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Structures, electronic and magnetic properties of transition metal atoms encapsulated in B12N12 cage
Chemical Physics Letters xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Structures, electronic and magnetic properties of transition metal atoms encapsulated in B12N12 cage ⁎
Zhen Zhaoa, , Zhi Lib, Qi Wangb a b
School of Chemistry and Life Science, Anshan Normal University, PO Box 114007, Anshan, People’s Republic of China School of Materials and Metallurgy, University of Science and Technology Liaoning, PO Box 114051, Anshan, People’s Republic of China
H I GH L IG H T S
TM atoms are more suitable for the B N cages. • 3d and Ni are more suitable for the B N cages than their neighbors. • TiTi@B N , Fe@B N and Ni@B N clusters display more kinetic stability. • The Y@BN ,NCr@B clusters prefer to display ionic bond features. • 12
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Keywords: B12N12 cages Density functional theory Structures Electrical properties Magnetic properties
The structures, electronic and magnetic properties of a transition metal (TM) atom encapsulated in a B12N12 cage have been investigated by PBE functional. The results show that 3d TM atoms are more suitable for the B12N12 cage. For 3d TM atoms, Ti and Ni are more suitable for the B12N12 cage than their neighbors. Ti@B12N12, Cr@ B12N12, Fe@B12N12 and Ni@B12N12 clusters exhibit more kinetic stability. Only the Y@B12N12 clusters prefer to display ionic bond features. The maximum spins for the TM atoms of the TM@B12N12 clusters are occurred at Mn@B12N12, Fe@B12N12 and Co@B12N12.
1. Introduction Boron nitride fullerene-like cages have been widely applied as the structural or electronic materials due to the high-temperature stability, low dielectric constant, large thermal conductivity and oxidation resistance [1,2]. Many experimental and theoretical studies have been performed on the (BN)n (n = 4–30) clusters [3–6]. Transition metal (TM) atoms exist commonly on the synthesis of BN nanostructures [7]. The synthesized boron nitride fullerene may be a compound of BN nanostructures and TM atoms [8]. High-resolution electron microscopy images reveal the existence of the hybrid nanostructures by fullerene cages and TM atoms [8]. Similar hybrid nanostructures have also been detected by mass spectroscopy experiments [9]. Several theoretical calculations have been performed on TM atoms interaction with the BN nanostructures. Baei et al. [10] have investigated the adsorption mechanisms of B12N12 nanocages with 3d TM atoms by density functional theory (DFT) using B3LYP and M05 functional. Abbasi et al. [11] have systematically investigated the first row TM adsorptions on B12N12 fullerene-like clusters. Beheshtian et al. [12] have investigated the
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adsorption of alkaline earth cations inside and outside of B12N12 cages by DFT. Ayub [13] has systemically investigated the stability and magnetic properties of 3d and 4d TM atoms doped in the BnNn (n = 12,16,20,24,28) cages by first-principles. However, the encapsulated metal atoms will impart certain novel properties of the pristine fullerene [13]. Oliaey et al. [14] have investigated the spins of the endohedral alkali-metal-encapsulated B24N24 cages (M@B24N24, M = Li, Na, K) using DFT within B3LYP functional. In principle, TM atoms can be encapsulated in the different BnNn cages [13]. Seifert et al. [4] have pointed out that B12N12 is more stable than the others using ab initio calculations. Moreover, B12N12 has been synthesized by Oku et al. [15] via laser desorption time-of-flight mass spectrometry. The structures, electronic and magnetic properties of TM@B12N12 clusters have been calculated using DFT. It is important to evaluate the potential possibility of fabricating novel B12N12-based materials. 2. Computational details The structure of the B12N12 cage was adopted from Ref. [1,2,11,15].
Corresponding author. E-mail address: [email protected] (Z. Zhao).
https://doi.org/10.1016/j.cplett.2019.136922 Received 13 August 2019; Received in revised form 29 September 2019; Accepted 31 October 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Zhen Zhao, Zhi Li and Qi Wang, Chemical Physics Letters, https://doi.org/10.1016/j.cplett.2019.136922
Chemical Physics Letters xxx (xxxx) xxxx
Z. Zhao, et al.
structural deformation of the B-N cages [1,32].
Initially, an individual TM atom was placed at the center of the B12N12 cage to build the TM@B12N12 core@shell cluster. The B12N12 cage and the hypothetical TM@B12N12 core@shell clusters must be optimized. The geometry optimization has been performed using the DFT implemented in the DMol3 package [16,17]. The Perdew-Burkle-Ernzerhof (PBE) forms generalized gradient approximation (GGA) corrections were adopted for the exchange-correction potential [7,18]. For the TM atoms, which have the d orbital, have a strong interaction with N atoms. Coulomb exclusion U must be considered [19]. Symmetry unconstraint must be selected [7,10,12,13]. Double numerical basis sets including polarization functions (DNP) on all atoms was adopted [7,16]. The electron relativity effects must be considered to TM atoms, specially 4d and 5d atoms, so all treatment relativistic was adopted. Self-consistent field calculations were performed with a convergence criterion of 1 × 10−5 Hartree on the total energy. All the structures were fully optimized with a convergence criterion of 2 × 10−3 Hartree/ Å for the force, 5 × 10−3 Å for the atomic displacement, 1 × 10−5 Hartree/Bohr for the energy gradient and 1 × 10−6 e/Å3 for the charge density, respectively. After the equilibrium configurations were obtained, Mülliken population analysis was performed to determine the charge transfer and spin on each atomic site [7,20,21]. The structural stability of the TM@B12N12 clusters can be predicted by the average binding energies Eb. The average binding energies for the TM@B12N12 clusters can be defined as follows [22]
Eb = [E (TM @B12 N12) − E (TM ) − 12E (B ) − 12E (N )]/25
3.2. Stability To investigate the tendency towards structural stability across the Periodic Table, the average binding energies of the 3d, 4d and 5d TM atoms encapsulated in the B12N12 cages have been calculated. To clarify the meaning of the abscissa of Figs. 2–6, the subgroup table has been placed under Fig. 2. To determine the structural stability of TM@B12N12 clusters, the calculated average binding energy Eb (6.601 eV/atom) of the B12N12 cages has been compared. It can be found that the structural stability of the B12N12 cages is higher than those of TM@B12N12 clusters. The 3d TM atoms are more suitable for the B12N12 cages than the corresponding 4d and 5d TM atoms. As for the 3d TM atoms, Ti and Ni are more suitable for the B12N12 cages than their neighbors. It is because the differences in electron affinity with the TM atoms [33]. Such as the Zn atoms have completely filled d orbitals, thereby, having smaller tendency to react with the B12N12 cages [10]. The kinetic stability of the TM@B12N12 clusters base chiefly on the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states [34]. The HOMO-LUMO gaps of the TM@B12N12 clusters have been displayed in Fig. 3. The calculated HOMO-LUMO gap (5.985 eV) of the B12N12 cages has been displayed to compare, it can be found that all the TM atoms can significantly increase the kinetic activity of the B12N12 cages [35,36]. It means that the encapsulated TM atoms will increase the conductivity [37] and the metallic character of the B12N12 cages [11]. The HOMO and LUMO states of the B12N12 cages are located mainly on the N and B atoms [32]. While the encapsulated TM atoms will cause new states between the HOMO and LUMO [37]. It attributes to the charge transfer of the cages and the cores [12]. As for the 3d TM encapsulated in the B12N12 cages, maximum values of the HOMO-LUMO gaps are occurred at n = 4, 6, 8 and 11. It means that Ti@B12N12, Cr@ B12N12, Fe@B12N12 and Ni@B12N12 clusters have more kinetic stability. As for the 4d TM encapsulated in the B12N12 cages, maximum values of the HOMO-LUMO gaps are occurred at n = 4, 6 and 11. It indicates that Zr@B12N12, Mn@B12N12 and Ag@B12N12 clusters exhibit more kinetic stability. As for the 5d TM encapsulated in the B12N12 cages, maximum values of the HOMO-LUMO gaps are occurred at n = 4, 6 and 11. It means that Hf@B12N12, W@B12N12 and Au@B12N12 clusters possess higher kinetic stability.
(1)
where E(TM@B12N12), E(TM), E(B) and E(N) represent the total energies of the TM@B12N12, TM, B and N, respectively. To confirm the appropriateness of PBE functional, the calculated bond lengths (r66 = 1.437 Å and r46 = 1.485 Å) of B-N bond of the B12N12 cages which are shared by two hexagons and another between a tetragon and a hexagon are compared, it is in good agreement with the calculated values (r66 = 1.439 Å and r46 = 1.486 Å) by B3LYP [1]. Considering the interaction TM atoms with the B12N12 cages, the calculated dissociation energy (De = 4.04 eV) of FeN dimer agrees well with the experimental value (De = 3.94 eV [23]) by spectroscopy/mass spectrometry. Furthermore, for the 3d, 4d and 5d TM atoms, the calculated bond lengths of Fe2, Cu2, Pd2 and Pt2 dimer are successively (2.072 Å, 2.210 Å, 2.483 Å and 2.322 Å), which are in good agreement with the corresponding experimental values (2.02 ± 0.02 Å [24], 2.219 Å [25], 2.48 Å [26] and 2.333 Å [27–29]), respectively. The calculated average binding energy of Fe2 and Pt2 dimer are successively (0.524 eV/atom and 1.512 eV/atom), which agree well with the corresponding results (0.57 eV/atom [30] and 1.57 eV/atom [27–29]), respectively. It means that PBE functional is reliable and accurate enough to describe the TM@B12N12 system.
3.3. Electronic properties To explore the effect of the TM atoms on the B12N12 cages and consider the similar properties of the TM@B12N12 clusters, only the HOMO and LUMO states of the 3d TM@B12N12 clusters have been displayed in Table 1. The HOMO describes the ability of a system to lose electrons, whereas the LUMO illustrates the ability to accept electrons [13,36]. It shows that the HOMO states are more located on the B atoms, while LUMO states are located on the N atoms. Moreover, for the Zn@B12N12 clusters, LUMO states are distributed partly on the encapsulated Zn atoms. It is different from the B12N12 cages adsorbed by alkali metal ions [36]. To expound the feature of chemical bonds of the TM@B12N12 clusters, the net-charges of the TM atoms for the TM@B12N12 clusters have been shown in Fig. 4. It can be seen that most of the TM@B12N12 clusters prefer to display covalent bond characteristics except for the Y@B12N12 clusters due to only the difference in electronegativity of the Y@B12N12 clusters is larger than the threshold 1.7. As for the 3d TM atoms, the transferred electrons are rare except for Cu and Zn atoms. As for the 4d and 5d TM atoms, the tendency towards the electron transfer are almost the same. the transferred electrons of Zr@B12N12, Rh@ B12N12 and Au@B12N12 are less than their neighbors. It is because the differences in the electron affinity with the TM atoms [33].
3. Results and discussion 3.1. Structures Once the hypothetical TM@B12N12 core@shell clusters are optimized, for subgroup 3–9 and Ni, the TM atoms deviate the centre of the B12N12 cage, however, for subgroup 10–12 except for Ni, the TM atoms remain in the centre of the B12N12 cage (see Fig. 1). It may derive from many valences of these TM atoms which cause the non-uniform bonds with the B12N12 cages [31]. On the other hand, compare the average bond lengths of the r66 = 1.439 Å and r46 = 1.486 Å of the B12N12 cages, the TM atoms will enlarge slightly the corresponding bond lengths of B-N of B12N12 cage. For example, for Ag@B12N12, the average lengths of the r66 and r46 bonds are about 1.472 Å and 1.516 Å, respectively. According to the natural bond orbital (NBO) analysis, it can be found that the natural charges (+0.373 |e| and −0.373 |e|) of B and N of the B12N12 cages are increased to + 0.427 |e| and −0.428 |e| as an Ag atom is encapsulated to the B12N12 cages, and then the natural charge of Ag is transferred to 0.006 |e|. It will induce the local 2
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Fig. 1. Structures of the TM@B12N12 core@shell clusters.
3d sub-shell in comparison with the Mn atoms [10]. While the Co atoms tend to complete the 3d sub-shell [10].
3.4. Spin properties Magnetic properties of the TM atoms encapsulated in the cages are an important physical features [7]. The bonding mechanism arises mainly from polarization [10]. The spins of the isolated TM atoms and the TM atoms for encapsulated in the B12N12 cages have been plotted in Figs. 5-6, respectively. It can be found that the spins of the TM atoms for the TM@B12N12 cages almost completely quenched which derived from the charge transfer of the TM atoms and the B12N12 cages [7]. It originates the level splitting of the d-orbital electrons [38]. From Fig. 6 it can be found that as for the 3d TM atoms, the maximum spins for the TM@B12N12 clusters are occurred at the subgroup number 7–9. That is, Mn@B12N12, Fe@B12N12 and Co@B12N12, respectively. It is because that the 3d wave function is more localized [39] and the 3d TM atoms have weaker hybridization with the cages [7]. The Fe atoms also have more tendency to give electrons in order to achieve the partially filled
4. Conclusions The structures, stability, electronic and magnetic properties of a 3d, 4d or 5d TM atom encapsulated in a B12N12 cage have been calculated using PBE functional. The results show that only subgroup 10–12 except for Ni, the TM atoms remain in the centre of the B12N12 cage. The structural stability of the B12N12 cages is higher than those of the TM@ B12N12 core@shell clusters. The 3d TM atoms are more suitable for the B12N12 cage than the corresponding 4d and 5d TM atoms. As for 3d TM atoms, Ti and Ni are more suitable for the B12N12 cage than their neighbors. For the 3d TM@B12N12 clusters, including Ti@B12N12, Cr@ B12N12, Fe@B12N12 and Ni@B12N12 clusters exhibit more kinetic stability by the HOMO-LUMO gaps. For 3d TM atoms, the transferred 3
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Fig. 5. Spins of the isolated TM atoms.
Fig. 2. Average binding energies of the TM@B12N12 clusters.
Fig. 6. Spins of TM atoms for the TM@B12N12 clusters. Table 1 The HOMO and LUMO distributions of the TM@B12N12 clusters. Clusters
Fig. 3. HOMO-LUMO gaps of the TM@B12N12 clusters.
Sc@B12N12
Ti@B12N12
V@B12N12
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Fig. 4. Net-charges of TM atoms for the TM@B12N12 clusters.
Co@B12N12
electrons are rare except for Cu and Zn atoms. Only the Y@B12N12 clusters prefer to display ionic bond features. The maximum spins for the TM atoms of the TM@B12N12 clusters are occurred at Mn@B12N12, Fe@B12N12 and Co@B12N12, respectively.
Ni@B12N12
Cu@B12N12
Zn@B12N12
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 4
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influence the work reported in this paper.
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Acknowledgments We gratefully acknowledge the financial support from the Key Fund Project of the National Science Foundation, People’s Republic of China (Grant No. 51634004), the Doctoral Scientific Research Foundation of Liaoning Province, China (Grant No. 20180551213), Key Laboratory of Chemical Metallurgy Engineering Liaoning Province, University of Science and Technology Liaoning, China (Grant No. USTLKFSY201711) and the Fund Project of University of Science and Technology Liaoning, China (Grant No. 2017YY02). References [1] H. Wang, A density functional investigation of fluorinated B12N12 clusters, Chin. J. Chem . 28 (2010) 1897–1901. [2] M.T. Baei, Adsorption of the urea molecule on the B12N12 nanocage, Turk. J. Chem. 38 (2014) 531–537. [3] D.-B. Zhang, E. Akatyeva, T. Dumitrica, Helical BN and ZnO nanotubes with intrinsic twisting: an objective molecular dynamics study, Phys. Rev. B. 84 (2011) 115431 (8 pages). [4] G. Seifert, P.W. Fowler, D. Mitchell, D. Porezag, Th. Frauenheim, Boron-nitrogen analogues of the fullerenes: electronic and structural properties, Chem. Phys. Lett. 268 (1997) 352–358. [5] D.L. Strout, ChemInform abstract: structure and stability of boron nitrides: the crossover between rings and cages, J. Phys. Chem. A 105 (2001) 261–263. [6] K.M. Rogers, P.W. Fowler, G. Seifert, Chemical versus steric frustration in boron nitride heterofullerene polyhedra, Chem. Phys. Lett. 332 (2000) 43–50. [7] J. Wang, L. Ma, J. Zhao, B. Wang, G. Wang, Stability and magnetic properties of transition metal atoms endohedral BnNn (n=12-28) cages, J. Chem. Phys. 128 (2008) 084306 (7 pages). [8] T. Oku, K. Suganuma, High-resolution electron microscopy and structural optimization of C36, B36N36 and Fe@B36N36 clusters, Diam. Relat. Mater. 10 (2001) 1205–1209. [9] T. Oku, I. Narita, A. Nishiwaki, Formation and structures of B36N36 and Y@B36N36 clusters studied by high-resolution electron microscopy and mass spectrometry, J. Phys. Chem. Solids 65 (2004) 369–372. [10] M.T. Baei, Z. Bagheri, A.A. Peyghan, Transition metal atom adsorptions on a boron nitride nanocage, Struct. Chem. 24 (2013) 1039–1044. [11] M. Abbasi, E. Nemati-Kande, M. Doust Mohammadi, Doping of the first row transition metals onto B12N12 nanocage: a DFT study, Comput. Theor. Chem. 1132 (2018) 1–11. [12] J. Beheshtian, M.B. Tabar, Z. Bagheri, A.A. Peyghan, Exohedral and endohedral adsorption of alkaline earth cations in BN nanocluster, J. Mol. Model. 19 (2013) 1445–1450. [13] K. Ayub, Are phosphide nano-cages better than nitride nano-cages? A kinetic, thermodynamic and non-linear optical properties study of alkali metal encapsulated X12Y12 nano-cages, J. Mater. Chem. C 4 (2016) 10919–10934. [14] A.R. Oliaey, A. Boshra, M. Khavary, Spin polarized bonding analysis of endohedral boron nitride nanocages: density functional theory study, Physica E 42 (2010) 2314–2318. [15] T. Oku, A. Nishiwaki, I. Narita, Formation and atomic structure of B12N12 nanocage clusters studied by mass spectrometry and cluster calculation, Sci. Technol. Adv. Mater. 5 (2004) 635–645.
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
Structures, electronic and magnetic properties of transition metal atoms encapsulated in B12N12 cage ⁎
Zhen Zhaoa, , Zhi Lib, Qi Wangb a b
School of Chemistry and Life Science, Anshan Normal University, PO Box 114007, Anshan, People’s Republic of China School of Materials and Metallurgy, University of Science and Technology Liaoning, PO Box 114051, Anshan, People’s Republic of China
H I GH L IG H T S
TM atoms are more suitable for the B N cages. • 3d and Ni are more suitable for the B N cages than their neighbors. • TiTi@B N , Fe@B N and Ni@B N clusters display more kinetic stability. • The Y@BN ,NCr@B clusters prefer to display ionic bond features. • 12
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Keywords: B12N12 cages Density functional theory Structures Electrical properties Magnetic properties
The structures, electronic and magnetic properties of a transition metal (TM) atom encapsulated in a B12N12 cage have been investigated by PBE functional. The results show that 3d TM atoms are more suitable for the B12N12 cage. For 3d TM atoms, Ti and Ni are more suitable for the B12N12 cage than their neighbors. Ti@B12N12, Cr@ B12N12, Fe@B12N12 and Ni@B12N12 clusters exhibit more kinetic stability. Only the Y@B12N12 clusters prefer to display ionic bond features. The maximum spins for the TM atoms of the TM@B12N12 clusters are occurred at Mn@B12N12, Fe@B12N12 and Co@B12N12.
1. Introduction Boron nitride fullerene-like cages have been widely applied as the structural or electronic materials due to the high-temperature stability, low dielectric constant, large thermal conductivity and oxidation resistance [1,2]. Many experimental and theoretical studies have been performed on the (BN)n (n = 4–30) clusters [3–6]. Transition metal (TM) atoms exist commonly on the synthesis of BN nanostructures [7]. The synthesized boron nitride fullerene may be a compound of BN nanostructures and TM atoms [8]. High-resolution electron microscopy images reveal the existence of the hybrid nanostructures by fullerene cages and TM atoms [8]. Similar hybrid nanostructures have also been detected by mass spectroscopy experiments [9]. Several theoretical calculations have been performed on TM atoms interaction with the BN nanostructures. Baei et al. [10] have investigated the adsorption mechanisms of B12N12 nanocages with 3d TM atoms by density functional theory (DFT) using B3LYP and M05 functional. Abbasi et al. [11] have systematically investigated the first row TM adsorptions on B12N12 fullerene-like clusters. Beheshtian et al. [12] have investigated the
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adsorption of alkaline earth cations inside and outside of B12N12 cages by DFT. Ayub [13] has systemically investigated the stability and magnetic properties of 3d and 4d TM atoms doped in the BnNn (n = 12,16,20,24,28) cages by first-principles. However, the encapsulated metal atoms will impart certain novel properties of the pristine fullerene [13]. Oliaey et al. [14] have investigated the spins of the endohedral alkali-metal-encapsulated B24N24 cages (M@B24N24, M = Li, Na, K) using DFT within B3LYP functional. In principle, TM atoms can be encapsulated in the different BnNn cages [13]. Seifert et al. [4] have pointed out that B12N12 is more stable than the others using ab initio calculations. Moreover, B12N12 has been synthesized by Oku et al. [15] via laser desorption time-of-flight mass spectrometry. The structures, electronic and magnetic properties of TM@B12N12 clusters have been calculated using DFT. It is important to evaluate the potential possibility of fabricating novel B12N12-based materials. 2. Computational details The structure of the B12N12 cage was adopted from Ref. [1,2,11,15].
Corresponding author. E-mail address: [email protected] (Z. Zhao).
https://doi.org/10.1016/j.cplett.2019.136922 Received 13 August 2019; Received in revised form 29 September 2019; Accepted 31 October 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Zhen Zhao, Zhi Li and Qi Wang, Chemical Physics Letters, https://doi.org/10.1016/j.cplett.2019.136922
Chemical Physics Letters xxx (xxxx) xxxx
Z. Zhao, et al.
structural deformation of the B-N cages [1,32].
Initially, an individual TM atom was placed at the center of the B12N12 cage to build the TM@B12N12 core@shell cluster. The B12N12 cage and the hypothetical TM@B12N12 core@shell clusters must be optimized. The geometry optimization has been performed using the DFT implemented in the DMol3 package [16,17]. The Perdew-Burkle-Ernzerhof (PBE) forms generalized gradient approximation (GGA) corrections were adopted for the exchange-correction potential [7,18]. For the TM atoms, which have the d orbital, have a strong interaction with N atoms. Coulomb exclusion U must be considered [19]. Symmetry unconstraint must be selected [7,10,12,13]. Double numerical basis sets including polarization functions (DNP) on all atoms was adopted [7,16]. The electron relativity effects must be considered to TM atoms, specially 4d and 5d atoms, so all treatment relativistic was adopted. Self-consistent field calculations were performed with a convergence criterion of 1 × 10−5 Hartree on the total energy. All the structures were fully optimized with a convergence criterion of 2 × 10−3 Hartree/ Å for the force, 5 × 10−3 Å for the atomic displacement, 1 × 10−5 Hartree/Bohr for the energy gradient and 1 × 10−6 e/Å3 for the charge density, respectively. After the equilibrium configurations were obtained, Mülliken population analysis was performed to determine the charge transfer and spin on each atomic site [7,20,21]. The structural stability of the TM@B12N12 clusters can be predicted by the average binding energies Eb. The average binding energies for the TM@B12N12 clusters can be defined as follows [22]
Eb = [E (TM @B12 N12) − E (TM ) − 12E (B ) − 12E (N )]/25
3.2. Stability To investigate the tendency towards structural stability across the Periodic Table, the average binding energies of the 3d, 4d and 5d TM atoms encapsulated in the B12N12 cages have been calculated. To clarify the meaning of the abscissa of Figs. 2–6, the subgroup table has been placed under Fig. 2. To determine the structural stability of TM@B12N12 clusters, the calculated average binding energy Eb (6.601 eV/atom) of the B12N12 cages has been compared. It can be found that the structural stability of the B12N12 cages is higher than those of TM@B12N12 clusters. The 3d TM atoms are more suitable for the B12N12 cages than the corresponding 4d and 5d TM atoms. As for the 3d TM atoms, Ti and Ni are more suitable for the B12N12 cages than their neighbors. It is because the differences in electron affinity with the TM atoms [33]. Such as the Zn atoms have completely filled d orbitals, thereby, having smaller tendency to react with the B12N12 cages [10]. The kinetic stability of the TM@B12N12 clusters base chiefly on the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states [34]. The HOMO-LUMO gaps of the TM@B12N12 clusters have been displayed in Fig. 3. The calculated HOMO-LUMO gap (5.985 eV) of the B12N12 cages has been displayed to compare, it can be found that all the TM atoms can significantly increase the kinetic activity of the B12N12 cages [35,36]. It means that the encapsulated TM atoms will increase the conductivity [37] and the metallic character of the B12N12 cages [11]. The HOMO and LUMO states of the B12N12 cages are located mainly on the N and B atoms [32]. While the encapsulated TM atoms will cause new states between the HOMO and LUMO [37]. It attributes to the charge transfer of the cages and the cores [12]. As for the 3d TM encapsulated in the B12N12 cages, maximum values of the HOMO-LUMO gaps are occurred at n = 4, 6, 8 and 11. It means that Ti@B12N12, Cr@ B12N12, Fe@B12N12 and Ni@B12N12 clusters have more kinetic stability. As for the 4d TM encapsulated in the B12N12 cages, maximum values of the HOMO-LUMO gaps are occurred at n = 4, 6 and 11. It indicates that Zr@B12N12, Mn@B12N12 and Ag@B12N12 clusters exhibit more kinetic stability. As for the 5d TM encapsulated in the B12N12 cages, maximum values of the HOMO-LUMO gaps are occurred at n = 4, 6 and 11. It means that Hf@B12N12, W@B12N12 and Au@B12N12 clusters possess higher kinetic stability.
(1)
where E(TM@B12N12), E(TM), E(B) and E(N) represent the total energies of the TM@B12N12, TM, B and N, respectively. To confirm the appropriateness of PBE functional, the calculated bond lengths (r66 = 1.437 Å and r46 = 1.485 Å) of B-N bond of the B12N12 cages which are shared by two hexagons and another between a tetragon and a hexagon are compared, it is in good agreement with the calculated values (r66 = 1.439 Å and r46 = 1.486 Å) by B3LYP [1]. Considering the interaction TM atoms with the B12N12 cages, the calculated dissociation energy (De = 4.04 eV) of FeN dimer agrees well with the experimental value (De = 3.94 eV [23]) by spectroscopy/mass spectrometry. Furthermore, for the 3d, 4d and 5d TM atoms, the calculated bond lengths of Fe2, Cu2, Pd2 and Pt2 dimer are successively (2.072 Å, 2.210 Å, 2.483 Å and 2.322 Å), which are in good agreement with the corresponding experimental values (2.02 ± 0.02 Å [24], 2.219 Å [25], 2.48 Å [26] and 2.333 Å [27–29]), respectively. The calculated average binding energy of Fe2 and Pt2 dimer are successively (0.524 eV/atom and 1.512 eV/atom), which agree well with the corresponding results (0.57 eV/atom [30] and 1.57 eV/atom [27–29]), respectively. It means that PBE functional is reliable and accurate enough to describe the TM@B12N12 system.
3.3. Electronic properties To explore the effect of the TM atoms on the B12N12 cages and consider the similar properties of the TM@B12N12 clusters, only the HOMO and LUMO states of the 3d TM@B12N12 clusters have been displayed in Table 1. The HOMO describes the ability of a system to lose electrons, whereas the LUMO illustrates the ability to accept electrons [13,36]. It shows that the HOMO states are more located on the B atoms, while LUMO states are located on the N atoms. Moreover, for the Zn@B12N12 clusters, LUMO states are distributed partly on the encapsulated Zn atoms. It is different from the B12N12 cages adsorbed by alkali metal ions [36]. To expound the feature of chemical bonds of the TM@B12N12 clusters, the net-charges of the TM atoms for the TM@B12N12 clusters have been shown in Fig. 4. It can be seen that most of the TM@B12N12 clusters prefer to display covalent bond characteristics except for the Y@B12N12 clusters due to only the difference in electronegativity of the Y@B12N12 clusters is larger than the threshold 1.7. As for the 3d TM atoms, the transferred electrons are rare except for Cu and Zn atoms. As for the 4d and 5d TM atoms, the tendency towards the electron transfer are almost the same. the transferred electrons of Zr@B12N12, Rh@ B12N12 and Au@B12N12 are less than their neighbors. It is because the differences in the electron affinity with the TM atoms [33].
3. Results and discussion 3.1. Structures Once the hypothetical TM@B12N12 core@shell clusters are optimized, for subgroup 3–9 and Ni, the TM atoms deviate the centre of the B12N12 cage, however, for subgroup 10–12 except for Ni, the TM atoms remain in the centre of the B12N12 cage (see Fig. 1). It may derive from many valences of these TM atoms which cause the non-uniform bonds with the B12N12 cages [31]. On the other hand, compare the average bond lengths of the r66 = 1.439 Å and r46 = 1.486 Å of the B12N12 cages, the TM atoms will enlarge slightly the corresponding bond lengths of B-N of B12N12 cage. For example, for Ag@B12N12, the average lengths of the r66 and r46 bonds are about 1.472 Å and 1.516 Å, respectively. According to the natural bond orbital (NBO) analysis, it can be found that the natural charges (+0.373 |e| and −0.373 |e|) of B and N of the B12N12 cages are increased to + 0.427 |e| and −0.428 |e| as an Ag atom is encapsulated to the B12N12 cages, and then the natural charge of Ag is transferred to 0.006 |e|. It will induce the local 2
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Fig. 1. Structures of the TM@B12N12 core@shell clusters.
3d sub-shell in comparison with the Mn atoms [10]. While the Co atoms tend to complete the 3d sub-shell [10].
3.4. Spin properties Magnetic properties of the TM atoms encapsulated in the cages are an important physical features [7]. The bonding mechanism arises mainly from polarization [10]. The spins of the isolated TM atoms and the TM atoms for encapsulated in the B12N12 cages have been plotted in Figs. 5-6, respectively. It can be found that the spins of the TM atoms for the TM@B12N12 cages almost completely quenched which derived from the charge transfer of the TM atoms and the B12N12 cages [7]. It originates the level splitting of the d-orbital electrons [38]. From Fig. 6 it can be found that as for the 3d TM atoms, the maximum spins for the TM@B12N12 clusters are occurred at the subgroup number 7–9. That is, Mn@B12N12, Fe@B12N12 and Co@B12N12, respectively. It is because that the 3d wave function is more localized [39] and the 3d TM atoms have weaker hybridization with the cages [7]. The Fe atoms also have more tendency to give electrons in order to achieve the partially filled
4. Conclusions The structures, stability, electronic and magnetic properties of a 3d, 4d or 5d TM atom encapsulated in a B12N12 cage have been calculated using PBE functional. The results show that only subgroup 10–12 except for Ni, the TM atoms remain in the centre of the B12N12 cage. The structural stability of the B12N12 cages is higher than those of the TM@ B12N12 core@shell clusters. The 3d TM atoms are more suitable for the B12N12 cage than the corresponding 4d and 5d TM atoms. As for 3d TM atoms, Ti and Ni are more suitable for the B12N12 cage than their neighbors. For the 3d TM@B12N12 clusters, including Ti@B12N12, Cr@ B12N12, Fe@B12N12 and Ni@B12N12 clusters exhibit more kinetic stability by the HOMO-LUMO gaps. For 3d TM atoms, the transferred 3
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3d
3
4
5
6
7
8
9
10
11
12
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
4d
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
5d
Lu
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Fig. 5. Spins of the isolated TM atoms.
Fig. 2. Average binding energies of the TM@B12N12 clusters.
Fig. 6. Spins of TM atoms for the TM@B12N12 clusters. Table 1 The HOMO and LUMO distributions of the TM@B12N12 clusters. Clusters
Fig. 3. HOMO-LUMO gaps of the TM@B12N12 clusters.
Sc@B12N12
Ti@B12N12
V@B12N12
Cr@B12N12
Mn@B12N12
Fe@B12N12
Fig. 4. Net-charges of TM atoms for the TM@B12N12 clusters.
Co@B12N12
electrons are rare except for Cu and Zn atoms. Only the Y@B12N12 clusters prefer to display ionic bond features. The maximum spins for the TM atoms of the TM@B12N12 clusters are occurred at Mn@B12N12, Fe@B12N12 and Co@B12N12, respectively.
Ni@B12N12
Cu@B12N12
Zn@B12N12
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 4
HOMO
LUMO
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influence the work reported in this paper.
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