Magnetic coupling induced by the interaction between endohedral metal borofullerenes

Abstract

Superatom-assembled materials have highly tunable magnetic and electronic properties and parameters of clusters. Here, eight superatom dimers composed of two U@B₄₀ motifs have been studied by the density functional theory. Calculation results show that U@B₄₀ dimers exhibit spin antiferromagnetic coupling, spin ferromagnetic coupling and nonmagnetic, that is, the magnetic coupling is induced by the interaction between the U@B₄₀ superatoms. In addition, the monomers in U@B₄₀ dimers still retain the superatomic orbitals, and some of the super atomic orbitals disappear due to the interaction between monomers. The assembly based on U@B₄₀ induced a decrease in the energy gap. This study provides a basis for a deep understanding of controlling the cluster-assembled materials for tailoring their functionalities.

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Introduction

Cluster-assembled materials (CAMs) have attracted wide interest in recent years^1–4 and have been applied in organic pollutant sensing and biomedical applications,⁵ gas sensors,^6,7 hydrogen storage,⁸ etc. Thus, numerous CAMs have been studied, such as CdO and ZnO clusters,^9,10 TM@Si₁₂ (TM = 3d transition metal),^11–13 M₁₂N₁₂ (M = Al, Ga) fullerene-like clusters¹⁴ and noble metal nanostructures.^5,15–17 CAM building blocks are clusters, meaning, more atoms and arrangements are available to select and assemble to adjust the properties of the materials.¹ Stable cluster building blocks for self-assembly are of crucial importance, as many clusters at these small sizes have lifetimes too short for controlled assembly into materials.¹ In addition, clusters with closed electronic shells and large HOMO–LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gaps have enhanced stability and reduced reactivity.¹⁸ Thus, superatoms, such as Al₁₃⁻,^19–21 As₇,^22,23 B₄₀,²⁴ C₆₀,^25–27 An@C₂₈,²⁸ can be used as building blocks in creating self-assembled cluster materials.

Previous studies on endohedral-metallofullerene (EMF) containing actinides have promoted the application of actinide compounds in functional nanomaterials and nanomedicine.^29–31 In 2014, a combination of experimental and theoretical research discovered the B₄₀ hollow cage.³² Subsequently, studies have shown that B₄₀ clusters exhibit superatomic properties, but their electronic configuration is not fully filled.³³ Moreover, the clusters of embedded atoms or small molecules can form stable core@shell systems.^34,35 The studies on U@B₄₀ prove that it is indeed a stable closed-shell electronic structure.³⁵ Therefore, the U@B₄₀ as building blocks for assembly are capable of tailoring more stable nanostructures or nanocrystals. Moreover, the interaction between EMFs of U@C₂₈ can lead to different chemical and physical adsorption structures, which are derived from different magnetic coupling.³⁶ Whether the interaction between U@B₄₀ superatoms also causes magnetic coupling, will be helpful for the study of functional CAMs.

Currently, cluster-assembled materials are explored and tailored to control their functions.¹ In this work, we constructed eight U@B₄₀ dimers based on the first principles. Unlike the U@B₄₀ monomer,³⁵ the assembly based on U@B₄₀ affects the magnetic properties of the structures, and different conformations exhibit different magnetic coupling. The monomers in the U@B₄₀ dimer also retain part of the superatomic orbitals, similar to the assembly of B₄₀ oligomers.²⁴ The energy gap of the U@B₄₀ dimer is smaller than that of U@B₄₀.³⁵ Therefore, we propose a possible route to construct cluster-assembled materials using U@B₄₀ superatoms.

Models and computational methods

The U@B₄₀ has two hexagons (6₁ and 6₂) and four heptagons (7₁–7₄), as the lower right corner of Fig. 1. In this work, we enumerated various possible directions along the two U@B₄₀ and obtained eight U@B₄₀ dimers, and arranged them according to their total energies. Structure (a) is formed by the 7₃ heptagons of one U@B₄₀ stacked onto the vertical 7₁ heptagons of another (denoted as 7₃⊥7₁); it has the lowest total energy. Structures (b) and (c) are formed by 7₃ heptagons of one cluster parallel and antiparallel to 7₁ heptagons of another (denoted as 7₃↗↗ 7₁ and 7₃↗↙7₁, respectively). Structures (d), (e), (g) and (h) are formed by the 7₃ heptagons or 6₁ hexagons of one cluster stacked onto the 6₁ or 6₂ hexagons of another. The structure (f) is formed by the B atoms of one cluster connecting to the B atoms of another cluster (represented as vertex–vertex). The relative energies between other structures and the lowest energy structure (7₃⊥7₁) are placed in brackets in Fig. 1. The relative energies of the U@B₄₀ dimers are listed in Table S1† in the ESI. Since the energy of the conformation 7₃⊥7₁ is the lowest, the following analysis and discussion are mainly performed on it.

Fig. 1 Structure diagrams for all the isomers formed by the interaction between two U@B₄₀ superatoms. (a) Stacking the 7₃ heptagons of one cluster vertical to the 7₁ heptagons of another. (b and c) Stacking the 7₃ heptagons of one cluster parallel or antiparallel to the 7₁ heptagons of another. (d and e) Stacking the 7₃ heptagons or 6₁ hexagons of one cluster onto the 6₁ hexagons of another. (f) Connecting the B atoms of one cluster with the B atoms of another cluster. (g and h) Stacking the 6₁ hexagons or 7₃ heptagons of one cluster onto the 6₂ hexagons of another. The values in brackets are the relative energies between each isomer and the lowest energy structure, given in eV. The structure of the U@B₄₀ is shown in the lower right corner. A similar drawing method refers to ref. 24 and 37.

The Amsterdam density functional package (ADF, 2012.01)³⁸ was employed to perform calculations. To ensure the reliability of the obtained structures, geometry optimizations were performed without imposing any symmetry constraints. All calculations presented in this work were performed using Perdew–Burke–Ernzerhof (PBE)³⁹ generalized gradient approximation exchange–correlation functionals. Scalar relativistic effects were accounted for using the zero-order regular approximation (ZORA) method. TZ2P Slater basis sets (relativistic valence triple-ζ) with two polarization functions were employed,⁴⁰ and the frozen-core approximation was used for 1s–4f electrons of the uranium atom. The empirical dispersion-corrected density functional theory (DFT-D3)⁴¹ was used to fully obtain the intermolecular interaction of the U@B₄₀ structures.

Results and discussion

The spin polarization of U@B₄₀ dimers was analyzed and the results were different from those of U@B₄₀ without spin polarization.³⁵ As shown in Fig. 2, the spin orientation of one U@B₄₀ monomer in the 7₃⊥7₁, 7₃↗↗7₁ and 6₁–6₂ conformations is spin-up, and that of another monomer is spin-down. The spin orientations of the two monomers are opposite, thus exhibiting the spin antiferromagnetic coupling phenomenon, which is consistent with (U@C₂₈)₂.⁴² For 7₃↗↙7₁, vertex–vertex and 7₃–6₂ conformations, the spin orientations of the two U@B₄₀ monomers are spin-up, and thus exhibiting spin ferromagnetic coupling. Distinct from 7₃–6₂, although the ground state of 7₃–6₁ conformation is also a triplet state, the two unpaired electrons are occupied on one monomer. Thus, one U@B₄₀ monomer exhibits spin polarization, while another monomer has no spin polarization (shown in Fig. 2(d)). In addition, the ground state of the 6₁–6₁ structure is a closed-shell singlet state without spin polarization, similar to U@B₄₀.³⁵ The results show that different U@B₄₀ dimers exhibit different spin polarization phenomena, thus U@B₄₀ as the motif for assembly can affect the magnetic properties.

Fig. 2 Spin density diagram of U@B₄₀ dimers for eight conformations. The green region represents spin up and the red region represents spin down. The isosurface value is 0.01 a.u.

To further explore the origin of the spin-polarized phenomenon, the MOs of U@B₄₀ dimers were analyzed. There are 232 α and 232 β MOs of the conformation 7₃⊥7₁, and the frontier MOs diagram is shown in Fig. 3. The HOMO for the α electron (denoted as HOMOα) is strongly localized on one U@B₄₀ monomer, while the HOMO for β electron (HOMOβ) mainly occupies another monomer. The other occupied MOs were delocalized on the U@B₄₀ dimer. Therefore, the spin density of 7₃⊥7₁ conformations is mainly contributed by HOMOα and HOMOβ. The spin density for spin-up comes from HOMOα, while that for spin-down derives from HOMOβ, thus exhibiting spin antiferromagnetic coupling. Furthermore, the MOs of other U@B₄₀ dimers were also analyzed, and the results show that the spin density comes from the frontier MOs of structures (as shown in Fig. S1–S7†).

Fig. 3 The frontier molecular orbital (MOs) diagram of the ground state of 7₃⊥7₁ conformations. The red and black lines represent α-MOs and β-MOs, respectively. The MOs indicated by blue and red are occupied MOs, while those indicated by orange and cyan are unoccupied MOs. The isosurface value is 0.01 a.u.

Previous studies on B₄₀ oligomers have shown that B₄₀ monomers still retain superatomic properties.²⁴ Similarly, the superatomic MOs of 7₃⊥7₁ conformations were also analyzed in detail. In the MOs with lower energy levels, we found that the monomeric superatomic orbitals are composed of B₄₀ cages. While superatomic orbitals are contributed by the 2s orbital of B atoms, similar to the superatomic orbital 1S, 1P, 1D and 1F of B₄₀ (ref. 33) (as shown in Fig. 4). The superatomic MOs of two monomers cooperate in in-phase and out-of-phase cooperation, denoted as 1S–1S, 1P–1P, 1D–1D, 1F–1F. In the MOs with higher energy levels, the U@B₄₀ monomer still retains superatomic MOs, and the superatomic orbitals are a hybridization of the 7s, 7p, 6d, and 5f orbitals of the U atom with the B₄₀ cage orbitals.³⁵ The superatomic MOs of two U@B₄₀ monomers cooperate in in-phase and out-of-phase, denoted as 2S–2S, 2P–2P, 2D–2D, 2F–2F, as shown in Fig. 5. However, U@B₄₀ exhibits a 32-electron closed-shell singlet configuration.³⁵ There should be two S–S, six P–P, ten D–D and fourteen F–F superatomic MOs in accordance with the in-phase and out-of-phase cooperation between each other. Here, we found that some monomeric superatomic orbitals disappeared due to the stronger orbital interaction. The disappearance of 1D–1D MOs is caused by the distortion of the B₄₀ cages and the disappearance of 2D–2D and 2F–2F MOs result from the deviation of the U atom from the cage center. Fig. 4 and 5 are the superatomic MOs diagrams of α electrons, and the superatomic MOs diagrams of β electrons are shown in Fig. S8 and S9† in ESI. In addition, we also analyzed the MOs of 6₁–6₁ conformation, as this conformation is less twisted and the U atom is not severely deviated from the B₄₀ cage center. The results show that only two 2F–2F MOs disappeared, as shown in Fig. S10† in the ESI.

Fig. 4 The MOs diagram for α electrons of 7₃⊥7₁ confirmations for the U@B₄₀ superatomic orbital components. Superatomic orbitals 1S, 1P, 1D, and 1F are composed of the B₄₀ cages. The blue and red areas indicate the positive and negative signs of the wave functions, respectively. Isovalue = 0.02 a.u.

Fig. 5 MOs-α of the 7₃⊥7₁ conformations for the U@B₄₀ superatomic orbital components. 2S, 2P, 2D, and 2F refer to the U@B₄₀ monomer superatomic orbitals.

To further explore the orbital composition, the density of states of 7₃⊥7₁ conformations was analyzed. The total density of states (TDOS) of the U@B₄₀ dimer for 7₃⊥7₁ conformations, the local density of states (LDOS) and the partial density of states (PDOS) of U atoms are displayed in Fig. 6. The results demonstrate that U atoms in 7₃⊥7₁ conformations mainly contribute to frontier and unoccupied MOs, and the occupied MOs are mainly contributed by the 5f orbitals of the U atoms. Therefore, 1S–1S, 1P–1P, 1D–1D and 1F–1F MOs are composed of B₄₀ cages, and 2S–2S, 2P–2P, 2D–2D, 2F–2F MOs are composed of B₄₀ cages and U atoms. Further, the DOS of other U@B₄₀ dimers, 7₃↗↙7₁, 7₃–6₁, 6₁–6₁ and 6₁–6₂, were also analyzed (as shown in Fig. S11–S14†). Furthermore, the HOMO–LUMO gap of the U@B₄₀ dimers was analyzed, as listed in Table 1. The results showed that the HOMO–LUMO gap of the eight conformations of U@B₄₀ dimers are 0.32 eV, 0.32 eV, 0.27 eV, 0.16, 0.45 eV, 0.30 eV, 0.30 eV and 0.12 eV, respectively. While the HOMO–LUMO gap of U@B₄₀ was 0.76 eV.³⁵ Therefore, U@B₄₀ assembly causes a reduction in the energy gap, which is similar to the result of previous studies on B₄₀ superatom-assembly.²⁴

Fig. 6 Density of states of structure 7₃⊥7₁. (a) The total density of states (TDOS) of 7₃⊥7₁ and the local density of states (LDOS) of U atoms. (b) and (c) The partial density of states (PDOS) of s, p, d, and f atomic orbital of two U atoms.

Table 1 The HOMO–LUMO gap of U@B₄₀ dimers

The HOMO–LUMO gap (eV)
73⊥71	73↗↗71	73↗↙71	73–61	61–61	Vertex–vertex	61–62	73–62
0.32	0.32	0.27	0.16	0.45	0.30	0.30	0.12

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Conclusions

In this study, U@B₄₀ superatom dimers were investigated using the first principles. The results show that different U@B₄₀ dimers exhibit different spin polarization phenomena, they have spin antiferromagnetic coupling, spin ferromagnetic coupling and nonmagnetic. As such, the magnetic coupling can be tuned according to different types of the U@B₄₀ assembly. Moreover, the spin density mainly comes from the frontier MOs. Further analysis of the MOs revealed that the monomer of the U@B₄₀ dimers still retained some superatomic properties. One kind of superatomic orbital is composed of B₄₀ cages and another kind of superatomic orbital is composed of B₄₀ and U atoms. In addition, the U@B₄₀ superatomic assembly causes the energy gap to decrease. This work mainly studied the interaction between embedded metal fullerenes, which provides a new idea for cluster assembly materials.

Author contributions

Jia Wang calculated and analyzed the results. All the authors contributed to the general discussion.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (grant number 11947039), the Natural Science Foundation Project of Jilin Province (grant number YDZJ202101ZYTS075).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: The relative energies, molecular orbitals diagram and density of states. See https://doi.org/10.1039/d2ra01591a

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