English

• 1. INTRODUCTION

  Boron, the left neighbor of carbon in the periodic table, is well-known for its electron efficiency. While extensive investigations were performed on carbon-based clusters and materials such as fullerenes, carbon-nanotubes, graphene and graphdiyne, pure boron clusters have been relatively less studied until about two decades ago^[1]. We found in 2003 that boron clusters display analogous geometric and electronic structures (e.g. planarity, aromaticity and anti-aromaticity) with hydrocarbon rings^[2]. A series of new boron clusters have been characterized by joint photoelectron spectroscopy (PES) and theoretical studies in the past decade. Fascinating electronic structures are found for these electron-deficient clusters featuring multi-center delocalized bonding as well as σ and π aromaticity^[3-11]. The discovery of planar or quasi-planar B₃₆^- and B₃₅^- clusters provides the first experimental viability of two-dimensional boron monolayers^{[12, 13]}, which we named as borophene akin to graphene. Borophene materials have been recently synthesized experimentally by several groups^{[14, 15]}. The recent experimental observation and computational confirmation of cage-like B₄₀^- and B₃₉^- clusters also represent a milestone of boron clusters, which leads to the identification of a new class of boron structures that we named as borospherene akin to fullerenes^{[16, 17]}.

  Among various structures of boron clusters, the ring structures are especially unique. The size of the boron monocyclic rings increases from B₃ to B₁₀ (Fig. 1), which makes B₇, B₈ and B₉ particularly fit for forming inverse sandwich compounds with large size metal ions^[18-23]. Inasmuch as the much higher orbital energies of boron 2s and 2p orbitals than those of carbon, nitrogen, oxygen and fluorine, boron clusters are especially interesting for binding electropositive metals with high-lying orbitals. As a result, rare-earth borides are ubiquitous as stable solid state compounds^[24-29].

  Figure 1

  

  Figure 1.  Size of monocyclic B_n rings with perfect D_nh symmetry. Structures are optimized by PBE/TZ2P with ADF program

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  Among the rare earth elements, lanthanide elements (Ln = La, Lu) feature high-energy 5d orbitals for weak yet non-negligible covalent orbital overlap with ligands, while the highly radially contracted 4f orbitals (Fig. 2) are available for preserving electrons that are often key for magnetic, optical and catalytic applications^[30-33]. This peculiarity of extremely contracted 4f orbitals (~0.4 Å for La and 0.25 Å for Lu) arises from the quantum primogenic effect^[34-36], which refers to the fact that the first-shell, nodeless atomic orbitals of each angular quantum number (i.e., 1s, 2p, 3d, 4f, 5g, ...)tend to be rather contracted in radial distribution due to lack of Pauli repulsion from any inner orbitals with the same angular momentum. These features make lanthanide borides a class of highly intriguing materials for practical applications^[27-29].

  Figure 2

  

  Figure 2.  Radial density distribution function D(r) = r²R² of rare earth metals^[37]

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  Rare-earth borides are important materials with unique magnetic, thermoelectric, and superhard properties^[38]. However, relatively less attention was paid to the rare-earth boron clusters. In order to explore their chemical bonding, electronic structures and spectroscopic properties, we have performed a series of joint PES and quantum chemical theoretical studies on lanthanide boride clusters, which reveals interesting geometric structures such as planar^{[39, 40]}, half-sandwich^[41], and inverse sandwich complexes^[42-44]. The inverse sandwich structures, adopting the M···L···M motif (M is the metal and L represents the ligand), have been widely known for the transition metals and actinide elements protected by organic hydrocarbon ring ligands^[45-50]. The interlayer ligands are mostly aromatic rings, which can form stable chemical bonds to metals on both faces via its delocalized ligand group orbitals. However, such structures have seldom been observed in boride clusters before. In this paper, we provide an overview on the recent results of lanthanide-boron inverse-sandwich compounds that feature a new class of clusters with unprecedented structures and chemical bonding patterns.

  2. PROGRESS OF RESEARCH

  As mentioned above, B₇, B₈ and B₉ rings have the suitable size to stably match with two lanthanide atoms. Recently, joint theoretical and PES studies have verified the existence of these Ln₂B_n^- (n = 7, 8, 9) species^{[42, 43]}. Local coordinate system (LCS) analysis is an effective tool to analyze the orbital interactions between metal atom and ligands, especially for molecules with high symmetry^{[24, 51]}. Fig. 3 presents the LCS analyses of B_n (n = 7, 8, 9) clusters to investigate how they interact with the two lanthanide elements. These rings have 4n 2s/2p valence orbitals which can be divided into four categories according to the different spatial orientation of the orbitals, classified into σ_s, σ(t)_p, σ(r)_p, and π_p orbitals, where "t" and "r" represent "tangential" and "radial" interaction, and s and p denote the B 2s and 2p orbitals, respectively. Number in the subscript corresponds to the number of the nodal plane (Fig. 3).

  Figure 3

  

  Figure 3.  Molecular orbital (MO) energy level of B_n (n = 7, 8, 9) in local coordinate system (LCS)."t" and "r" represent "tangential" and "radial" orbitals, respectively^[43]

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  The BB bonds in the boron rings are found to arise from the occupied σ_s and σ(t)_p orbitals that are bonding or nonbonding on the basis of a tightbinding Hückeltype consideration. The covalent interaction between BB atoms of the ring is rather strong so that the splitting of the occupied and unoccupied regions in σ_s and σ(t)_p groups are much larger than that in the delocalized σ(r)_p, and π_p orbitals, which dominantly constitute the interaction between lanthanide metals and boron rings. When forming the Ln₂B_n inverse sandwich complexes, two Ln atoms donate four electrons to the boron ring, giving rise to the fully occupied σ_r1 orbitals that are doubly degenerate. It is interesting to note that similar to the C_nH_n rings that fulfill the (4n + 2) π-electron rule for forming ring ligands with different charges, C₃H₃⁺, C₄H₄^2-, C₅H₅^-, C₆H₆ (or C₆H₆^4-), C₇H₇^3- (C₇H₇⁺), and C₈H₈^2-[52], the boron ring ligands B₆^6-, B₇^5-, B₈^4-, B₉^3- and B₁₀^2- are perfect for closed shells. In other words, one can view these pure boron ring ligands as hexavalent, pentavalent, tetravalent, trivalent, and divalent, respectively. These B_n^x- ligands often have highlying valence bonding orbitals because of the low electronegativity of boron, which make them suitable for matching energetically with lanthanide 5d orbitals. Besides, they can force metal atoms to form uncommon oxidation states, as in the case of Pr(I) and Pr(Ⅱ)^[39].

  We performed canonical molecular orbital (CMO) analysis for La₂B₈ inverse sandwich clusters as an example to figure out the interactions between two La atoms and the B₈ ring, as shown in Fig. 4. The unoccupied π₂ orbital from B_n is significantly stabilized by a symmetrymatching La···La d-δ_u type of orbital, which leads to the formation of the unique

  Figure 4

  

  Figure 4.  Chemical bonding interactions between the La···La and B₈ fragments in D_8h La₂B₈ at the level of PBE0/TZP^[42]

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  (d-p)δ chemical bonding. This (d-p)δ interaction has an enormous contribution (La₂B₇^-: 6.9%, La₂B₈^-: 16.9%, La₂B₉^-: 42.4%) to the total orbital interaction. The only difference between the neutral and anion species originates from the occupation number of electrons on such (d-p)δ molecular orbital, where there is slight Jahn-Teller effect in the La₂B₈^- system due to degeneracy. In the Ln₂B_n sandwich clusters, LUMOs are primarily composed of Ln 6s orbital displaying a huge gap from the HOMOs with (d-p)δ bonding, indicating the overwhelming stability of the rare-earth inverse sandwich compounds.

  The semi-localized natural bonding orbital approach, AdNDP (Adaptive Natural Density Partitioning method), is another powerful tool to understand the chemical bonding in Ln₂B_n^- inverse sandwich clusters^[53]. The AdNDP analyses yield both localized and semi-localized multi-center bonds, providing a chemically intuitive bonding picture for complicated molecular systems that cannot be described with the two-electron, two center (2c-2e) bonding formalism. As shown in Fig. 5, the n 2c-2e σ bonds constitute the frame of B_n^- rings, and all other bonds are more or less delocalized due to the electron deficiency of boron. The delocalized n-center two-electron (nc-2e) σ and π bonds give rise to double aromaticity features for the inverse sandwich clusters, each satisfying the (4n + 2) Hückel rule. The (d-p)δ bonding in Ln₂B_n^- (n = 7~9) are different. The Ln₂B₉^- inverse sandwich has two full (d-p)δ bonds, whereas the Ln₂B₇^- and Ln₂B₈^- inverse sandwich clusters only possess partial (d-p)δ bonds, which renders extraordinary stability for the Ln₂B₉^- cluster.

  Figure 5

  

  Figure 5.  Localized and semi-localized MOs from AdNDP analysis of MB_xM (x = 7, 8, 9)^[43]

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  The La₂B_n species demonstrates magnetic properties because of the partially occupied (d-p)δ orbitals. Other Ln₂B_n inverse sandwich clusters with 4f electrons have more complicated magnetic coupling character due to more local 4f electrons on each Ln center, such as the Pr₂B₈ complex^[54]. The multi-configurational wavefunction dominantly comes from different 4f-shell occupancy, but the general bonding pattern in Pr₂B₈ remains the same as that in La₂B₈. Theoretical calculations obtained from ab initio CASPT2 method found that electronic state with ferromagnetic coupling is at least 8.73 kcal/mol lower in energy than that of the antiferromagnetic case. Due to the similar patterns of photoelectron spectra and chemical bonding for La₂B₈^-, Pr₂B₈^- and Tb₂B₈^-, all Ln₂B₈ complexes are assumed to have similar structures and bonding, providing opportunities to design highly magnetic Ln₂B₈ sandwich complexes, as well as one-dimensional (1D) magnetic nanowires.

  As shown in Fig. 6, combined PES and theoretical studies have revealed that the global-minimum-energy structure of La₃B₁₄^- anion cluster^[44] has closed-shell configuration with a C_2v symmetry, which can be viewed as an "inverse tripledecker" with two conjoined B₈ rings sharing a BB unit due to strong inter-layer BB bonding. Theoretically, the oligomers formed by elongation of such deformed inverse triple-decker are also found to be stable. Presumably, infini-tely long 1D lanthanide-boron nanostructures consisting of conjoint B₈ rings are viable or could be found in crystalline lattices of new lanthanide boride materials.

  Figure 6

  

  Figure 6.  Schematic illustration of the transformation from a perfect linear inverse triple-decker, La···B₈···La···B₈···La, the bent triple-decker of La₃B₁₄^-, with two conjoined B₈ rings by sharing a B₂ unit

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  Another interesting aspect is that the D_8h-[LnB₈Ln] gaseous inverse sandwich cluster is reminiscent of the structural motif in the popular material of LnB₆, as shown in Fig. 7. This structural connection is interesting as it well establishes a relationship between gaseous clusters and solid phase materials^[55]. And in fact, the bulk crystal structure can be viewed through a different angle using the Ln₂B₈ clusters. The crystal structure of LnB₆ has simple cubic space group: Pm-3m, with B₆-octahedra in body-centered positions and La atoms at the corners of the unit cell. From another perspective, we can takeLn₂B₈ as a repeat unit extending indefinitely in the three-dimensional(3D) space in three perpendicular directions, as shown in Fig. 6. Each B atom in Ln₂B₈ region belongs to eight vertexes in four B₆-octahedra in the same plane. Taking PrB₆ solid material as an example, the bond lengths between two neighboring B atoms are measured to be 1.708 and 1.706 Å for internal and external octahedral respectively, and the distance between two Pr atoms in one unit is 4.121 Å, which are longer than those in the Pr₂B₈ cluster because of different bonding conditions in periodic constructions^[56].

  Figure 7

  

  Figure 7.  Connection of Ln₂B₈ sandwich cluster with structural unit of solid LnB₆ material. Red and grey atoms correspond to B and La, respectively^[55]

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  In addition, the two systems resemble each other in terms of electronic structure, as shown in Fig. 8. The orbital interaction between La 5d and B 2p is the primary contribution to the La-B bonding, but Ln₂B₈ inverse sandwich clusters demonstrate increased covalent character despite the major bonding between Ln and B₈ cluster is ionic in nature. The curves in proximity to the Fermi level look spiky or even discrete for isolated La₂B₈ but continuous or broadened for solid-state LaB₆.

  Figure 8

  

  Figure 8.  a) and b) Density of states (DOS) for both solid LaB₆ and gaseous La₂B₈ with majority (right) and minority (left) spins. c) MO levels and the 3D orbital contours of La­₂B₈

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  The Ln₂B₈ clusters provide a new perspective to view the bulk LnB₆ crystal structures as repeating units of clusters in three perpendicular directions. The similarity between clusters and crystals is unrecognized in such compounds. Since the bulk LnB₆ represents a series of important magnetic, electric and superconducting materials, exploring the bonding and electronic structures of clusters provides us a new avenue to understand the bonding and physical mechanisms for these unique properties via establishing a link by repetitions of cluster structures.

  3. CONCLUSION AND PERSPECTIVE

  In this article, we have summarized our recent research progresses on a series of rare-earth boron inverse-sandwich clusters Ln₂B_n (n = 7~9), which provide a new class of cluster complexes with unique geometric structures, interesting bonding mechanism, and magnetic properties. Two lanthanide elements interact with the boron rings via lanthanide 5d orbitals and 2s/2p delocalized group orbitals from B_n, giving rise to multi-center bonding and aromaticity to cause the structures to be stable. Especially noteworthy is the rare (d-p)δ type bonding in this kind of clusters, which renders extraordinary stability and contributes unexpectedly to the whole orbital interactions. The electron-deficiency features of boron elements and the more extended 2s/2p valence orbitals make the B_n rings better ligands for interac-ting with lanthanides than the C_nH_n hydrocarbon rings^[4].

  Especially noteworthy is the finding that the highly symmetric Ln₂B₈ clusters can be viewed as a structural unit to build well-known LnB₆ solid materials. The concept of structural unit assembly into cluster compounds has been in place for a long time, as was initially proposed by Jia-Xi Lu et al. in the unit construction approach to the rational synthesis of transition-metal cubane-like clusters^[57]. The connection of rare-earth boride clusters and the relevant solid materials provides a new insight in establishing relationships between gaseous phase clusters and cluster-assembled solid phase materials. Further study of the relationship of cluster structural unit and cluster-assembled materials of rare-earth borides would be interesting for further research in this area.

  Since lanthanides have different unpaired 4f-electrons and high spins, these Ln-B clusters and solids with a variety of possible spin couplings can form a basis for exploring innovated materials for applications in electronic, magnetic, optical, and thermoelectric fields. The multifaceted and novel magnetic features of these compounds may find future applications in electronics. Because of the high-lying yet radially extended 5d orbitals and low-lying but core-like 4f orbitals, the lanthanides are unique in the periodic table^[58]. The unusual behavior of lanthanides in forming borides with significantly different properties from those of transition metals can be utilized to discover new cluster molecules and innovative materials in f-element chemistry. We are working on further exploring the solid-state materials of rare-earth metal boron clusters to provide understanding of such novel properties of the solid materials.

  
  
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  Figure 1  Size of monocyclic B_n rings with perfect D_nh symmetry. Structures are optimized by PBE/TZ2P with ADF program

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  Figure 2  Radial density distribution function D(r) = r²R² of rare earth metals^[37]

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  Figure 3  Molecular orbital (MO) energy level of B_n (n = 7, 8, 9) in local coordinate system (LCS)."t" and "r" represent "tangential" and "radial" orbitals, respectively^[43]

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  Figure 4  Chemical bonding interactions between the La···La and B₈ fragments in D_8h La₂B₈ at the level of PBE0/TZP^[42]

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  Figure 5  Localized and semi-localized MOs from AdNDP analysis of MB_xM (x = 7, 8, 9)^[43]

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  Figure 6  Schematic illustration of the transformation from a perfect linear inverse triple-decker, La···B₈···La···B₈···La, the bent triple-decker of La₃B₁₄^-, with two conjoined B₈ rings by sharing a B₂ unit

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  Figure 7  Connection of Ln₂B₈ sandwich cluster with structural unit of solid LnB₆ material. Red and grey atoms correspond to B and La, respectively^[55]

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  Figure 8  a) and b) Density of states (DOS) for both solid LaB₆ and gaseous La₂B₈ with majority (right) and minority (left) spins. c) MO levels and the 3D orbital contours of La­₂B₈

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