Ab Initio Study of Structural, Electronic and Magnetic Properties of TM&(B@C60) (TM = V, Cr) Sandwich Clusters and Infinite Molecular Wires

The geometrical structure, electronic and magnetic properties of B-endoped C60 (B@C60) ligand sandwich clusters, TM&(B@C60)2 (TM = V, Cr), and their one-dimensional (1D) infinite molecular wires, [TM&(B@C60)]∞, have been systematically studied using first-principles calculations. The calculations showed that the TM atoms can bond strongly to the pentagonal (η5-coordinated) or hexagonal rings (η6-coordinated) of the endoped C60 ligands, with binding energies ranging from 1.90 to 3.81 eV. Compared to the configurations with contrast-bonding characters, the η6- and η5-coordinated bonding is energetically more favorable for V-(B@C60) and Cr-(B@C60) complexes, respectively. Interestingly, 1D infinite molecular wire [V&(B@C60)-η6]∞ is an antiferromagnetic half-metal, and 1D [Cr&(B@C60)-η5]∞ molecular wire is a ferromagnetic metal. The tunable electronic and magnetic properties of 1D [TM&(B@C60)]∞ SMWs are found under compressive and tensile stains. These findings provide additional possibilities for the application of C60-based sandwich compounds in electronic and spintronic devices.


Introduction
Since the discovery of C 60 in 1985 [1,2], various fullerenes and their derivatives have attracted great attention due to their extraordinary stability and unique chemical and physical properties [3][4][5][6][7]. Particularly, versatile polygons, such as pentagons and hexagons, in fullerenes enabled them to be potential ligands bonding in external metal elements. Using a laser vaporization method, Nakajima et al. [8][9][10] successfully synthesized TM-C 60 (TM= 3d transition metal) complexes in the 1990s, and predicted that the TM n (C 60 ) m clusters exhibit sandwich-like structures for m = n + 1, n ≤ 3 or ring-like structures for m = n, n > 3. These structure characteristics were later confirmed via theoretical studies [11]. In addition, the TM-C 60 coordinated bonds in TM n (C 60 ) m complexes were found to be dependent on the choice of TM atom [12,13]. However, differently from the comprehensively studied benzene (Bz)-ligand [10,14] or cyclopentadienyl (Cp)-ligand [15] sandwich complexes, most C 60 sandwich complexes were confirmed to be non-magnetic or weakly magnetic [11][12][13], severely limiting their application in spintronic devices. Therefore, tuning the electronic and magnetic properties of fullerene-ligand sandwich complexes remains challenging.

Models and Method
All the calculations were performed in the Vienna ab initio simulation package (VASP) [36,37] under the spin-polarized DFT framework. The exchange correlation interaction was described by the Perdew-Burke-Ernzerhof (PBE) [38] functional, and the interaction between valence electrons and ion nuclei was described by the projector-augmented wave potential (PAW) [39] method. In the process of calculations, the van der Waals (vdW) interaction was considered by using the DFT-D2 [40] method. In order to further consider the Coulomb interaction and exchange interactions of the d-electron in the transition metal atom, we adopted the GGA + U method [41], in which the parameter U was set to 3.0 Ev [42,43]. In order to find the magnetic ground state of the 1D [TM&(B@C 60 )] ∞ SMWs, a 1 × 1 × 2 supercell consisting of two TM atoms and two (B@C 60 ) units was used. The criteria for energy and atom force convergence were set to 10 −4 eV and 0.01 eV/Å, respectively. To determine the magnetic ground states of the TM&(B@C 60 ) clusters and molecular wires, diverse magnetic states with different magnetic moments were calculated and compared.

TM&(B@C 60 ) 2 (TM = V, Cr) Sandwich Clusters
First, we explored the structural characters of the endohedral B@C 60 cluster (see Figure 1a). Similar to the C 60 molecule, the point group symmetry of the B@C 60 molecule is Ih, with the B atom sitting on the mass center of C 60 . The diameter of B@C 60 is 7.09 Å and the C-C bond length is 1.45 Å. As shown in the spin density plot (see Figure 1b), the B atom in B@C 60 is spin-polarized with a local magnetic moment of 1.0 µ B . The partial density of state (PDOS) of B@C 60 ( Figure 1b) shows that the p states of the B atom is spin-polarized in the energy around the Fermi level, accounting for the 1.0 µ B net magnetic moment. Two types of TM&(B@C 60 ) 2 configurations were considered: (i) TM&(B@C 60 ) 2 -η 5 , in which the sandwiched TM atoms are bonded to two pentagonal rings of two B@C 60 molecules forming η 5 -coordinate bonds; and (ii) TM&(B@C 60 ) 2 -η 6 , in which the TM atoms are bonded to two hexagonal rings of two B@C 60 s forming η 6 -coordinate bonds. Figure 1c,d show the optimized structures of V&(B@C 60 ) 2 and Cr&(B@C 60 ) 2 . Clearly, all the TM&(B@C 60 ) 2 s favor normal sandwich configurations, with the TM atom sitting above the mass center of the pentagon or hexagon rings. For V&(B@C 60 ) 2 , the η 6 coordinated configuration is more stable than the η 5 coordinated one, with an energy difference of 0.32 eV. On the contrary, the η 5 coordinated configuration is energetically more stable for Cr&(B@C 60 ) 2 , with approximately 0.50 eV less energy. For V&(B@C 60 ) 2 and Cr&(B@C 60 ) 2 , the distances of TM atoms from the mass center of the faced C n ring (n = 5, 6) (d TM-C60 ) to the nearest carbon rings are in the range of 1.73-2.00 Å (see Table 1), which are a bit larger than those in the TM-Bz (1.70 Å) [44], TM-Cp (1.72 Å-1.81 Å) [15] and TM-C 60 (1.75 Å) [6] sandwich compounds. In the compounds, the d TM-C60 s in η 5 coordinated systems are longer than those in the η 6 coordinated ones by around 0.21~0.28 Å. Moreover, the B atoms in the TM&(B@C 60 ) 2 s (Figure 1c,d) deviate from the center of C 60 with 0.02~0.08 Å (see Table 1). In order to investigate the stability of these TM&(B@C 60 ) 2 sandwich clusters, the binding energies (E b ) are calculated based on the following formula: where E TM , E B@C60 and E TM&(B@C60)2 are the energies of the isolated TM atom, B@C 60 molecule and TM&(B@C 60 ) 2 , respectively. Shown in Table 1, the E b s of V&(B@C 60 ) 2 and Cr&(B@C 60 ) 2 with η 5 /η 6 coordinated bonding are approximately −1.90/−2.23 eV and −3.81/−3.31 eV, respectively, implying that these sandwich clusters are energetically stable. As a result, the most energetically stable configuration is Cr&(B@C 60 ) 2 -η 5 .  To determine the magnetic ground states of these TM&(B@C 60 ) 2 clusters, we considered different spin states for each system (see Table S1 in the supporting information, SI). For V&(B@C 60 ) 2 , the magnetic moment of its ground state is 3.0 µB and 1.0 µB in their η 5 /η 6 coordinated configurations. Their second lower-energy isomers are found to have magnetic moments of 5.0 µB and 3.0 µB, which are less stable than the ground states by approximately 0.01 eV and are 0.03 eV higher in energy, respectively. In addition, for Cr&(B@C 60 ) 2 -η 5 and Cr&(B@C 6 0) 2 -η 6 , the magnetic moment of 6.0 µB and 2.0 µB is observed for their ground states, which are approximately 0.03 eV and 0.17 eV lower in energy, respectively, than their second higher-energy isomers with the same magnetic moment of 4.0 µB. The inset in Figure 2 shows the spin densities of V&(B@C 60 ) 2 and Cr&(B@C 60 ) 2 . Clearly, the magnetic moments of both systems are mainly contributed to the B atoms and TM atoms. The B atom and TM atom for V&(B@C 60 ) 2 -η 5 and Cr&(B@C 60 ) 2 -η 6 contribute to opposite spins. In contrast, the same spins are found for the B atom and Cr atom in Cr&(B@C 60 ) 2 -η 5 . As for V&(B@C 60 ) 2 -η 6 , its magnetic moments mainly arise from two B atoms with opposite spins.  Table 1 and Figure 3a,b). Meanwhile, B atoms in the endoped C 60 are separate from the mass center of C 60 , with the deviation values (∆h) of 0.32 Å and 0.09 Å, respectively. Table 1 shows that the d TM-C60 in 1D [V&(B@C 60 )-η 6 ] ∞ SMW and [Cr&(B@C 60 )-η 5 ] ∞ SMW are approximately 1.70 Å and 2.01 Å, respectively, and are a bit shorter than that in the finite sandwich clusters. To evaluate the stability of these SMWs, we defined the binding energy (E b ) of SMWs as:

Conclusions
Using first principles calculations, we systematically investigated the structure, electronic and magnetic properties of 3d transition metal atoms and B@C 60 sandwich clusters, TM&(B@C 60 ) 2 (TM = V, Cr), and their 1D infinite SMWs, [TM&(B@C 60 )] ∞ . Our results showed that all the studied systems possess normal sandwich structures with extremely thermodynamic stabilities. It was found that respective η 6 -and η 5 -bonding configurations are confirmed for the systems with TM = V and Cr. One-dimensional [V&(B@C 60 )-η 6 ] ∞ and [Cr&(B@C 60 )-η 5 ] ∞ SMWs are an antiferromagnetic half-metal and a ferromagnetic metal. Furthermore, the magnetic properties can be modulated by exerting biaxial compressive and tensile strains. Finally, we should state that the diverse electronic and magnetic properties of the studied complexes may be highly sensitive to their surroundings [48,49]. Therefore, exploring their performance in a complicated environment, instead of non-freestanding states, is also of importance.

Conflicts of Interest:
The authors declare no conflict of interest.