Structure evolution of chromium-doped boron clusters: toward the formation of endohedral boron cages

The electron-deficient nature of boron endows isolated boron clusters with a variety of interesting structural and bonding properties that can be further enriched through metal doping. In the current work, we report the structural and electronic properties of a series of chromium-doped boron clusters. The global minimum structures for CrBn clusters with an even number of n ranging from 8 to 22 are proposed through extensive first-principles swarm-intelligence structure searches. Half-sandwich structures are found to be preferred for CrB8, CrB10, CrB12 and CrB14 clusters and to transform to a drum-like structure at CrB16 cluster. Endohedral cage structures with the Cr atom located at the center are energetically most favorable for CrB20 and CrB22 clusters. Notably, the endohedral CrB20 cage has a high symmetry of D2d and a large HOMO–LUMO gap of 4.38 eV, whose stability is attributed to geometric fit and formation of an 18-electron closed-shell configuration. The current results advance our understanding of the structure and bonding of metal-doped boron clusters.


Introduction
Boron is an element of fascinating structural and chemical complexity, leading to topics of considerable interest in chemistry. It has three valence electrons that are decient compared with the four valence orbitals, and it prefers to share rather than donate the valence electrons. These characteristics make it difficult for B to achieve lled octets through classical 2c-2e bonds, giving rise to a rich variety of structures along with electron-decient multicentered bonds, both in its elemental form and chemical compounds. 1 Sixteen polymorphs have been discovered for bulk B with B 12 icosahedron being a prevalent motif. 2 1D nanotubes 3-5 and 2D sheets [6][7][8] have been fabricated in which triangular planar B lattices with hexagonal holes are found to be energetically favorable. 9 For 0D B clusters, the situation is even more interesting. Joint photoelectron spectroscopy and theoretical studies carried out over the past decades show that anionic B n À clusters up to n ¼ 38 are planar or quasi-planar, 10,11 in which delocalized multicentered bonds are responsible for the stabilities. 12 Theoretical calculations suggested a planar-to-tubular structure transition taking place at B 20 for neutrals. 13 Subsequently, combined collision cross section measurements and theoretical calculations conrmed the existence of tubular structures for cationic B n + clusters with n ¼ 16-25. 14 Most strikingly, the longsought B fullerene analogue (borospherenes) was rst observed at B 40 (ref. 15) aer extensive theoretical investigations, [16][17][18][19] and a series of axially chiral borospherenes were subsequently identied at B 39 À , 20 B 41 + and B 42

2+
. 21 For larger B clusters, recent theoretical studies have suggested quasi-planar, 22,23 tubular, 24 cage-like 25 and bilayered 23 structures as ground states at certain sizes, and core-shell structures are generally expected to be energetically most favorable for n > $68. [26][27][28] The structural diversity of B clusters can be further enriched through metal doping. Metal-centered monocyclic B rings can be formed by transition metal doping of small B 8-10 anionic clusters 29 37 Metal doping has been proven to be an effective avenue to achieve intriguing structure motifs in B clusters. Given the large number of possible combinations between metal atoms and the number of B atoms yet to be investigated, it not unreasonable to expect more fascinating phenomena in this group of chemical species. As such, in this paper, we report systematic investigations on the structure and bonding of a series of chromium (Cr) doped B clusters by means of the swarm-intelligent CALYPSO structure searching method and rst-principles density functional calculations. Ground-state structures are proposed for CrB n clusters with an even number of n ranging from 8 to 22, revealing an intriguing transition from half-sandwich to drumlike and then endohedral cage-like structures. In particular, a symmetric D 2h endohedral cage is revealed as the ground-state structure for the CrB 20 cluster. The rest of the manuscript is organized as follow. The second section describes the computational details. Section 3 presents the results and discussion, and the conclusions from the present results are given in Section 4.

Calculation details
The unbiased structure searches of CrB n clusters with an even number of n ranging from 8 to 22 are based on the global minimization of the potential energy surfaces, merging ab initio total energy calculations via the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) package. [38][39][40][41] Several major techniques are included in the algorithm to achieve high efficiency, e.g., point group symmetry constraints in structural generation, bond characterization matrix technique for ngerprinting structures, and a local version of the particle swarm optimization algorithm enabling simultaneous search in different energy funnels. 39 Its validity has been manifested by successful identication of the ground-state structures for a large number of systems. More than 2000 trial structures were generated for each cluster.
During the structure searches, the underlying energy calculations and structure relaxations are carried out in the framework of density functional theory (DFT) with the PBE functional 42 implemented in the ABACUS (Atomic-orbital Based Ab initio Computation at USTC) package. 43 ABACUS was developed to perform large-scale DFT simulations using linear combinations of atomic orbitals. 44,45 The recently developed systematically improvable optimized numerical atomic orbitals 44,45 were found to be an excellent choice to describe various materials, such as molecules, crystalline solids, surfaces, and defects. 43 The atomic orbitals basis set of B includes two s, two p and one polarized d orbitals (2s2p1d), whereas the basis set of Cr includes four s, two p, two d and one polarized f orbitals (4s2p2d1f). The radii of the numerical atomic orbitals are set to 7 bohr for B and 8 bohr for Cr in the rst-round local structure optimization, while 8 bohr for B and 9 bohr for Cr are used in the second-round local structure optimization. We adopt the SG15 Optimized Norm-Conserving Vanderbilt pseudopotentials, 46 and the energy cutoff for charge density is 240 Ry.
The low-lying isomers obtained from the structure searches were reoptimized at different spin states at PBE0/Cr/Stuttgart/B/ 6-311+G* level of theory using the Gaussian 09 Package. 47 The calculation of harmonic vibrational frequencies ensures that the cluster geometries are true local minima on the potential energy surface (no imaginary frequencies obtained). At this step, singlet, triplet, quintet and septet states were considered for all of these even-number-electrons clusters. In a previous benchmark calculation, the PBE0 functional was conrmed to be suitable for describing the energy difference of isomers of medium-sized boron clusters (e.g., B 20 ) compared to the highlevel CCSD(T) results. 28 The natural bond orbital (NBO) and adaptive natural density partitioning (AdNDP) analytical methods were carried out with the Multiwfn package 48 in order to achieve a better understanding of the bonding mechanism.

Results and discussion
The global minimum structures for CrB n (n ¼ 8, 10, 12, 14, 16, 18, 20 and 22) clusters obtained from the current structure searches are depicted in Fig. 1. To facilitate understanding of the structures via visualization, top and side views are given along with their point group symmetries, spin multiplicity values (M) and HOMO-LUMO energy gaps (E g ). Other low-lying isomers are shown in the ESI, Fig. S1-S8. † Generally, the effect of Cr doping on the structures of B clusters gradually is enhanced as the number of B atoms increases. For small-sized CrB n (n ¼ 8, 10 and 12) clusters, the B structures are similar to those in bare B clusters, while larger CrB n clusters exhibit B structures different from the corresponding bare B clusters. This leads to interesting transitions from half-sandwich to drum-like and then to endohedral cage-like structures as the number of B atoms increases. High spin states (triplet and quintet states) are preferred for small-sized CrB n clusters with n < 14, and the magnetism is completely quenched for CrB n clusters with n $ 16.
3.1 CrB 8 , CrB 10 , CrB 12 and CrB 14 clusters with half-sandwich structures As depicted in Fig. 1, small-sized CrB n clusters with n ¼ 8, 10, 12 and 14 exhibit half-sandwich structures, whereas quasi-planar or bowl-like B n moieties are coordinated to the Cr atom. High spin states are found to be the ground states for these globalminimum structures (quintets for CrB 8 , CrB 10 , CrB 12 , and triplets for CrB 14 ). Other low-lying isomers are given in Fig. S1-S8 in the ESI. † Spin density distributions shown in ESI, Fig. S9 † indicates that the magnetism mainly originates from the unpaired 3d electrons of the Cr atom.
The B structures in CrB 8 , CrB 10 and CrB 12 are very similar to those in bare B clusters, which are quasi-planar with one, two and three interior B atoms surrounded by seven-, eight-and nine-membered B rings, respectively. Due to the existence of the Cr atom, the interior B atoms in the B moieties display slight out-of-plane distortions. Note that, although CrB 10 is isovalent to NbB 10 À and TaB 10 À , it does not adopt the metal-centered monocyclic B rings in NbB 10 À and TaB 10 À as the ground state.
This may be due to the smaller size of the Cr atom (1.39Å) compared with those of Nb (1.64Å) and Ta (1.70Å), which is not optimal for tting the cavity of the ten-membered B ring. The half-sandwich structure of CrB 12 is the same as those in experimental CoB 12 À and RhB 12 À , further indicating that the double aromatic B 12 moiety is a promising inorganic ligand.
Inserting two B atoms into the B 12 moiety in the CrB 12 cluster leads to the formation of CrB 14 . The B 14 moiety in CrB 14 has a bowl-like structure with ve interior B atoms surrounded by a nine-membered B ring, which is different from the structures of neutral or charged bare B 14 clusters. 10,49 In contrast to CrB 8 , CrB 10

The CrB 16 cluster with a drum-like structure
The well-known drum-like structure with the Cr atom located at the center of a B 16 double-ring tube occurs with the CrB 16 cluster, having a point group of C 2v (Fig. 1). Within this structure, the magnetism is completely quenched due to the strong coordination interactions between the Cr atom and the B 16 tube. This type of structure was initially observed in CoB 16 À (ref.  26Å). Thus, it seems that whether drum-like structures can be formed in metal-doped B clusters is closely related to the size of the doping atom and the cavity of the B tube, as well as the charge and spin states of the metal-doped B clusters.

32) and
The chemical bonding of the current drum-like CrB 16 cluster was analyzed using the Adaptive Natural Density Partitioning (AdNDP) 52 method, which is an extension of the Natural Bond Orbital method. 53 AdNDP analyses can display both localized and delocalized bonding in molecules simultaneously, providing relatively simple bonding pictures for complicated molecular structures. 33 The AdNDP analyses revealed a similar bonding character for CrB 16 Fig. 2. The occupation numbers (ON) of all the identied bonds range from 1.71 to 2.00 |e|. The rst type represents localized bonds (Fig. 2a), which can be described in two manners: (1) as sixteen 3c-2e s bonds on the sixteen B 3 triangles on the drum surface with ON ¼ 1.94 |e| or (2) as sixteen 2c-2e s bonds within the two B 8 rings with ON ¼ 1.73 |e|. In fact, the sixteen 3c-2e s bonds can also be represented by sixteen 2c-2e s bonds on the two B 8 rings on the drum surface are shown in Fig. S10 in ESI. † The remaining three bonding types describe totally delocalized bonds (Fig. 2b-d, e-i and j-m) and account for bonding between the two B 8 rings and between the Cr atom and the B 16 tube. Following the previous work on CoB 16 À and MnB 16 À , the "+" sign is used to denote that the delocalized bonds between the two B 8 rings overlap positively, while the "À" sign means a negative overlap. The second bonding type (Fig. 2b-d) consists of one 16c-2e s À s bond with ON ¼ 1.78 |e| and two 17c-2e s À s bonds with ON ¼ 2.00 |e|. The one 16c-2e s À s bond represents a bonding interaction within each B 8 ring and an antibonding interaction between the two B 8 rings, while the two 17c-2e s À s bonds represent mainly covalent bonding between Mn (3d xz and 3d yz ) and the B 16 tube. The third bonding type (Fig. 2e-h) contains two 16c-2e s + s bonds with ON ¼ 1.74 |e| and two 17c-2e s + s bonds with ONs ¼ 2.00 |e|. The two 16c-2e bonds represent delocalized s bonding in the B 16 frame, and the two 17c-2e s + s bonds represent covalent bonding between Cr (3d xy and 3d x 2 Ày 2 ) and the B 16 tube. The fourth bonding type consists of three 16c-2e p À p bonds and one 17c-2e p À p bond. These four bonds account for p bonding interactions between the two B 8 rings.

Transition from drum-like to endohedral cage-like structures in CrB 18 , CrB 20 and CrB 22 clusters
As depicted in Fig. 1, capping  However, the transition metal should possess both geometric and electronic states that can t in high symmetric endohedral B cage-like clusters that eventually lead to the high stability structures that can be formed. The current endohedral D 2d CrB 20 cage should be one such paradigm. The geometric factor responsible for the stability is straightforward. Our previous calculations have demonstrated that the Cr atom is too small to t a large B 24 cage, indicating smaller B cages are suitable for accommodating one Cr atom.
To understand electronic factors responsible for the stability of the endohedral CrB 20 cage, the chemical bonding of the bare D 2d B 20 cage and endohedral D 2d CrB 20 cage were analyzed based on canonical molecular orbitals (CMOs). Fig. 3 shows the comparison of eigenvalue spectra for the D 2d cage without (a) and with (b) Cr encapsulation. One can clearly note that the Cr encapsulation signicantly increases the HOMO-LUMO gap from 0.87 eV for the bare D 2d B 20 cage to 4.38 eV for the D 2d CrB 20 . For bare D 2d B 20 (Fig. 3a), there are 6 occupied p-orbitals (HOMO, HOMOÀ1, HOMOÀ4, two HOMOÀ7, and HOMOÀ11) and 3 unoccupied p-orbitals (LUMO, LUMO+1 and LUMO+2). The moderate HOMO-LUMO gap in bare D 2d B 20 is attributed to the mid-lying binding energies of these out-of-surface delocalized p-orbitals, and they will interact with the electronic orbitals of Cr atoms in the endohedral CrB 20 cages. Cr has an electronic conguration of [Ar]4s 1 3d 5 with 6 valence electrons, adding the 12 p-electrons (from 6 occupied p-orbitals) of bare D 2d B 20 gives a total of 18 electrons. This special electron counting number of 18 is favorable for forming a stable 18electron closed-shell conguration, similar to that of previous MnB 20 + , MoB 24 and WB 24 clusters. Indeed, nine CMOs involved in the "spd-p interaction" have been identied for the D 2d CrB 20 endohedral cage as depicted in Fig. 3b, i.e., HOMOÀ13 (slike), HOMOÀ11 (d x 2 Ày 2-like), HOMOÀ8 (double degenerate, p xlike and p y -like), HOMOÀ7 (d xy -like), HOMOÀ6 (p z -like), HOMOÀ5 (double degenerate, d xz -like and d yz -p like) and HOMOÀ1 (3d z 2 -like). Thus, the CrB 20 cluster represents another example of having a symmetric endohedral cage conguration stabilized by the 18-electron conguration.

Conclusions
In summary, we systematically investigated the structural and electronic properties of CrB n clusters with n ¼ 8, 10, 12, 14, 16, 18, 20 and 22 through extensive swarm-intelligent structure searches and rst-principles calculations. It is found that Cr doping signicantly modies the structural evolution of B clusters. Intriguing transitions from half-sandwich to drum-like and then to endohedral cage-like structures are revealed as the number of B atoms increases. CrB 8 , CrB 10 and CrB 12 clusters exhibit half-sandwich structure with quasi-planar B moieties similar to the bare B cluster, indicating that small-sized B clusters are promising inorganic ligands. A drum-like structure is formed with CrB 16 clusters, while endohedral cage structures emerge with the larger CrB 20 and CrB 22 clusters. The endohedral CrB 20 cage has a high symmetry of D 2d and the largest HOMO-LUMO gap among CrB n in the current work, indicating its high chemical stability, which is attributed to the geometric t between the size of the Cr atom and the void of the B cage as well as the formation of the 18-electron conguration.

Conflicts of interest
The authors declare no competing nancial interest.