Structures and Properties of CoB19 +/0/- Clusters.

A global search for the lowest energy structure of Co atom-doped boron clusters (CoB19 +, CoB19, and CoB19 - clusters) was conducted. The lowest energy structures of them are remarkably different from those of B20 and CoB18 - clusters. CoB19 + clusters have a bowl-shaped geometry, where the Co atom is at the bottom of the bowl and is coordinated with eight B atoms. The CoB19 cluster presents seven- and eight-membered B rings. The CoB19 - cluster can be viewed as a structure that evolves from a Co-doped boron plane. The coordination number of CoB19 and CoB19 - clusters are 16 and 14, respectively. Several low-lying isomers have quasi-planar structures for the CoB19 - cluster. Some properties including charge transformation and distribution, HOMO-LUMO gaps, molecular orbital distribution, and stability of neutral CoB19 are discussed. CoB19 + and CoB19 - exhibit magnetism with a net moment of 1.0 and 0.94 μB because of odd number of electrons.

Introduction

Boron clusters (B) have been extensively studied experimentally and theoretically over the past decades because of their unique characteristics. Elemental B has three valence electrons and four valence orbitals. Electron deficiency results in multicentered bonds and various structures. B clusters can form several different structural forms with planar or quasi-planar, bowl-shaped, tubular (double and multiple rings), and cage-like configurations.[1−16] Wang et al.[11,17−29] found that planar or quasi-planar structures are preferred for anionic B clusters within a large size range of up to n = 38. A bowl-shaped quasi-planar structure has been obtained for the large cluster B84.[30] Theoretical investigations have shown that planar to tubular geometrical transitions occur at B20 clusters in the neutral state.[31]

Doping with other atoms can considerably alter the structural, electronic, and bond characteristics of B clusters.[32] The B atom has a strong tendency to form bonds with transition metal (TM) atoms owing to its electron deficiency. TM-doped B clusters have received intense attention. TM-doped B clusters can be coordinated at the centers of planar species, such as CoB6,[33] CoB8–, RuB9–, NbB10–, and TaB10–.[34−37] Drum-like species have been found in TaB16–,[37] CoB16–,[38] MnB16–,[39] and TaB20–[40] clusters, among which the TaB20– cluster sets the coordination number (CN) to 20. A detailed study of TM-doped clusters, including those of Co, was conducted and reported the presence of drum-shaped boron clusters and the formation of nanotubes.[41] Theoretical studies revealed that an endohedral metalloborospherence TaB22– cluster has a high CN of 22.[42] Li et al.[43] reported that the TaB283+ cluster possesses the highest CN of 28 in chemistry. Two previous studies found that the structures of CoB18– and RhB18– clusters have planar forms.[44,45] The structures for large Co-doped boron clusters remain unknown. Based on these studies on TM-doped 2D and 3D B clusters, we systematically investigated the structures and properties of Co-doped B19 clusters.

Results and Discussion

The ground states of CoB19+, CoB19, and CoB19– at the CCSD(T) level are presented in Figure . The structures of CoB19+, CoB19, and CoB19– clusters are remarkably different from those of B20 and CoB18– clusters.[12,31,44,46,47] Charge has a strong influence on their structures. The CoB19+ cluster has a bowl-shaped geometry, where the Co atom is located at the bottom of the bowl and coordinated with eight B atoms. The CoB19 cluster presents seven- and eight-membered B rings, with four B atoms inserted in the waist of the tube. The ground state of the CoB19– cluster can be viewed as a structure that evolved from Co-doped boron plane. Four B atoms cap on each side of the same edge of the planar. The CNs of CoB19 and CoB19– clusters are 16 and 14, respectively. The binding energy of the Co atom was calculated using the following equationwhere the structures of B19+/0/– clusters are based on the ground states of CoB19+/0/– clusters minus the Co atom. The Eb values obtained are 5.52, 6.59, and 7.40 eV for CoB19+, CoB19, and CoB19– clusters, respectively. The Eb value increases with increasing number of electrons. A large magnitude indicates a strong interaction between the B19 moiety and the Co atom.

Figure 1

Ground states of CoB19+, CoB19, and CoB19– at the CCSD(T) level.

The representative low-lying isomers and relative energies of CoB19+/0/– clusters are illustrated in Figures S1–S3 in the Supporting Information. For the CoB19+ cluster, the six nearest isomers 2–7 are tubular-based structures with the Co atom located at the center of the tube. Isomer 8 also possesses a bowl-shaped geometry with the Co atom at the bottom of the bowl. Isomers 9 and 10 have disk-like structures, where the Co atom is located at the center of a B7 ring. Figure S1 shows that several layered or endohedral cage structures are low-lying isomers of the most stable state. For the CoB19 cluster, the structure of the most stable state is similar to that of isomer 6 of the CoB19+ cluster. Notably, isomer 2 is a three-layered structure that can also be viewed as an endohedral cage structure with Co at the center. The CN of this isomer is up to 19. The families of the CoB19– cluster are remarkably different from those of CoB19+ and CoB19 clusters, where several low-lying isomers have quasi-planar structures. For example, isomers 7–10 have quasi-planar shapes, and the Co atom is located at the center of the B7 ring (Figure S3).

Pauling’s electronegativity value of the Co atom (1.88) is slightly smaller than that of the B atom (2.04). The Hirshfeld population analysis revealed that the Co atom is positively charged with 0.23, 0.07, and 0.04 e for CoB19+, CoB190, and CoB19– clusters, respectively. A small magnitude indicates that the charge is mainly distributed in the B19 moiety. Spatially deformed charge distribution, which is defined as the total charge density minus the density of the isolated atoms, can depict changes in the charge. The deformation electron density of CoB19+/0/– clusters is shown in Figure . A large amount of charge difference is mainly distributed between two B atoms, indicating the covalent characteristics of the B–B bond. The Co atom carries a small charge, and the charge distribution between Co and B is negligible. The charge distribution between Co and B is consistent with the Hirshfeld population analysis.

Figure 2

Deformation electron density of CoB19+/0/– clusters at an iso-value of 0.08 electron/Å3.

CoB19+ and CoB19– have one unpaired electron and exhibit magnetism with a net moment of 1.0 and 0.94 μB, respectively. CoB19 is nonmagnetic. Figure displays the spin density distribution of CoB19+ and CoB19–. For CoB19+, almost all of the density is carried by the Co atom. Nineteen boron atoms have −0.15 μB magnetic moment. The case of CoB19– is significantly different from that of CoB19+. Almost all of the spin densities are contributed by the boron atoms on the peripheral positions. The Co atom possesses less than −0.01 μB magnetic moment.

Figure 3

Spin density distribution of CoB19+ and CoB19– at an iso-value of 0.02 μB/Å3 (μB is Bohr magneton).

The chemical bonding of the closed shell CoB190 was analyzed using the AdNDP method[48] and is shown in Figure . The presence of three 3d lone pairs on Co with the occupation numbers (ONs) ranging from 1.90 to 1.74 |e| indicates that few electrons participate in bonding with the surrounding boron atoms. Figure displays two types of 2c–2e bonds. Thirteen 2c–2e B–B bonds are located on the two boron rings. Two 3d orbitals of Co involve the two other 2c–2e bonds with the surrounding B atoms. The two boron rings are bound via 10 3c–2e delocalized bonds. Two 6c–2e bonds associated with the Co atom maintain the stability of the core. The two other 6c–2e bonds are located on the wall of the tube to maintain the stability of the framework. Two 16c–2e bonds associated with the inner Co atom are observed. These highly delocalized multicenter bonds confer CoB190 as a stable species.

Figure 4

Chemical bonding analysis of the closed shell CoB19 cluster. ON denotes as the occupation number.

The calculated energy gaps between the highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) are 0.81, 1.57, and 0.59 eV for CoB19+, CoB190, and CoB19– clusters, respectively. The CoB190 cluster possesses a large energy gap because of their closed electron shell. Figure shows that Co has a fivefold degenerate unfilled HOMO. Three electrons occupy five HOMOs. The B19 moiety has three LUMOs which are slightly lower than the HOMO of the Co atom. Hybridization of the orbitals of Co with the HOMO of B19 leads to a closed-shell status for CoB190. The filled level induced by Co lies at about −5.36 and −5.71 eV. The downward shifts of the level will result in a sizable HOMO–LUMO gap (1.57 eV) of CoB190.

Figure 5

Molecular orbital levels of Co, CoB19, and B19. Only the most important levels that participate in the interaction are given. Occupied levels are solid and unoccupied levels are dot. The number 5 indicates the degeneracy type for electron levels.

Figure shows the distribution of these molecular orbitals. For the CoB19+ cluster, large amounts of HOMO are localized in one B atom at the edge of the bowl mouth. The Co atom has small contributions to the orbital. The LUMO is mainly located on the Co atom. Meanwhile, for the CoB190 cluster, few HOMO electrons are localized to the Co atom. LUMO is predominantly scattered on B atoms. For the HOMO of the CoB19– cluster, numerous electrons are located on the Co atom. LUMO is mainly distributed in peripheral B atoms.

Figure 6

Charge density of the HOMO (left column) and the LUMO (right column) at an iso-value of 0.04 electron/Å3.

Conclusions

Structural transitions of the CoB19 cluster at different charge states were determined by density functional theory (DFT) calculations. Their structures are remarkably different from those of B20 and CoB18– clusters. The CoB19+ cluster has a bowl-shaped structure, wherein the Co atom is located at the bottom of the bowl and surrounded by eight B atoms. The CoB190 cluster presents seven- and eight-membered B rings, with four B atoms inserted in the waist of the tube. For the CoB19– cluster, the structure evolved from the Co-doped boron plane. The CNs of CoB19+, CoB19, and CoB19– clusters are 8, 16, and 14, respectively. Cluster properties including on-site charge on the Co atom, deformed charge distribution, spin density, and molecular frontier orbital are also discussed. Highly delocalized electrons and closed electronic shells confirm the stability of CoB190. CoB19+ and CoB19– possess 1.0 and 0.94 μB magnetic moments, respectively. Doping and charging can affect the structural properties of the boron-based clusters. Two bowl-shaped CoB19+ clusters can be imaged to construct a cage with unique properties and thus expand the range of potential nanostructures based on boron.

Computational Methods

More than 50,000 CoB19 structures were randomly generated using the Molclus program[49] and adopted as the initial structures for semiempirical quantum mechanical optimization at the PM7 level by utilizing MOPAC2016.[50] Molclus is a portable program aimed to search cluster configurations and molecular conformations. Molclus automatically invokes the Gaussian, ORCA, or MOPAC2012/2016 program to optimize a batch of initial geometries recorded in a .xyz trajectory file and performs statistical analysis of the results. Initial geometries are generated randomly by the genmer and gentor tool in the Molclus package. Cage-, ring-, and planar-like structures can also be generated on demand. After optimization of MOPAC2016, the energy sequence of these structures can be listed using Molclus. Compared with other algorithms, the Molclus program can more simply and widely sample potential energy surfaces (PESs) and cannot fall into one region of the PES. The program can obtain the global minimum of the PES if the sample structures are good enough. Low-lying energy isomers obtained from MOPAC2016 were used as candidate structures and reoptimized by all-electron DFT. Manual constructions were based on the reported isomers of B20 clusters.[12,31,46,47] Finally, more than 2000 possible candidate structures were obtained for each system. These structures were then fully optimized to determine the most stable structures at the PBE/DNP level of the theory by using the Dmol3 package[51] on the basis of DFT. The convergence criterion for the total energy was set to 10–6 au. All structures were fully relaxed without any symmetry constraint. All calculations were spin-unrestricted, and smearing was set to 0.002 hartree to ensure convergence. Vibrational frequencies were calculated using harmonic approximation to check whether the optimized structure is a true minimum of the system. Given that the relative energies among the first few structures are small, the single-point energies of the top 10 lowest energy isomers were further refined at the CCSD(T)/Co/Stuttgart/B/cc-pVTZ level by using the Gaussian 09 package.[52]