Structures and Stability 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 Fig. S1, Fig. S2, and Fig. 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 Fig. S4, Fig. S5, and Fig. S6, respectively.
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 B4010 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 Table S1 and Table S2.
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 thermodynamics27, 34, 50. 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 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 C50B3434 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 C50B40 33 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 C12B6830–32.
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 (Fig. 1 and Fig. S2). Cs C88B78 (4) as the second local minimum on the Ef ~ n/(n + m) curve (Fig. 2a) with Ef = -0.209 eV/atom appears to be 0.005 and 0.020 eV/atom 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 (Fig. 2a and Fig. S7).
As an extension of the previously reported most stable mononuclear Cs B112 based on the framework of D5h C7028, 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 (Fig. 2b and Fig. S3). The almost electron-sufficient Cs B188 with the cohesive energy of Ec = -5.673 eV/atom (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 at PBE0, respectively (Fig. 2 (b) 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 at the same theoretical level28. 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 ~ 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, nd 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-B σ bonds on the waist and 2 2c-2e C-B 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.
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 (similar to the π-bonding pattern of 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 exists 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.
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 experiments 51. 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.