Introduction

Boron (1s22s22p1) exhibits unique structures and bonding patterns in chemistry to compensate for its prototypical electron-deficiency1. Dicoordinated boranes and tricoordinated borylenes are found to possess special reactivities on dinitrogen (N2) activations in both recent experimental and theoretical investigations2,3,4. At least sixteen distinct bulk boron allotropes have been experimentally known to be predominately constructed by interconnected icosahedral-B12 cages that in many cases are accompanied by interstitial boron atoms lying outside the icosahedrons, the most widely accepted structural model of boron-rich boron carbide B4C has CB11 icosahedrons with C-B-C intericosahedral chains, while the most frequently encountered boranes and carboranes contain icosahedral-CnB12-n skeletons (n = 0, 1, 2)1,5,6,7,8. Derivatives of icosahedral borane B12H122− and carborane C2B10H12 bound to tumor-specific antigens have been the main focus of interests in the area of boron neutron capture therapy (BNCT)1 and globular B12Br122− was recently found to function as anionic inorganic membrane carriers for a broad range of hydrophilic cargo molecules9, further indicating the importance of closo-CnB12-n icosahedrons in boron chemistry and materials science. In contrast, persistent joint photoelectron spectroscopy (PES) and first-principles theory investigations in the past two decades have shown that size-selected Bn−/0 nanoclusters exhibit a great structural diversity in an unexpectedly wide size range, including the planar or quasi-planar (2D) boron clusters (n = 3–38, 41, 42) which provided experimental evidence for the viability of monolayer borophenes10,11,12, cage-like borospherenes D2d B40−/0 and C3/C2 B3913,14 which were late extended to the Bnq borospherene family (n = 36–42, q = n−40) at first-principles theory level15,16,17,18, and bilayer D2h B48−/0 which was recently expanded to the bilayer B50–B72 series and a bottom-up approach from medium-sized boron nanoclusters to bilayer borophenes at density functional theory (DFT)19,20,21,22,23,24. Seashell-like borospherenes C2 B28− and Cs B29− were observed in PES measurements as minor isomers of the systems25,26. Neutral fullerene-like D2d B14 and double-ring tubular D2d B20 have also been predicted at first-principles theory levels27,28. Inspired by the previously predicted icosahedral-B12 stuffed amorphous B74, B84, B101, and B10229,30,31,32 and based on the structural motif of D5h C70 and extensive DFT calculations, our group recently reported the high-symmetry core–shell C5v B111+ which satisfies the Wade’s n + 1 and n + 2 skeletal electron counting rules exactly and the approximately electron sufficient Cs B111, Cs B112, Cs B113, and Cs B114 which are the most stable neutral core–shell borospherenes with a superatomic icosahedral-B12 core at the center reported to date in the size range between B68-B130, with Cs B112 being the thermodynamically most favorite species in the series33. The newly proposed high-symmetry core–shell Th B9634 appears to be about 0.020 eV atom−1 less stable than our Cs B112 and Cs B113 at DFT. However, core–shell borospherene nanoclusters with more than one B12 icosahedrons at the center still remain unknown in both experiments and theory, missing an important step to form bulk boron allotropes from medium-sized boron nanoclusters in bottom-up approaches.

Facile gas-phase formations of cage-like borafullerenes C59B and C69B by atomic exchange resulting from exposure of pristine C60 and C70 to boron vapor were firstly realized in 2013, with doubly and triply doped molecules, as well as C56B4 and higher doped fullerenes formed at lower abundances, depending on exposure time and the amount of B available for reaction35. Meanwhile, theoretical investigations on the structural and electronic properties of the borafullerenes C60-nBn (n = 1–12) and core–shell borafullerene C12B68 have been reported in the literature36,37. Borafullerenes B40C30, B40C40, and B40C50 isovalent with C60, C70, and C80, respectively, have also been predicted at DFT38. Prasad and Jemmis considered the stability of core–shell borafullerenes (C50B34 and C48B362−) based on Wade’s skeletal electron counting rules at DFT level39. Nevertheless, the thermodynamically most stable core–shell borafullerene nanoclusters stuffed with one or more than one CnB12-n icosahedrons (n = 0, 1, 2) at the center have not been reported to date.

Keeping the inspiration in mind and based on extensive DFT calculations, we predict herein the walnut-like Ci C50B54 (1) (C2B10@C48B44), C1 C50B54 (2) (CB11@C49B43), S10 C50B54 (3) (B12@C50B42) based on the structural motif of Ih C80 which possess one CnB12-n icosahedron (n = 0, 1, 2) at the center and the peanut-like Cs C88B78 (4), Cs C88B78 (5), Cs C88B78 (6), Cs B180 (7), Cs B182 (8), Cs B184 (9) which possess two interconnected icosahedral-CnB12-n cores as the most stable species in the corresponding cluster size ranges reported to date. The icosahedral-CnB12-n cores (n = 0, 1, 2) in these core–shell borafullerene and borospherene nanoclusters possess prototypical superatomic electronic configurations, rendering spherical aromaticity and extra stability to the systems.

Computational procedures

Based on the structural motif of Ih C80, we manually constructed the initial structures of the icosahedral-CnB12-n (n = 0, 1, 2) stuffed core–shell C50B54 clusters which follow the Wade’s n + 1 and n + 2 skeletal electron counting rules1 exactly (Fig. S1). However, locating the most stable isomer of such a medium-sized C–B binary cluster with huge numbers of possible positional isomers appeared to be a computationally daunting task. To solve the problem, we compiled the Fixed Motif Local Minimum Search (FMLMS) program in this work which includes random structural generations based on the designated structural motifs, symmetry recognitions using the Symmol code40, and structural similarity checks using the Ultrafast Shape Recognition (USR) approach41,42. Semi-empirical quantum mechanical calculations using the GFNn-xTB program were implemented to optimize the constructed structures from FMLMS initially and screen out the most concerned low-lying isomers, followed by structural optimizations using the CP2K software suite43,44,45. Such a procedure proved to work well in locating the recently reported most stable core–shell borospherenes of B111-B114 based on the structural motif of D5h C7033. The low-lying isomers of the core–shell C50B34, C50B44, C50B54 and C88B78 binary nanoclusters based on the structural motifs of Ih C60, D5h C70, Ih C80, and D5d C120, were located using FMLMS in this work, respectively (Figs. S4, S5 and S7). Similar processes were implemented on the binuclear core–shell C2 B172, Cs B176, C2 B178, Cs B180, Cs B182, Cs B184, C2 B186, Cs B188, Cs B190, Cs B192 (Figs. 2b, S8) based on the structural pattern of C2v C110 as an extension of the previously reported most stable mononuclear Cs B11233. The lowest-lying ten to twenty isomers were then fully optimized at both DFT-PBE046 and TPSSh47 levels with the all-electron basis sets of 6-31G(d) for both C and B48 implemented in Gaussian 09 suite49, with the relative energies further refined for the first few competitive lowest-energy isomers at PBE0/6-311G(d)46,47,48. Extensive Born–Oppenheimer molecular dynamics (BOMD) simulations were implemented for 30 ps on Ci C50B54 (1) and S10 C50B54 (3) at 1500 K and Cs B184 (9) at 500 K using the CP2K program45 to verify their dynamic stability at high temperatures. Natural bonding orbital (NBO) analyses were performed using the NBO 6.0 program50. Nucleus-independent chemical shifts (NICS)51,52 were calculated at the centers of the CnB12-n icosahedrons (n = 0, 1, 2) to assess the spherical aromaticity of core–shell systems. Detailed bonding analyses on Ci C50B54 (1), S10 C50B54 (3), Cs C88B78 (4), Cs B182 (8) and Cs B184 (9) were carried out using the adaptive natural density partitioning (AdNDP 2.0) method53,54 at the PBE0/6-31G level46,48. The Electron Density of Delocalized Bonds (EDDB) was calculated using the EDDB code55,56, with the EDDB isosurfaces generated using the visual molecular dynamics (VMD) software57 to visualize the distribution of delocalized bonds. The IR and Raman spectra of Ci C50B54 (1), Cs C88B78 (4), and Cs B184 (9) were theoretically simulated at PBE0/6-31G(d).

Results

Structures and stabilities

The structural constructions of mononuclear C50B54 (1, 2, 3), binuclear Cs C88B78 (4, 5, 6), and binuclear B180 (7), B182 (8), and B184 (9) starting from the structural motifs of the corresponding fullerenes are illustrated in Figs. S1, S2 and S3, respectively. The optimized core–shell borafullerenes Ci C50B54 (1) (C2B10@C48B44), C1 C50B54 (2) (CB11@C49B43), and S10 C50B54 (3) (B12@C50B42) with one icosahedral-CnB12-n (n = 0, 1, 2) core at the center, core–shell borafullerenes Cs C88B78 (4) ((C2B10)2@C84B58), Cs C88B78 (5) ((CB11)2@C86B56), Cs C88B78 (6) ((B12)2@C88B54) with two interconnected icosahedral-CnB12-n (n = 0, 1, 2) cores, and core–shell borospherenes Cs B180 (7) ((B12)2@B156), Cs B182 (8) ((B12)2@B158), and Cs B184 (9) ((B12)2@B160) with two interconnected icosahedral-B12 cores are collectively shown in Fig. 1, with more alternative low-lying isomers obtained for C50B54, C88B78, and B184 depicted in Figs. S4, S5 and S6, respectively.

Figure 1
figure 1

Optimized structures of Ci C50B54 (1), C1 C50B54 (2), S10 C50B54 (3), Cs C88B78 (4), Cs C88B78 (5), Cs C88B78 (6), Cs B180 (7), Cs B182 (8), and Cs B184 (9) at PBE0/6-311G(d) level, with the icosahedral-CnB12-n (n = 0, 1, 2) cores at the centers highlighted in purple.

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The calculated formation energies per atom Ef = (Et−mμB−nμC)/(m+ n) for the CmBn borafullerenes are diagrammatically shown in Fig. 2a where Et, μB = EB40/40, and μC = EC60/60 are the total energy of CmBn binary clusters and chemical potentials of the experimentally observed D2d B4013 and Ih C60, respectively, while the cohesive energies per atom Ec = (Et−nE)/n) for Bn core–shell borospherenes are depicted in Fig. 2b where E is the energy of a free B atom in vacuum. The calculated nucleus-independent chemical shift (NICS) values at the geometric centers of the CnB12-n (n = 0, 1, 2) icosahedral cores of the concerned core–shell borafullerenes and borospherenes and their HOMO–LUMO gaps (△Egap) at PBE0/6-311G(d) are comparatively tabulated in Tables S1 and S2.

Figure 2
figure 2

(a) Calculated formation energy per atom (Ef, eV atom−1) as a function of the n/(m + n) ratio in the optimized boron–carbon clusters CmBn and (b) cohesive energy per atom (Ec, eV atom−1) of the optimized core–shell boron clusters Bn (n = 110–192) as a function of the cluster size (n) at PBE0/6-311G(d).

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As shown in Fig. S1, with one closo-B12 icosahedron located at the center and twelve nido-B6 pentagonal pyramids symmetrically distributed on the cage surface, the high-symmetry core–shell Ih B104 (B12@B92) based on the structural motif of Ih C80 is deficient by 50 electrons according to the Wade’s n + 1 and n + 2 skeleton electron counting rules and should therefore not be expected to be stable in thermodynamics32,39,58. Ih B104 can be made electron sufficient by substitution of 50 B atoms on the cage surface with 50 C atoms. Eighteen such low-lying walnut-like C50B54 positional isomers within 1.91 eV were obtained using FMLMS in Fig. S4. The high-symmetry S10 C50B54 (B12@C50B42) (3) (Fig. 1) as the ninth lowest-lying isomer possesses an almost ideal closo-B12 icosahedron at the center, ten nido-C4B2 pentagonal pyramids symmetrically distributed on the waist, and two nido-C5B pentagonal pyramids on the top and bottom. The core–shell C1 C50B54 (CB11@C49B43) (2) can be obtained by replacing the central B12 core in C50B54 (3) with a closo-CB11 icosahedron, with the top nido-C5B simultaneously changed into a nido-C4B2 pentagonal pyramid. The most stable C50B54 (C2B10@C48B44) (1) contains an icosahedral closo-C2B10 core at the center and twelve nido-C4B2 pentagonal pyramids evenly distributed on the cage surface in an overall symmetry of Ci. C50B54 (1), C50B54 (2), and C50B54 (3) prove to be true minima on the potential surface of C50B54 with the smallest vibrational frequencies of vmin = 230.2, 222.4, and 208.4 cm−1 at PBE0/6-31G(d), respectively.

As shown in Fig. 2a and Table S1, as one of the two local minima on the formation energy Ef ~ n/(n + m) curve, Ci C50B54 (1) is the most stable core–shell borafullerene obtained to date, with the average formation energy per atom of Ef = − 0.213 eV atom−1 with respect to the experimentally known C60 and B40. It is 0.11 eV more stable than the second lowest-lying C1 C50B54 (2) and 0.58 eV more stable than the ninth lowest-lying S10 C50B54 (3) at PBE0/6-311G(d) level (Fig. S4). Other approximately electron sufficient close-lying species Ci C48B56 (B12@C48B44), C2 C52B52 (B12@C52B40), and C2 C54B50 (B12@C54B38) all appear to be obviously less favorable in thermodynamics than Ci C50B54 (1). The seventeenth high-symmetry isomer C5 C50B54 in the structural motif of D5h C80 with a B12 icosahedron at the center lies 1.87 eV less stable than C50B54 (1) (Fig. S1). As indicated in Table S1, C50B54 (1/2/3) have the largest calculated HOMO–LUMO gaps of ∆Egap = 2.24/2.28/2.75 eV in the low-lying core–shell borafullerene series obtained in this work, well supporting the high chemical stabilities of these mononuclear core–shell borafullerenes. The previously predicted electron sufficient core–shell C2h C50B3439 in the structural motif of Ih C60 (which was distorted to a more stable C1 C50B34 obtained in this work, Fig. S7), core–shell C5 C50B44 in the structural motif of D5h C70 obtained in this work (Fig. S7), and the previously reported cage-like borafullerenes C30B40, C40B40, and C50B4038 all appear to be obviously less favorable than C50B54 (1) (Fig. 2a). It is also noticed that C50B54 (1), C50B54 (2), and C50B54 (3) are all considerably more favorable in formation energies than the experimentally observed C59B, C58B2, and C56B4 and theoretically predicted amorphous core–shell C1 C12B6835,36,37.

The walnut-like core–shell borafullerenes C50B54 (1, 2, 3) can be extended in axial dimension to form the approximately electron sufficient peanut-like Cs C88B78 (4) ((C2B10)2@C84B58), Cs C88B78 (5) ((CB11)2@C86B56), Cs C88B78 (6) ((B12)2@C88B54) based on the structural framework of D5d C120 which contain two interconnected icosahedral C2B10, CB11, and B12 cores inside the outer shells, respectively (Figs. 1 and S2). Cs C88B78 (4) as the second local minimum on the Ef ~ n/(n + m) curve (Fig. 2a) with Ef = − 0.209 eV atom−1 appears to be 0.005 and 0.020 eV atom−1 more stable than C88B78 (5) and Cs C88B78 (6) in formation energy, respectively, indicating again that icosahedral-C2B10 cores are better favored in energy over both CB11 and B12 icosahedrons in core–shell borafullerenes. The electron-precise C92B74 and approximately electron sufficient C90B76 with two interconnected icosahedral-CnB12-n cores (n = 0, 1, 2) appear to be slightly less stable in thermodynamics than their C88B78 (4) counterpart (Fig. 2a). The prediction of mononuclear C50B54 (1, 2, 3) and binuclear C88B78 (4, 5, 6) as the two minima on the Ef ~ n/(n + m) curve indicates that Ih C80 and its expanded fullerene analog D5d C120 provide the right cavities and optimum structural motifs to form core–shell borafullerenes with one and two icosahedral-CnB12-n (n = 0, 1, 2) cores (Fig. 2a), respectively. In contrast, the structural motifs generated from both Ih C60 and D5h C70 appear to be too small in size to host icosahedral-CnB12-n (n = 0, 1, 2) cores comfortably in core–shell borafullerenes, as demonstrated in the cases of core–shell C2h/C1 C50B34 and C5 C50B44 (Figs. 2a and S7).

As an extension of the previously reported most stable mononuclear Cs B112 based on the framework of D5h C7033, a series of binuclear core–shell borospherenes B172-B192 with two interconnected B12 icosahedrons at the center based on the structural motif of C2v C110 are obtained in this work (Figs. 2b and S3). The almost electron-sufficient Cs B188 with the cohesive energy of Ec = − 5.673 eV atom−1 (Table S2) appears to be a local minimum on the Ec ~ n curve, but it is obviously less stable in thermodynamics than the approximately electron-sufficient Cs B180 (7) ((B12)2@B156), Cs B182 (8) ((B12)2@B158), and Cs B184 (9) ((B12)2@B160) which all lie within a deeper local minimum with Ec = − 5.681, − 5.679, and − 5.691 eV atom−1 at PBE0, respectively (Fig. 2b and Table S2). Cs B184 (9) as the most stable species on the Ec ~ n curve contains two closo-B12 icosahedral cores doubly bound to an interstitial B2 unit. It is even more stable than the previously reported mononuclear Cs B112 where Ec = − 5.678 eV atom−1 at the same theoretical level33. Similar results are obtained at TPSSh/6-311G(d) in Fig. S8 where Cs B184 also appears to be the most stable species in cohesive energy in the size range between B110 and  B192. Binuclear B184 (9) with two icosahedral-B12 cores and one interstitial B2 unit is therefore the most stable core–shell borospherene reported to date in thermodynamics.

Extensive BOMD simulations provide strong evidence to support the dynamic stability of these core–shell nanoclusters. As demonstrations in Fig. S9, the thermodynamically stable Ci C50B54 (1), S10 C50B54 (3), and Cs B184 (9) were highly dynamically stable at 1500 K, 1500 K, and 500 K, with the small calculated average root-mean-square-deviations of RMSD = 0.10, 0.10, 0.07 Å and maximum bond length deviations of MAXD = 0.37, 0.34, and 0.31 Å, respectively. No other low-lying isomers were observed during the dynamical simulations in 30 ps.

Bonding pattern analyses

The high stability of these core–shell nanoclusters originates from their unique electronic structures and bonding patterns. As demonstrations, detailed AdNDP bonding analyses on both closed-shell Ci C50B54 (1) and Cs C88B78 (4) are presented in Fig. 3. The icosahedral-C2B10 cores in both C50B54 (1) and C88B78 (4) are connected to the outer shells through radial B–B and C–B bonding interactions. To better understand the bonding nature of these binary core–shell structures, detailed bonding analysis on the prototypical carborane D5d C2B10H12 is performed in Fig. 3a first. As expected, C2B10H12 possesses 12 2c-2e σ bonds in radial directions perpendicular to the cage surface, including 10 2c-2e B–H σ bonds on the waist and 2 2c-2e C–H σ bonds on the top and bottom with the occupation numbers of ON = 1.97–1.99 |e|. The remaining 26 valence electrons are distributed in 13 12c-2e delocalized bonds over the whole D5d icosahedral-CB10C skeleton with ON = 1.93–2.00 |e|, including 1 12c-2e S-type bond, 3 12c-2e P-type bonds, 5 12c-2e D-type bonds, and 4 12c-2e F-type bonds. Such a bonding pattern well corresponds to the superatomic electronic configuration 1S21P61D101F8 of D5d C2B10H12 (Fig. S10) which is spherically aromatic in nature, as evidenced by the negative calculated NICS = − 29.22 ppm at the cage center.

Figure 3
figure 3

AdNDP bonding patterns of (a) D5d C2B10H12, (b) Ci C50B54 (1), and (c) Cs C88B78 (4) with the occupation numbers (ONs) indicated.

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The bonding pattern of Ci C50B54 (1) in Fig. 3b well demonstrates the superatomic behavior of its Ci icosahedral-CB10C core. C50B54 (1) contains 10 2c-2e B–B bonds and 2 2c-2e C–B σ bonds in radial directions between the CB10C icosahedron and outer shell to saturate the dangling valences of icosahedral core, 120 B-B or B-C or C–C 2c-2e σ bonds on the cage surface, and 36 6c-2e π bonds on 12 nido-C4B2 pentagonal pyramids in the first row, with 3 6c-2e π bonds over each C4B2 pentagonal pyramid matching the 4n + 2 aromatic rule with n = 1 (suggesting the existence of local π-aromaticity over each C4B2 pentagon in on the surface of C50B54 (1), similar to the situation in benzene C6H6). Its remaining 13 12c-2e bonds are delocalized over the whole closo-CB10C icosahedral core, including 1 12c-2e S-type bond, 3 12c-2e P-type bonds, 5 12c-2e D-type bonds, and 4 12c-2e F-type bonds, well corresponding to the 13 12c-2e delocalized bonds of D5d C2B10H12 in Fig. 3a. Such a bonding pattern clearly indicates that the icosahedral-CB10C core in Ci C50B54 (1) possesses a typical superatomic electron configuration, similar to the situation in D5d C2B10H12. Similar bonding patterns exist in C1 C50B54 (2) and S10 C50B54 (3) which contain negatively charged icosahedral-CB11- and icosahedral-B122− cores, respectively (Fig. S11). The binuclear Cs C88B78 (4) possesses a similar but more complicated bonding pattern. As shown in Fig. 3c, C88B78 (4) contains 1 C–C 2c-2e σ bond between the two icosahedral-CB10C cores and 22 B-B or 2 C-B σ bonds in radial directions, 180 B-B or C-B or C–C 2c-2e σ bonds on the cage surface, and 20 3c-2e σ bonds on the waist between ten capping B atoms and the corresponding hexagonal holes on the surface in an overall symmetry of Cs. In addition to the 36 6c-2e π bonds over 12 C5B or C4B2 pentagonal pyramids on the top and bottom, C88B78 (4) also possesses 8 50c-2e π bonds delocalized over the “girdle” composed of ten hexagonal pyramids on the waist in between. Most interestingly, with 26 12c-2e bonds over the CB10C-CB10C binuclear core in C88B78 (4), there exist 13 12c-2e bonds over each closo-CB10C icosahedron, including 1 12c-2e S-type bond, 3 12c-2e P-type bonds, 5 12c-2e D-type bonds, 4 12c-2e F-type bonds, well corresponding to the 13 12c-2e delocalized bonds of D5d C2B10H12 in Fig. 3a. Thus, each closo-CB10C icosahedron in C88B78 (4) follows the superatomic electronic configuration of 1S21P61D101F8, corresponding again to the 13 12c-2e delocalized bonds of D5d C2B10H12 in Fig. 3a.

The local π-aromaticities over the twelve C4B2 pentagons and spherical aromaticities over each C2B10 icosahedral core in both C50B54 (1) and C88B78 (4) are also demonstrated in their calculated EDDB isosurface maps depicted in Fig. S13. The average values of atomic contribution of EDDB = 1.31, 1.33 e in the C2B10 icosahedrons in C50B54 (1) and C88B78 (4) are obviously larger than the corresponding values of EDDB = 0.93 and 1.00 e in the remaining parts, respectively, well supporting the spherical aromaticity of superatomic cores, while the observed high EDDB values over each C4B2 pentagon on the cage surface in continuous distributions indicate the existence of local π-aromaticity in the systems.

Such bonding patterns render spherical aromaticity to both Ci C50B54 (1) and Cs C88B78 (4), as evidenced by the negative calculated NICS = − 23.23 ppm and NICS = − 32.47, − 28.04 ppm at the cage centers of their C2B10 icosahedral cores, respectively. With the calculated NICS = − 17.70 ppm and NICS = − 32.68, − 32.65 ppm at the cage centers of their C2B10 and B122− icosahedral cores, respectively, both C50B54 (3) and B184 (9) also appear to be spherically aromatic in nature. Similar NICS values exist in the spherically aromatic C50B54 (2), C50B54 (3), C88B78 (5), Cs C88B78 (6), B180 (7), and B182 (8).

IR and Raman spectral simulations

The infrared (IR) and Raman spectra of Ci C50B54 (1) and Cs C88B78 (4) are computationally simulated at PBE0/6-31G(d) in Fig. 4 to facilitate their spectral characterizations. Ci C50B54 (1) exhibits three major IR peaks at 640 (au), 1026 (au), and 1294 cm−1 (au), while Cs C88B78 (4) possesses two major IR peaks at 1234 (a’’) and 1391 cm−1 (a’), respectively. The three major Raman active peaks of C50B54 (1) occur at 383 (ag), 1152 cm−1 (ag), and 1405 cm−1 (ag), with the weak peak at 242 cm−1 (ag), strong peaks at 383 (ag), and strong peak at 1405 cm−1 (ag) representing typical “radial breathing modes” (RBMs) of the outer shell, the core + shell system as a whole, and the inner icosahedral-C2B10 core of Ci C50B54 (1), respectively. Such RBMs can be used to characterize the hollow boron-based nanostructures in experiments59. Similarly, Cs C88B78 (4) exhibits two major Raman peaks at 1264 cm−1 (a’) and 1360 cm−1 (a’) and three RBM vibrational modes at 211 cm−1 (a’), 329 cm-1 (a’), 858 cm-1 (a’), respectively.

Figure 4
figure 4

Simulated IR and Raman spectra of (a) Ci C50B54 (1) and (b) Cs C88B78 (4) at PBE0/6-31G(d) level.

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Conclusions

The analyses above indicate that, based on the structural motifs of the related fullerenes and extensive DFT calculations, the mononuclear C50B54 (1, 2, 3) and binuclear Cs C88B78 (4, 5, 6), B180 (7), B182 (8), and B184 (9) nanoclusters obtained in this work with one or two icosahedral-CnB12-n cores at the center are the most stable core–shell borafullerenes and borosphenrenes in thermodynamics in the corresponding cluster size ranges reported to date. The B122−, CB11-, and C2B10 icosahedrons encapsulated in these core–shell nanostructures possess the superatomic electronic configurations (1S21P61D101F8) of the experimentally known icosahedral Ih B12H122−, C5 CB11H12-, and D5d C2B10H12, respectively, rendering prototypical spherical aromaticity to the systems. Theoretical investigations on core–shell borafullerenes and borospherenes with more than two superatomic icosahedral-CnB12-n cores accompanied by suitable numbers of interstitial boron atoms are currently in progresses. Experimental investigations are invited to synthesize icosahedral-CnB12-n stuffed core–shell borafullerenes and borospherenes to form bulk boron allotropes and their carbon-boron binary counterparts with novel electronic and mechanic properties in bottom-up approaches.