Buckminsterfullerene C60 and its precursor graphene have been superstars in chemistry and materials science ever since their discoveries1, 2. As the light neighbor of carbon, boron has a rich chemistry dominated with multicenter two-electron bonds (mc-2e bonds) in both bulk allotropes and polyhedral molecules to compensate for its electron-deficiency3. Multicenter bonds also appear to be responsible for the planar or quasi-planar (2D) structures of an unprecedentedly wide range of boron clusters B n −/0 (n = 3−30, 35, 36) characterized in gas phase in the past decade, unveiling a flat world of boron analogous to polycyclic aromatic hydrocarbons4,5,6,7,8,9,10,11,12,13,14,15,16,17,18. The possibility of all-boron fullerenes was not considered until 2007 when the high-symmetry I h B80 cage was constructed from C60 by capping the twenty hexagons19. However, this celebrated structure was later found to be much less stable than its core-shell rivals at various density functional theory (DFT) levels20, 21. The first all-boron fullerenes D 2d  B40 −/0, referred to as borospherenes in literature, were discovered in 2014 in a combined experimental and theoretical investigation22. In stark contrast to C60 which consists of twenty hexagons and twelve pentagons, D 2d B40 features four equivalent B7 heptagons with large cavities on the waist which may serve as effective ligands to coordinate transition metal centers. The first axially chiral borospherenes C 3/C 2 B39 with three/four B7 heptagons were observed in 201523. In the past two years, the Bn q (q = n−40) borospherene family has been expanded at first-principles theory level to include the cage-like B41 +, B42 2+24, B40 +25, B38 2− (in Ca@B38)26, B37 3− (in Ca@B37 )27, and B36 4− (in Li4&B36)28 which are all composed of twelve interwoven boron double chains (BDCs) with six hexagonal and heptagonal faces on thesurface. These borospherenes follow the universal bonding pattern of σ + π double delocalization. Endohedral and exohedral charge-transfer complexes M@B40 (M = Ca, Sr, La, Y, Sc) and M&B40 (M = Be, Mg) were also predicted to be stable species29, 30. The experimentally observed quasi-planar B36 −/0 and B35 clusters with one or two adjacent hexagonal vacancies appeared to be molecular motifs of infinite 2D borophene monolayers9, 10. The first 2D borophene monolayers deposited on Ag(111) substrates were successfully synthesized by two independent groups in 201531, 32. Interestingly, the most stable χ3-borophene deposited on Ag(111) is composed of zigzag BDCs in alternation with columns of adjacent hexagonal vacancies32, further indicating the importance of BDCs in low-dimensional boronanostructures. A boron monolayer with octagons, heptagons, and hexagons was recently considered to be a 2D structural precursor of the B40 cage33 though it is not a stable low-energy 2D polymorph compared to the well-known boron α-sheet and other low-lying structures33,34,35,36. Buckled FeB2 and FeB6 monolayers were recently proposed to be stable species with hexa-, hepta-, and octa-coordinate Fe centers37, 38. Furthermore, the recent observation of the perfectly planar C 2v Co  B18 with a planar heptacoordinate Co center opened vast opportunities to design 2D heteroborophene monolayers39 and other heteroboronanostructures with planar or quasi-planar heptacoordinate transition-metal (phTM) centers. However, to the best of our knowledge, cage-like heteroborospherenes with phTM centers on the surface and stable heteroborophene monolayers as precursors of such heteroborospherenes have not been reported in either experiments or theory.

Based on extensive global minimum (GM) searches and first-principles theory calculations, we predict herein the existence of the perfectly planar heteroborophene-type cluster Ni  B18 (1), cage-like heteroborospherenes Nin B40 (n = 1–4) (25), and the nearly degenerate heteroborophene monolayers Ni2 B14 (6, 7) which all contain phNi centers in η7-B7 heptagons on the boron frameworks, with Ni2 B14 (6) composed of interwoven BDCs being the structural precursor of the cage-like Nin B40 (n = 1–4) (25). These heteroboronanostructures possess the universal bonding pattern of σ + π double-delocalization on the boron frameworks, with each phNi center forming two effective 8c-2e σ-coordination bonds with the η7-B7 heptagon around it, inheriting the structural and bonding characteristics of the experimentally observed cage-like B40 22 and perfectly planar Co  B18 39.

Computational procedures

Extensive GM searches were performed using both the Minima Hopping (MH)40, 41 and TGmin42 algorithms on NiB18 and NinB40 clusters (n = 1–2), in combination with manual structural constructions based on the low-lying isomers of CoB18 39 and B40 −/022. Low-lying structures were then fully optimized with frequencies checked at both PBE043 and TPSSh44 levels with the 6–311 + G* basis set45 to ensure they are all true minima of the systems. The relative energies were further refined at the more accurate CCSD(T)46,47,48 level with 6–31 G* basis set for the five lowest-lying isomers of NiB18 and NiB40. A general global search based on the PSO technique implemented in the Crystal Structure Analysis by Particle Swarm Optimization (CALYPSO)49 package was performed on 2D Ni2B14 monolayer. The underlying plane-wave based DFT structrual optimization were performed using the Vienna ab initio simulation package (VASP)50, 51, within the framework of projector augmented wave (PAW) pseudopotential method52, 53 and PBE generalized gradient approximation (GGA)54. The Heyd−Scuseria−Ernzerhof (HSE06) approach55 was used to calculate the band structures and densities of states of the PBE structures.

Results and Discussions

Structures and Stabilities of Heteroborospherenes

As expected from chemical intuition, the perfectly planar neutral C 2v Ni  B18 (1) which is isovalent with the experimentally known C 2v Co  B18 39 turns out to be the global minimum of the cluster at CCSD(T) level (Fig. 1 and Fig. S1), with the Ni center and the η7-B7 heptagon around it matching nicely both geometrically and electronically. The existence of a planar Ni  B7 coordination unit in Ni  B18 (1) presents the possibility of forming Ni-B binary nanostructures with phNi centers in η7-B7 heptagons. Given the fact that the experimentally observed borospherene D 2d B40 possesses four quasi-planar B7 heptagons on the waist22, it is reasonable to expect that D 2d B40 may serve as an effective ligand with four quasi-planar η7-B7 coordination sites to accommodate phNi centers on the cage surface. It turns out to be true. As indicated in Fig. 1a, Figs S3, and S4, both the cage-like C s Ni  B40 (2) and C 2 Ni2 B40 (3) are the global minima of the systems, while C s Ni3 B40 (4) and D 2d Ni4 B40 (5) are true minima. All the phNi centers in the Nin B40 series (n = 1–4) (25) form effective Ni-B coordination interactions with the η7-B7 heptagons around them, as indicated by the average Ni-B distance of \({\overline{{\rm{r}}}}_{\mathrm{Ni}-B}\) = 2.02 Å in these clusters which is only slightly longer than the sum (1.95 Å) of the recommended single-bond covalent radii of Ni and B56. The twenty low-lying isomers of NiB40 all possess cage-like geometries, with the second (C 1 ) and third (C 2v ) lowest-lying isomers lying about 0.41 eV higher than C s Ni  B40 (2) at PBE0 (Fig. S3). The C 2 Ni2 B40 (3) with two phNi centers in two neighboring B7 heptagons lies 0.12 eV lower than the second lowest-lying C 2v Ni2 B40 which possesses two phNi centers at the opposite sites of the cage (Fig. S4). All the other isomers of Ni2B40 lie at least 0.42 eV higher than Ni2 B40 (3) at PBE0. As shown in Fig. S5, the relative stabilities of the most concerned low-lying isomers are found to remain unchanged with Gibbs free energy corrections included at finite temperatures below 600 K. Interestingly, the coordination energies (Ec) of the Nin B40 (n = 1–4) series (25) with respect to NinB40 = Ni(n−1)B40 + Ni (n = 1–4) (referring to triplet Ni and singlet NinB40 in gas phases) increase almost perfectly linearly with the number of Ni atoms in the systems, with the large average Ec of 95.90 kcal/mol (4.16 eV/Ni) at PBE0 (Fig. 1b). The Ec~n linear relation indicates that the four η7-B7 heptagons in D 2d B40 can be practically viewed as four independent coordination sites to accommodate phNi centers. In comparison, the hexacoordinate Ni centers in Ni5 B40 (8) and Ni6 B40 (9) at the top and bottom of the B40 cage (Fig. S2) possess obviously lower average coordination energies (Ec = 75.54 kcal/mol) (Fig. 1b), indicating that phTM centers are favored over hexacoordinate transition-metal centers in the formation of heteroborospherenes. Nin B40 (n = 1–4) (25) have the large HOMO-LUMO energy gaps of 2.85 eV, 2.59 eV, 2.39 eV, and 2.32 eV at PBE0 level, respectively, well supporting their high chemical stabilities. Similar heteroborospherenes with phPd and phPt centers have also been obtained (Fig. S6).

Figure 1
figure 1

Optimized structures and calculated coordination energies. (a) Optimized structures of perfectly planar C 2v Ni  B18 (1) and cage-like C s Ni  B40 (2), C 2 Ni2 B18 (3), C s Ni3 B40 (4), and D 2d Ni4 B40 (5) at PBE0/6-311 + G* level. (b) Calculated coordination energies (Ec) of the Nin B40 heteroborospherenes with respect to NinB40 = Ni(n-1)B40 + Ni (n = 1–6).The optimized structures of the C2v Ni5 B40 (8) and D2d Ni6 B40 (9) are depicted in Fig. S2.

Molecular Dynamics Simulations

Extensive molecular dynamics simulations were performed on Ni  B40 (2) and Ni2 B40 (3) for 30 ps to allow for crossing of small energy barriers at finite temperatures (Figs S7 and S8). As shown in Figs S7 and S8, both of them are dynamically stable at 500 K, with the root-mean-square-deviation and maximum bond length deviation values of RMSD = 0.07 Å, 0.08 Å and MAXD = 0.25 Å, 0.25 Å, respectively. The two species remain dynamically stable at 700 K, with RMSD = 0.09 Å, 0.09 Å and MAXD = 0.31 Å, 0.31 Å. However, at 1000 K, C s Ni  B40 (2) starts to hop between the two lowest-lying C s and C 1 isomers with RMSD = 0.15 Å and MAXD = 0.66 Å, while C 2 Ni2 B40 (3) still keeps its structural integrity.

Bonding Analyses

The high stabilities of these heteroborospherenes originate from their electronic structures and bonding patterns. We performed detailed adaptive natural density partitioning (AdNDP)57, 58 analyses on the perfectly planar Ni  B18 (1) and cage-like Ni  B40 (2) (Fig. 2) which show obvious similarity in bonding patterns though the η7-B7 heptagon in the latter is slightly off-planed on the cage surface. The phNi center in Ni  B40 (2) forms three lone pairs in radial direction (3d z 2 , 3d xz 2 , and 3d yz 2) with the occupation numbers of |ON| = 1.81–1.94 |e| and two nearly in-plane 8c-2e σ-coordination bonds between the remaining tangential Ni 3d orbitals (3 x2−y2 and 3d xy ) and the η7-B7 heptagon around it with |ON| = 1.86 |e|. The 48 delocalized σ bonds (40 3c-2e and 8 6c-2e) and 12 delocalized π bonds (4 5c-2e, 4 6c-2e, and 4 7c-2e) on the boron framework in Ni B40 (2) (Fig. 2b) are basically inherited from the parent D 2d B40 22. A similar bonding pattern exists in Ni  B18 (1) in which the phNi center carries three lone pairs (3d z 2 , 3d xz 2 , and 3d yz 2) in vertical direction with |ON| = 1.83–1.99 |e| and forms two perfectly in-plane 8c-2e σ-coordination bonds with the η7-B7 heptagon around it with |ON| = 1.80–1.85 |e|, with 22 σ bonds (13 2c-2e, 2 3c-2e, and 7 4c-2e) and 5 4c-2e π bonds on the boron framework outside. Natural bonding orbital (NBO) analyses indicate that the phNi centers in Ni  B18 (1) and Ni  B40 (2) possess the electronic configurations of [Ar]4s 0.00 3d 9.26 and [Ar]4s 0.17 3d 9.34, natural atomic charges of + 0.48 |e| and + 0.47 |e|, and total Wiberg bond orders of 1.78 and 1.59, respectively. These results show that the phNi center in 1 and 2 donates its 4 s 2 electrons almost completely to the boron framework and, in return, accepts about the same amount of electrons in its partially occupied 3d tangential orbitals (3 x2−y2 and 3d xy ) from the η7-B7 heptagon via effective p → d back-donations. The phNi centers in 1 and 2 have therefore approximately the total bond order of two corresponding to the two 8c-2e σ-coordination bonds between phNi and its η7-B7 ligand. Such a bonding pattern exists in other phNi-doped Nin B40 heteroborospherenes (n = 2–4) as well (Figs S911). The double delocalization bonding pattern on the B40 framework renders 3D aromaticity to these heteroborospherenes, as evidenced by the negative calculated nucleus independent chemical shift (NICS)59 values of −43.1, −43.4, −42.4, and −42.2 ppm at the cage centers of Ni  B40 (2), Ni2 B40 (3), Ni3 B40 (4), and Ni4 B40 (5), respectively, which are well comparable with the corresponding value of −43 ppm calculated for D 2d B40 22.

Figure 2
figure 2

Comparison of the AdNDP bonding patterns of (a) C 2v Ni  B18 (1) and (b) C s Ni  B40 (2).

IR, Raman, and UV-vis spectra

We computationally simulate the IR, Raman, and UV-vis absorption spectra of C 2v Ni  B18 (1) (Fig. S12) and C s Ni  B40 (2) (Fig. 3 and Fig. S13) to facilitate their spectral characterizations. With major IR peaks at 1276 cm−1(a’), 1153 cm−1 (a”), 783 cm−1 (a’), 566 cm−1 (a’), and 368 cm−1 (a”) and Raman peaks at 1320 cm−1 (a’), 1161 cm−1 (a’), 646 cm−1 (a’), 432 cm−1 (a’), 182 cm−1 (a’), and 148 cm−1 (a’) (Fig. 3), Ni  B40 (2) exhibits similar spectral features with the parent D 2d B40 and D 2d B40 + 24, 25, 60. These IR and Raman active modes mainly originate from the vibrational transitions of the B40 framework. The Raman peaks at 182 cm−1 (a’) and 148 cm−1 (a’) represent typical radial breathing modes (RBMs) of the C s Ni  B40 (2) cage in two perpendicular directions. An intense peak at 210 cm−1 was used to characterize the hollow structure of single-walled boron nanotubes61. The simulated UV-vis absorption spectroscopy of Ni  B40 (2) (Fig. S13) using the time-dependent DFT approach62 also exhibits certain similarity with that of D 2d B40, with the main spectral features located at 201, 217, 242, 275, 301, 324, 415, 501, and 622 nm. Most of the strong absorptions originate from electronic transitions from the deep inner shells to high-lying unoccupied molecular orbitals of the neutral, with the weak absorptions above 500 nm involving transitions from frontier orbitals with Ni 3d contributions. We also simulated the photoelectron spectra (PES) of the cage-like C s Ni  B40 , C 2 Ni2 B40 , C s Ni3 B40 , and D 2d Ni4 B40 monoanions (Fig. S14) which appear to have the low calculated first vertical and adiabatic detachment energies of VDE/ADE = 2.40/2.30, 2.39/2.29, 2.40/2.32, and 2.34/2.26 eV, respectively, followed by a sizable energy gap of about 1.0 eV, similar to the measured PES of the cage-like D 2d B40 22.

Figure 3
figure 3

Simulated (a) IR and (b) Raman spectra of C s Ni  B40 (2) at PBE0/6-311 + G* level.

Heteroborophene monolayers Ni2 B14 (6, 7)

To locate the planar monolayer precursor of the cage-like heteroborospherenes (25), we performed an extensive GM search on a Ni2B14 monolayer which contains a unit cell doubling the size of a planar NiB7 coordination unit. With more than 950 valid structures probed, the nearly degenerate Ni2 B14 (6) (P2 1 /m) and Ni2 B14 (7) (P-1) monolayers (Fig. 4) which may coexist in experiments turn out to be the two lowest-lying 2D polymorphs of the system (Fig. S15) without imaginary phonon dispersion frequencies at PBE level54 (Fig. S16). Slight buckling occurs in these heteroborophene monolayers with the maximum buckled heights of 1.16 Å in 6 and 1.51 Å in 7 at the pentacoordinate B sites, similar to the symmetric buckling observed in silicene63. Ni2 B14 (6) and Ni2 B14 (7) possess the average cohesive energies of E coh = 5.932 eV and 5.939 eV per atom (E coh = (2E Ni + 14E BE Ni2B14)/16), respectively, which are higher than the cohesive energies of the recently proposed FeB6 (5.79 eV/atom) and FeB2 (4.87 eV/atom) at the same theoretical level37, 38. The current prediction of heteroborophene monolayers 6 and 7 with nearly in-plane phNi centers is supported by the recently observed perfectly planar heteroborophene-type Co  B18 cluster which contains a phCo center39. More intriguingly, the Ni2 B14 (6) monolayer composed of interwoven BDCs with two equivalent phNi centers per unit cell turns out to be the precursor of the cage-like heteroborospherenes (25) which, with four heptagons on the waist and two hexagons at the top and bottom, can be unfolded into Ni2 B14 (6) monolayer by repetition simultaneously along the orthogonal direction (Fig. S17). This observation builds an interesting link between heteroborophene monolayers and cage-like heteroborospherenes. Lying 0.007 eV/atom higher in cohesive energy than Ni2 B14 (6), Ni2 B14 (7) with both capped pentagons (B6) and hexagons (B7) also contains two equivalent phNi centers per unit cell. Both Ni2 B14 (6) and Ni2 B14 (7) monolayers turn out to be metallic in nature, as shown in their calculated band structures and total densities of states (Fig. 4) which possess non-zero densities at Fermi levels, similar to boron α-sheet and other low-lying boron monolayers34,35,36. Detailed SSAdNDP bonding analyses57, 58 (Fig. S18) show that both Ni2 B14 (6) and Ni2 B14 (7) possess a σ + π double delocalization bonding pattern on their boron frameworks, with each phNi center forming three lone pairs (3d z 2 , 3d xz 2 , and 3d yz 2) in vertical direction and two nearly in-plane 8c-2e σ-coordination bonds with the η7-B7 pentagon around it. Such a bonding pattern is well in line with the bonding patterns in both planar Ni  B18 (1) and cage-like Nin B40 (n = 1–4) (25) discussed above. The σ + π double delocalization bonding pattern on the boron frameworks renders metallicity to these 2D heteroborophenes.

Figure 4
figure 4

Top and side views of the structures of 2D heteroborophenes. Ni2 B14 (6) and Ni2 B14 (7) were optimized at PBE and their band structures and total densities of states (TDOS) were calculated at HSE06. The insets represent the shapes of first Brillouin zones. Γ, X, A and Z of (6) correspond to the (0, 0, 0), (0, 0.5, 0), (0.5, 0.5, 0) and (0.5, 0, 0) k-points, while Γ, X, H2, Y, H and C of (7) correspond to the (0, 0, 0), (0.5, 0, 0), (0.440, 0.389, 0), (0, 0.5, 0), (−0.440, 0.611, 0) and (−0.5, 0.5, 0) k-points.

In summary, based on extensive first-principles calculations, we have presented the possibility of the novel planar heteroborophene-type cluster Ni  B18 (1), 3D aromatic heteroborospherenes Nin B40 (n = 1–4) (25), and 2D metallic heteroborophenes Ni2 B14 (6, 7) which all contain phNi centers in η7-B7 pentagons with the universal bonding pattern of σ + π double delocalization on their boron frameworks, with each phNi forming two effective 8c-2e σ-coordination bonds with the η7-B7 heptagon around it. Initial investigations suggest that phNi centers in 27 can be substituted by phPd, phPt, or other phTM dopants with the right atomic radii and electronic configurations to form stable heteroborospherenes, heteroborophenes, and heteroboronanotubes. Possible free-standing heteroboronanostructures stabilized by phTM centers guarantee further experimental and theoretical investigations to expand the chemistry and materials science of boron which are expected to be complementary to that of carbon31,32,33,34,35,36,37,38.