the nucleus-independent chemical shifts (NICS)[66,67] values at all the ring centers on the cage surfaces of the three endohedral complexes. The obtained NICS values range from 236.1 ppm to 211.4 ppm, from 243.6 ppm to 228.8 ppm, and from 241.1 ppm to 223.2 ppm for Gd@B38, Eu@B40, and Gd@B40, respectively, suggesting their good electron delocalization.
3.4 | Dynamic stability To further verify the dynamic stability of Gd@B38, Eu@B40, and Gd@B40, we carried out two 5 ps BO-MD simulations for each of them at 1 fs interval at 300 K and 800 K using the DMol3 code. Figure 7 depicts the snapshots at three different time steps (0 fs, 2500 fs, and 5000 fs). From the
XI
|
ET AL.
9 of 11
figure, we can see that the structural integrity of each complex was well preserved at 300 K and only a slight cage distortion occurred. At the temperature as high as 800 K, although the cage distortions increased and the metals became more flexible, the endohedral structure remained almost intact throughout the whole process of simulation (Supporting Information Figure S1). These results indicate the extreme stability of these endohedral borofullerenes.
3.5 | Spectra simulation The theoretical predictions of various spectra are very helpful for the structural characterization of new complexes. Figures 8 and 9 depict the simulated infrared spectra of M@B38 and M@B40, respectively. The strongest infrared absorption peak of the empty B38 cage appears at 1194 cm21 (b1u), and two peaks of lesser intensity are located at 1092 cm21 (b2u) and 1158 cm21 (b3u). The IR active modes of Gd@B38 possess the irreducible representation of a and the most intense peak shifts to 1164 cm21 (a). The above vibrations are due to the tangential movements of boron atoms on the sphere surface. Some other relatively strong absorptions include 1107 cm21 (a), 986 cm21 (a), 752 cm21 (a), 602 cm21 (a), 462 cm21 (a), and 394 cm21 (a). For empty B40, its most intense IR peak lies in the position of 1236 cm21(e), followed by the peak at 1217 cm21(e). The IR active modes of Eu@B40/Gd@B40 possess the irreducible representations of e and b2/a’ and a00 . The strongest peaks shift to 1233 cm21 (e) and 1195 cm21 (a’) for Eu@B40 and Gd@B40, respectively. Some relatively strong absorptions include 1209 cm21 (b2), 1180 cm21 (e), 1148 cm21 (e), 771 cm21 (b2) for Eu@B40, and 1267 cm21 (a0 ), 1256 cm21 (a00 ), 1149 cm21 (a00 ), and 1129 cm21 (a0 ) for Gd@B40. Furthermore, we simulated the UV/vis spectra of Gd@B38, Eu@B40, and Gd@B40 by using the TD-DFT approach (Figure 10). The main absorption peaks may be observed at 872, 1007, 1012, and 1092 nm for Gd@B38; 525, 714, 899, and 1409 nm for Eu@B40; 531, 601, 759, and 764 nm for Gd@B40. According to the assignment of the dominant orbital transitions, the above spectral features mainly stem from the electron transitions from the highest and second highest occupied molecular orbitals (i.e., HOMO and HOMO-1) to the high lying unoccupied molecular orbitals. Finally, we calculated the vertical ionization potential (VIP) and vertical electron affinity (VEA) of the three endofullerenes. The calculated VIP (VEA) values are 5.94 (2.30) eV, 6.13 (2.21) eV, and 5.79 (2.38) eV for Gd@B38, Eu@B40, and Gd@B40, respectively, indicating they are hard to be oxidized and are prone to accept electrons.
4 | CONCLUSIONS In summary, our DFT calculations suggested three new endohedral borofullerenes Gd@B38, Eu@B40, and Gd@B40, which represent the first lanthanide-based EMBFs with jailed f electrons. Their large binding energies and sizable HOMO-LUMO energy gaps promise their possible synthesis in the experiments. Their electronic structures, magnetic properties, bonding nature and r plus p double aromaticity were disclosed, and the excellent dynamic stabilities at different temperatures were confirmed. The simulated spectra could help the future experimental characterization. We believe that as their famous EMFs cousins, the EMBFs containing lanthanides with f electrons may find potential applications in many fields such as magnetic materials and biomedicines.
AC KNOW LE DGME NT S Support by the National Natural Science Foundation of China (21103224 and 21603052) is gratefully acknowledged.
OR CID Peng Jin
http://orcid.org/0000-0001-6925-9094
R E FER E NCE S [1] H. W. Kroto, J. R. Heath, S. C. O’brien, R. F. Curl, R. E. Smalley, Nature 1985, 318, 162. [2] X. Lu, L. Feng, T. Akasaka, S. Nagase, Chem. Soc. Rev. 2012, 41, 7723. [3] A. Popov, S. Yang, L. Dunsch, Chem. Rev. 2013, 113, 5989. [4] P. Jin, C. Tang, Z. Chen, Coord. Chem. Rev. 2014, 270–271, 89. [5] J. Zhao, X. Huang, P. Jin, Z. Chen, Coord. Chem. Rev. 2015, 289–290, 315. [6] S. Yang, T. Wei, F. Jin, Chem. Soc. Rev. 2017, 46, 5005. [7] P. Jin, C. Liu, Y. Li, L. Li, Y. Zhao, Int. J. Quantum Chem., 2017, https://doi.org/10.1002/qua.25501. [8] P. P. Fatouros, M. D. Shultz, Nanomedicine 2013, 8, 1853. [9] K. B. Ghiassi, M. M. Olmstead, A. L. Balch, Dalton Trans. 2014, 43, 7346. [10] T. Li, H. C. Dorn, Small 2017, 13, 1603152.
10 of 11
|
XI
ET AL.
[11] D. Suter, K. Lim, Phys. Rev. A 2002, 65, 052309. [12] H. J. Zhai, Y. F. Zhao, W. L. Li, Q. Chen, H. Bai, H. S. Hu, Z. A. Piazza, W. J. Tian, H. G. Lu, Y. B. Wu, Y. W. Mu, G. F. Wei, Z. P. Liu, J. Li, S. D. Li, L. S. Wang, Nat. Chem. 2014, 6, 727. [13] J. Zhao, X. Huang, R. Shi, H. Liu, Y. Su, R. B. King, Nanoscale 2015, 7, 15086. [14] Y. J. Wang, Y. F. Zhao, W. L. Li, T. Jian, Q. Chen, X. R. You, T. Ou, X. Y. Zhao, H. J. Zhai, S. D. Li, J. Li, L. S. Wang, J. Chem. Phys. 2016, 144, 064307. [15] H. R. Li, T. Jian, W. L. Li, C. Q. Miao, Y. J. Wang, Q. Chen, X. M. Luo, K. Wang, H. J. Zhai, S. D. Li, L. S. Wang, Phys. Chem. Chem. Phys. 2016, 18, 29147. [16] W. J. Tian, Q. Chen, H. R. Li, M. Yan, Y. W. Mu, H. G. Lu, H. J. Zhai, S. D. Li, Phys. Chem. Chem. Phys. 2016, 18, 9922. [17] Q. Chen, H. R. Li, W. J. Tian, H. G. Lu, H. J. Zhai, S. D. Li, Phys. Chem. Chem. Phys. 2016, 18, 14186. [18] J. Lv, Y. Wang, L. Zhu, Y. Ma, Nanoscale 2014, 6, 11692. [19] T. B. Tai, M. T. Nguyen, Nanoscale 2015, 7, 3316. [20] Q. Chen, H. R. Li, C. Q. Miao, Y. J. Wang, H. G. Lu, Y. W. Mu, G. M. Ren, H. J. Zhai, S. D. Li, Phys. Chem. Chem. Phys. 2016, 18, 11610. [21] Q. Chen, W. L. Li, Y. F. Zhao, S. Y. Zhang, H. S. Hu, H. Bai, H. R. Li, W. J. Tian, H. G. Lu, H. J. Zhai, S. D. Li, J. Li, L. S. Wang, ACS Nano 2015, 9, 754. [22] T. T. Gao, Q. Chen, Y. W. Mu, H. Lu, S. D. Li, AIP Adv. 2016, 6, 065110. [23] H. R. Li, Q. Chen, X. X. Tian, H. G. Lu, H. J. Zhai, S. D. Li, J. Mol. Model. 2016, 22, 124. [24] Q. Chen, S. Y. Zhang, H. Bai, W. J. Tian, T. Gao, H. R. Li, C. Q. Miao, Y. W. Mu, H. G. Lu, H. J. Zhai, S. D. Li, Angew. Chem. Int. Ed. 2015, 54, 8160. [25] T. B. Tai, S. U. Lee, M. T. Nguyen, Phys. Chem. Chem. Phys. 2016, 18, 11620. [26] T. B. Tai, M. T. Nguyen, Chem. Commun. 2016, 52, 1653. [27] T. B. Tai, M. T. Nguyen, RSC Adv. 2017, 7, 22243. [28] X. Zhao, Q. Chen, H. Li, Y. Mu, H. Lu, S. Li, Phys. Chem. Chem. Phys. 2016, 19, 10998. [29] L. Si, C. Tang, Int. J. Hydrogen Energy 2017, 42, 16611. [30] P. Jin, C. Hao, Z. Gao, S. B. Zhang, Z. Chen, J. Phys. Chem. A 2009, 113, 11613. [31] P. Jin, C. Liu, Q. Hou, L. Li, C. Tang, Z. Chen, Phys. Chem. Chem. Phys. 2016, 18, 21398. [32] C. Liu, L. Yang, P. Jin, Q. Hou, L. Li, Chem. Phys. Lett. 2017, 676, 89. [33] H. Bai, Q. Chen, H. J. Zhai, S. D. Li, Angew. Chem. Int. Ed. Engl. 2015, 54, 941. [34] N. M. Tam, H. T. Pham, L. V. Duong, M. P. Pham-Ho, M. T. Nguyen, Phys. Chem. Chem. Phys. 2015, 17, 3000. [35] L. Zhao, X. Qu, Y. Wang, J. Lv, L. Zhang, Z. Hu, G. Gu, Y. Ma, J. Phys. Condens. Matter 2017, 29, 265401. [36] H. R. Li, H. Liu, X. X. Tian, W. Y. Zan, Y. W. Mu, H. G. Lu, J. Li, Y. K. Wang, S. D. Li, Phys. Chem. Chem. Phys. 2017, 19, 27025. [37] J. Lv, Y. Wang, L. Zhang, H. Lin, J. Zhao, Y. Ma, Nanoscale 2015, 7, 10482. [38] R. N. Zhao, Y. H. Yuan, J. G. Han, Y. Duan, Chem. Phys. Lett. 2016, 648, 41. [39] Z. Mahdavifar, M. Poulad, J. Mol. Liq. 2016, 219, 1144. [40] Q. Xu, C. Liu, L. Yang, P. Jin, C. Tang, Z. Chen, J. Mol. Model. 2016, 22, 184. [41] Q. Lu, Q. Luo, Y. Li, S. Huang, Phys. Chem. Chem. Phys. 2015, 17, 20897. [42] A. J. Stasyuk, M. Sola, Phys. Chem. Chem. Phys. 2017, 19, 21276. [43] Q. Chen, T. Gao, W. J. Tian, H. Bai, S. Y. Zhang, H. R. Li, C. Q. Miao, Y. W. Mu, H. G. Lu, H. J. Zhai, S. D. Li, Phys. Chem. Chem. Phys. 2015, 17, 19690. [44] P. Jin, Q. Hou, C. Tang, Z. Chen, Theor. Chem. Acc. 2015, 134,13. [45] W. Fa, S. Chen, S. Pande, X. C. Zeng, J. Phys. Chem. A 2015, 119, 11208. [46] W. Wang, Y. D. Guo, X. H. Yan, RSC Adv. 2016, 6, 40155. [47] Y. An, M. Zhang, D. Wu, Z. Fu, T. Wang, C. Xia, Phys. Chem. Chem. Phys. 2016, 18, 12024. [48] E. Shakerzadeh, Z. Biglari, E. Tahmasebi, Chem. Phys. Lett. 2016, 654, 76. [49] T. Yu, Y. Gao, D. Xu, Z. Wang, Nano Res. 2017, https://doi.org/10.1007/s12274-017-1637-9. [50] P. Jin, L. Yang, C. Liu, Q. Hou, L. Li, Theor. Chem. Acc. 2017, 136, 56. [51] L. Yang, P. Jin, Q. Hou, L. Li, J. Mol. Model. 2016, 22, 297. [52] S. B. Cheng, C. Berkdemir, A. W. Castleman, Jr, Phys. Chem. Chem. Phys. 2014, 16, 533. [53] P. J. Robinson, X. Zhang, T. McQueen, K. H. Bowen, A. N. Alexandrova, J. Phys. Chem. A 2017, 121, 1849. [54] T. T. Chen, W. L. Li, T. Jian, X. Chen, J. Li, L. S. Wang, Angew. Chem. Int. Ed. Engl. 2017, 56, 6916. [55] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865. [56] F. Li, P. Jin, D. Jiang, L. Wang, S. B. Zhang, J. Zhao, Z. Chen, J. Chem. Phys. 2012, 136, 074302. [57] R. Krishnan, J. S. Binkley, R. Seeger, J. A. Pople, J. Chem. Phys. 1980, 72, 650.
XI
ET AL.
|
11 of 11
[58] T. R. Cundari, W. J. Stevens, J. Chem. Phys. 1993, 98, 5555. [59] R. Bauernschmitt, R. Ahlrichs, Chem. Phys. Lett. 1996, 256, 454. [60] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian 09, Revision D. 01, Gaussian, Inc., Wallingford, CT 2013. [61] A. D. Becke, K. E. Edgecombe, J. Chem. Phys. 1990, 92, 5397. [62] H. L. Schmider, A. D. Becke, J. Mol. Struct: THEOCHEM 2000, 527, 51. [63] T. Lu, F. Chen, J. Comput. Chem. 2012, 33, 580. [64] B. Delley, J. Chem. Phys. 1990, 92, 508. [65] B. Delley, J. Chem. Phys. 2000, 113, 7756. [66] P. v. R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N. J. R. v. E. Hommes, J. Am. Chem. Soc. 1996, 118, 6317. [67] Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta, P. v. R. Schleyer, Chem. Rev. 2005, 105, 3842.
S UPP ORT ING IN FORMAT ION Additional Supporting Information may be found online in the supporting information tab for this article.
How to cite this article: Xi C, Yang L, Liu C, You P, Li L, Jin P. Lanthanide metals in the boron cages: Computational prediction of M@Bn (M 5 Eu, Gd; n 5 38, 40). Int J Quantum Chem. 2018;118:e25576. https://doi.org/10.1002/qua.25576
