{'fraction_non_alphanumeric': 0.044510020902496006, 'fraction_numerical': 0.05065781384482971, 'mean_word_length': 3.784313725490196, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lithium-Decorated Borospherene B40: A Promising Hydrogen Storage Medium

The recent discovery of borospherene B40 marks the onset of a new kind of boron-based nanostructures akin to the C60 buckyball, offering opportunities to explore materials applications of nanoboron. Here we report on the feasibility of Li-decorated B40 for hydrogen storage using the DFT calculations. The B40 cluster has an overall shape of cube-like cage with six hexagonal and heptagonal holes and eight close-packing B6 triangles. Our computational data show that Lim&B40(1–3) complexes bound up to three H2 molecules per Li site with an adsorption energy (AE) of 0.11–0.25 eV/H2, ideal for reversible hydrogen storage and release. The bonding features charge transfer from Li to B40. The first 18 H2 in Li6&B40(3) possess an AE of 0.11–0.18 eV, corresponding to a gravimetric density of 7.1 wt%. The eight triangular B6 corners are shown as well to be good sites for Li-decoration and H2 adsorption. In a desirable case of Li14&B40-42 H2(8), a total of 42 H2 molecules are adsorbed with an AE of 0.32 eV/H2 for the first 14 H2 and 0.12 eV/H2 for the third 14 H2. A maximum gravimetric density of 13.8 wt% is achieved in 8. The Li-B40-nH2 system differs markedly from the previous Li-C60-nH2 and Ti-B40-nH2 complexes.

Due to its merits of cleanness, renewability, abundance in nature, and high energy density per unit mass, hydrogen has been recognized as an appealing energy carrier for the future world. It has the potential to reduce our dependence on fossil fuels, which are limited in resource and harmful to the environment [1][2][3][4] . One bottleneck of using hydrogen for vehicular applications is the lack of safe and efficient hydrogen storage materials 5-7 that store molecular H 2 reversibly with high gravimetric density and fast kinetics for adsorption, as well as desorption, under the conditions of moderate temperature and pressure 8,9 . An ideal H 2 storage system would be one that binds hydrogen in molecular form and with an adsorption energy (AE) in the regime of 0.1-0.5 eV per H 2 , that is, intermediate between the physisorbed and chemisorbed states 10,11 . Although advances have been made towards meeting the U.S. DOE's targets for hydrogen storage, an ideal system is yet to be designed and synthesized. Therefore, seeking novel hydrogen storage materials has remained an important issue.
Previous experiments and theoretical calculations have shown that metal-decorated carbon fullerenes and nanotubes [12][13][14][15][16][17][18][19] , as well as their boron-, nitrogen-and beryllium-substituted nanostructures [20][21][22] , might be good candidates for the storage of H 2 molecules. For instance, Zhang and co-workers showed that the reversible hydrogen storage of transition-metal-coated C 60 and C 48 B 12 may be as high as 9 wt% 21 . Yildirim et al. revealed that Ti-coated single-walled carbon nanotubes can store 8 wt% of H 2 23 . To avoid the clustering problem of transition metal atoms on the surface of carbon nanostructures, Yoon and co-workers 18 found that Ca can achieve homogeneous monolayer coating, which is superior to other metal elements. They concluded that up to 8.4 wt% of hydrogen can be stored in Ca 32 C 60 with an AE of 0.2-0.4 eV/H 2 . Through first-principles computations, Sun et al. 13 predicted that Li-decorated fullerene C 60 (Li 12 C 60 ) can store up to 9 wt% of H 2 , albeit with a rather weak AE of 0.075 eV/H 2 . Furthermore, Yoshida et al. 17 measured the hydrogen absorption of Li 9 C 60 based on experiments and confirmed that up to ~2.6 wt % H 2 can be stored at 250 °C and 30 bar H 2 . For lithium-doped fullerenes (Li x -C 60 -H y ) with a Li:C 60 mole ratio of 6:1, a reversible uptake of 5 wt% H 2 at 350 °C and 105 bar H 2 and desorption onset temperature of ~270 °C was observed 15 . Subsequently, another experimental results 16 showed that up to 9.5 wt % deuterium (D 2 ) are absorbed in Li 12 C 60 under a pressure of 190 bar and a temperature below 100 °C.
Boron is the lighter neighbor of carbon in the periodic table, which possesses the similar merit as carbon in terms of light weight and potential applications for hydrogen storage. For this purpose, its chemical hydrides [24][25][26] were studied, as were relevant model nanostructures, such as boron monolayer sheets, fullerenes, and nanotubes [27][28][29] . In particular, following the proposal of the celebrated I h B 80 buckyball 30 , which is built upon the C 60 motif by capping all 20 surface hexagons, a number of papers were devoted to hydrogen storage using B 80 coated with metals (M = Li, Na, K, Be, Mg, Ca, Sc, Ti, and V) 27,[31][32][33] . However, B 80 was subsequently found to favor core-shell type structures at various theoretical levels 34,35 . It is thus not feasible to pursue any realistic technological applications of B 80 buckyball as hydrogen storage materials.
Very recently, the first all-boron fullerenes or borospherenes, D 2d B 40 and D 2d B 40 − , were observed in a combined experimental and theoretical study 36 , marking the onset of the borospherene chemistry, whose future development may be envisioned to parallel that of the fullerenes. Endohedral M@B 40 (M = Ca, Sr) and exohedral M&B 40 (M = Be, Mg) metalloborospherenes were also predicted, which further support the structural, electronic, and chemical robustness of the B 40  borospherenes were also studied 38,39 , which expand the borospherene family and may eventually lead to new boron-based nanomaterials. Borospherene B 40 possesses a cube-like cage structure, whose six hexagonal and heptagonal holes each occupy a face of the cube. It also has eight triangular, close-packing B 6 structural blocks, each on an apex of the cube. All B atoms are on the surface of the cage, which is an ideal, well-defined system for chemistry. B 40 differs from carbon fullerenes in terms of structure and bonding, and the pursuit of borospherene-based nanomaterials for hydrogen storage is thus intriguing from a fundamental point-of-view. Furthermore, borospherenes are lighter than carbon fullerenes, which make the former systems better candidates to reach a higher gravimetric capacity for hydrogen storage. Relevant to this topic, Dong et al. 40 predicted on the basis of density-functional theory (DFT) calculations that Ti-decorated B 40 fullerene (Ti 6 B 40 ) is capable of storing up to 34 H 2 molecules with a maximum gravimetric density of 8.7 wt% and a reversible storage capacity of 6.1 wt%. To our knowledge, the U.S. DOE has set a target of 7.5 wt% for hydrogen storage capacity for the year of 2015 41,42 .
In this work, we choose to study lithium-decorated borospherene B 40 as a potential candidate for hydrogen storage via extensive DFT calculations. Since boron-based nanomaterials are also candidates for lithium storage, the current ternary B-Li-H system is quite unique 28,29,43,44 . Compared to transition metal, Li as the lightest metal definitely will facilitate the improvement of hydrogen storage capacity for the metal-decorated B 40 system. The Li m -B 40 -nH 2 system differs markedly from Li m -C 60 -nH 2 or Ti 6 -B 40 -nH 2 , which have an AE value that is either rather small (0.075 eV) 13 or too large (up to 0.82 eV) 40 . Even the recently proposed Li 8 -B 6 -nH 2 system 44 only has an AE of less than 0.1 eV. Our computational data show that Li-decorated B 40 appears to be a promising medium for hydrogen storage. The Li atoms readily attach to the top of hexagonal and heptagonal holes on B 40 , forming a series of charge-transfer complexes from C s Li&B 40 (1), C 2v Li&B 40 (2), up to D 2d Li 6 &B 40 (3). The Li m &B 40 complexes can adsorb three H 2 molecules per Li site with a moderate AE of 0.11-0.25 eV/H 2 . The Li 6 &B 40 (3) complex stores up to 34 H 2 with an average AE of 0.10 eV/H 2 . The first 18 H 2 of these possess ideal AEs, which suggest a gravimetric density of 7.1 wt%. Furthermore, the eight close-packing, triangular B 6 corner sites of B 40 are also suitable for Li-decoration and H 2 adsorption. In a desirable Li 14 &B 40 (7) complex, up to 42 H 2 molecules can be stored with AEs of 0.12-0.32 eV/H 2 , which corresponds to a gravimetric density of 13.8 wt%.

Results and Discussion
Isolated B 40 Borospherene for H 2 Adsorption. The first all-boron fullerene called as borospherene 36 , D 2d B 40 ( 1 A 1 ), possesses a very large HOMO-LUMO gap of 3.13 eV at the PBE0 level that indicates its overwhelming stability, which is comparable to that of I h C 60 ( 1 A g ) (3.02 eV) calculated at the same level. All the valence electrons in B 40 are either delocalized σ or π bonds and there is no localized 2c-2e bond, unlike the C 60 fullerene. In fact, the surface of B 40 is not perfectly smooth and exhibits unusual heptagonal faces which may play a role that release the surface strains, in contrast to C 60 fullerene whose surface makes up of pentagons and hexagons and presents the least strain. And the diameter of B 40 is 6.2 Å, slightly smaller than the value of C 60 (7.1 Å), which makes B 40 more comfortable to accommodate a range of small molecules inside the cage.
We initially studied H 2 adsorption on the isolated B 40 borospherene. The optimized structures of B 40 H 2 , H 2 @ B 40 and 2H 2 @B 40 are shown in Fig. 1. In the C 2 B 40 H 2 dihydride, the H 2 molecule tends to form two B-H covalent bonds with the tetracoordinate-B sites, which dissociate H 2 . The dissociative AE of a single H 2 is up to 1.30 eV. For H 2 storage inside the cage, only one H 2 molecule can be encapsulated into B 40 , which is marginally exothermal with an AE of 0.24 eV. Interestingly, once such an encapsulation is completed, the H 2 molecule cannot escape due to substantial energy barriers (> 3 eV). The AE of a second H 2 inside the cage is found to be endothermic by 1.32 eV, which is thus not feasible experimentally. In short, the above results show that an isolated B 40 borospherene is not a good candidate for hydrogen storage directly. The B 40 -H 2 interactions appear to be different from the case of C 60 . The latter is known to interact with H 2 via weak van der Waals forces 45 . As a comparison, our calculation results show that the dissociative AE of a single H 2 for C 60 H 2 is only ~0.18 eV at the same level. However, similar to B 40 , only one hydrogen molecule can reside inside the C 60 cage with a negative AE value of ~0.22 eV. Fig. 2, we start with a single Li atom interacting with B 40 . Relative stability of Li atom bound on heptagonal and hexagonal holes were considered. The exohedral C s Li&B 40 (1), in which Li caps a heptagon, turns out to be more stable by 0.20 eV with respect to C 2v Li&B 40 (2). In the latter species, Li caps a hexagon. The BE for Li is 3.08 and 2.88 eV in 1 and 2, respectively. Thus, Li prefers to bind on top of the heptagonal hole of B 40 . The Li-B distance in 1 is 2.34 Å, compared to 2.33 Å in 2 (Table 1). Clearly, the BE of Li on the center of heptagon or hexagon in B 40 is substantially higher than those on the pentagon of C 60 (1.80 eV), in Li 2 dimer (0.95 eV), and in the Li bulk (1.63 eV) 13 . This should help suppress the potency of Li aggregation to form clusters on B 40 surface, suggesting that Li is a suitable adsorbate to decorate B 40 . As shown in Table 1, electron transfer occurs from Li to borospherene B 40 cage in 1 and 2, resulting in a positive charge of 0.87-0.88 |e| on Li as revealed in the Bader charge analysis. The ionized Li atom hints a possibility for H 2 adsorption via the polarization mechanism 18 .

Configurations of Li-Decorated B 40 . As shown in
To increase the coverage of Li on B 40 , we place one Li atom on top of every hexagon and heptagon hole and reach exohedral D 2d Li 6 &B 40 (3) (Fig. 2). In complex 3, six Li atoms remain isolated on the surface holes, resulting in a highly symmetric D 2d geometry. The average BE of Li in 3 is 3.07 eV/Li, which is comparable to that in Li&B 40 (1) (3.08 eV) and is slightly larger than that in Li&B 40 (2) (2.88 eV). There appears to be a collective effect for Li adsorption because six Li atoms in 3 have a higher total BE (18.48 eV) than six individual Li atoms in 1 and 2 combined (18.08 eV). This fact suggests that Li 6 &B 40 (3) is a favorable configuration for Li-decoration. Remarkably but not surprisingly, our computational data indicate that 3 is at least 6.29 eV more stable than B 40 attached by a compact Li 6 cluster (Fig. S1). Therefore, surface aggregation of Li for island clusters is unlikely in the Li 6 &B 40 system. The Li-B distance in 3 is 2.33 Å, nearly identical to those in 1 and 2. Bader charge analysis shows that the atomic charge on each Li atom in 3 is + 0.87 |e|.
We further analyzed the isosurfaces of charge density differences in complexes C s Li&B 40 (1), C 2v Li&B 40 (2), and D 2d Li 6 &B 40 (3), as depicted in Fig. 3. Here the yellow and blue colors represent electron accumulation and depletion regions, respectively. From the charge density variations of 1-3, which are induced by the adsorption of Li atoms onto B 40 , it is obvious that charge transfer from Li atom to B 40 indeed takes place upon Li decoration. Figure 4 shows the frontier canonical molecular orbitals (CMOs) of 1-3, which are compared with those of D 2d B 40 . Upon attachment of the first Li atom on B 40 , the lowest unoccupied molecular orbital (LUMO) of B 40 (Fig. 4d) becomes half-filled due to charge transfer, which are the singly occupied molecular orbitals (SOMOs) in 1 and 2 (Fig. 4a,b). Note these three CMOs are virtually identical. Likewise, in line with their lower symmetry, LUMO (a′ ) of 1 and LUMO (b 2 ) of 2 correspond to the degenerate LUMO + 1 of D 2d B 40 . In D 2d Li 6 &B 40 (3) (Fig. 4c), six electrons are transferred from Li to the B 40 cage, which successively occupy the LUMO and degenerate LUMO + 1 of D 2d B 40 . The latter LUMO + 1 become the highest occupied molecular orbital (HOMO) in 3, which are also doubly degenerated due to the same high symmetry of D 2d . As a consequence, the LUMO + 2 (b 1 ) of D 2d B 40      When one H 2 molecule is introduced to 1, due to the polarization interaction between the charged Li atom and the H 2 molecule, the Li-B bond distance is slightly enlarged (by 0.01 Å) to 2.35 Å. The H-H distance is found to be 0.76 Å. The equilibrium Li-H distance is 1.97 Å, which is comparable to the value of 2.04 Å in the case of a free Li + ion interacting with H 2 46 . The AE of the first H 2 to 1 is 0.25 eV, which is in quantitative agreement with that in Li + H 2 (0.25 eV) 46 .
With more H 2 molecules being attached to 1, the average AE of H 2 , consecutive AE of H 2 , the Li-B distance, and the distances between H 2 and Li change accordingly. As shown in Table S1 and Fig. 5a, a single Li atom in 1, coated on a heptagonal hole, can adsorb up to six H 2 molecules with an average AE of 0.11 eV/H 2 . From one to six H 2 , the average AE decreases from 0.25 to 0.11 eV/H 2 , whereas the consecutive AE decrease from 0.25 to 0.05 eV/H 2 . This effect may be partially due to the steric repulsion 47 when the number of H 2 molecules increases. In line with this trend, the Li-B distances are elongated gradually from 2.35 to 2.43 Å. However, the H-H bond distance is nearly constant in the range of 0.75-0.76 Å, which is the value of free H 2 molecule, consistent with the nature of molecular adsorption. The Li-H distances span a rather wide range from 1.97 to 2.91 Å. Notably, there is an abrupt increase in the Li-H distances from 1-3 H 2 to 1-4 H 2 , so that the first three H 2 are closer to the Li site than the next three. In other words, the adsorption of the first three H 2 molecules forms an inner core with Li, upon which the additional H 2 molecules adsorb loosely. The data of consecutive AE confirm this to be indeed the case: The first three H 2 possess an AE of 0.25-0.11 eV, in contrast to 0.04-0.05 eV for the next three (Table S1). In fact, the structure of 1-4 H 2 can be constructed on the basis of 1-3 H 2 by adding one H 2 on the top of Li. However, when the fifth and sixth H 2 are put on successively in 1-5 H 2 and 1-6 H 2 , they flee away after structural optimization as shown in Fig. 5a. Therefore, the Li site in 1 may adsorb three H 2 molecules comfortably, whereas additional H 2 are only physisorbed.
Basically, the adsorption of H 2 on 2 is rather similar to that on 1. Up to five H 2 molecules may be adsorbed on the Li site in 2 (Fig. 5b). Again, the first three H 2 are located closely to Li, with the fourth H 2 being situated symmetrically on top of Li at a substantially larger distance. For the 2-5 H 2 case, there is a structural rearrangement   (3), whose optimized structures are shown in Fig. S2 and 6. The former four cases correspond to the adsorption of one to four H 2 on each Li site. For the 34 H 2 case, that is, Li 6 &B 40 -34 H 2 (4), 6 H 2 are adsorbed on each heptagonal Li site and 5 H 2 are on each hexagonal Li site, as depicted in Fig. 6. The total interaction energy of 34 H 2 in 4 is 3.43 eV, yielding an average AE of 0.10 eV/H 2 . The calculated consecutive AEs are collected in Table 2, which reflects the adsorption nature more faithfully. Similar to 1 and 2   16 B-H bonds for the tetracoordinate B sites, which can also be decorated with six Li atoms, resulting in a D 2d Li 6 &B 40 H 16 (5) complex as depicted in Fig. 7. The Li-B distance in 5 remains to be 2.33 Å, which is very close to that in 3. In complex 5, each Li atom carries a charge of 0.88 |e|. Interestingly, the B-H bonds markedly alter the Li-decoration properties in 5 and the average BE of Li atom now increases to 4.17 eV per Li, compared to 3.07 eV in Li 6 &B 40 (3). Li 6 &B 40 H 16 (5) can also adsorb from 6 H 2 , 12 H 2 , 18 H 2 , 24 H 2 , and up to 34 H 2 molecules, resulting in a series of 5-nH 2 complexes (Fig. S3). The optimized structure for Li 6 &B 40 H 16 -34 H 2 (6) is shown in Fig. 7. Note that hydrogen remains in the molecular state with a uniform H-H distance of 0.75 Å in all 5-nH 2 species. For the first 6 H 2 molecules in 5-6 H 2 , the average AE amounts to 0.22 eV/H 2 . The average Li-B and Li-H distances, 2.33 and 1.97 Å, respectively, are almost the same as those in Li 6 &B 40 -6 H 2 (that is, 3-6 H 2 ). With further H 2 adsorption, the average AEs for the first 18 H 2 in 5-nH 2 decrease slightly down to 0.17 eV/H 2 , which are in the ideal thermodynamic range for reversible hydrogen storage 10,11 . The Li 6 &B 40 H 16 (5) complex thus behaves rather similar to Li 6 &B 40 (3) in terms of hydrogen storage properties, except for the B-H passivation in 5. The 18 "core" H 2 in Li 6 &B 40 H 16 -34 H 2 (6) represents a gravimetric density of 6.5 wt%, where an additional 8.6 wt% of dissociated H atoms and loosely physisorbed 16 H 2 are not counted.

On the Possibility of Doubling the H 2 Adsorption Sites: Li-Decorated Triangular B 6 Corners.
To further improve the hydrogen storage capacity of Li-decorated B 40 , we also attempted to place Li atoms on top of the close-packing, triangular B 6 corner sites of the cube-like B 40 cage. As a test case, adsorption of a single H 2 molecule on a corner Li site is optimized (Fig. S4). The BE of Li is 1.87 eV, which is lower than those in Li&B 40 (1) and Li&B 40 (2), but the value still represents a reasonable strength. In fact, it is comparable to the corresponding value for C 60 (1.80 eV) 13 . Moreover, the AE for the first H 2 amounts to 0.28 eV, which is comparable to and even slightly   (5) to fourteen in Li 14 &B 40 (7), owing to the eight triangular B 6 corners (versus six hexagonal/heptagonal holes). The optimized structure of Li 14 &B 40 (7) is shown in Fig. 8. Here, upon Li decoration, the boron structure distorts considerably from the free-standing B 40 borospherene, but the cage motif maintains. The average BE is 2.57 eV/Li. Following the strategy for Li 6 10,11 . For the extreme case of 8, a maximum gravimetric density of 13.8 wt% is obtained. We do not exclude the possibility of further H 2 adsorption onto the 8 complex, albeit those additional H 2 are anticipated to interact rather loosely with the Li sites.

Concluding Remarks
In conclusion, we have carried out a comprehensive density-functional study on the lithium-decoration of B 40 borospherene and the potential utilization of Li-B 40 complexes as a novel nanomaterial for hydrogen storage. We showed that all six heptagonal and hexagonal holes on B 40 surface can be decorated with Li atoms and each Li site is capable of adsorbing up to six or five H 2 molecules. This results in an ultimate Li 6 &B 40 -34 H 2 complex, in which 18 H 2 are bound to Li sites with ideal adsorption energies of 0.11-0.18 eV per H 2 , corresponding to a gravimetric density of 7.1 wt%. The additional 16 H 2 are physisorbed in nature. We further showed that the eight close-packing, triangular B 6 corner sites on the B 40 cage are also readily decorated with Li, which more than double the number of sites for hydrogen storage. The corresponding Li 14 &B 40 -42 H 2 complex can store all 42 H 2 molecules at adsorption energies of 0.12-0.32 eV per H 2 , suggesting a maximum gravimetric density of 13.8 wt%. The Li-B 40 -H 2 complexes as a hydrogen storage material differ markedly from the prior Li-C 60 -H 2 and Ti-B 40 -H 2 systems. The Li-C 60 -H 2 complex 13 adsorbs H 2 rather loosely and is thus not efficient for hydrogen storage, whereas the Ti-B 40 -H 2 complex 40 bounds H 2 too strongly, for which a substantial portion of H 2 stored are not reversible for release. In fact, preliminary attempts also suggest that the structural integrity of B 40 unit is maintained when they are allowed to interact with each other. Considering the presence of chemical bondings between them, we forecast it is possible to construct boron-based nanomaterials for hydrogen storage using lithium-decorated B 40 unit as a building block or connecting the exohedral metalloborospherene with organic linkers. And the hydrogen storage capacity of the boron-based nanomaterials could be better than previously reported carbon-based counterparts.

Methods
All calculations were based on DFT, using a plane-wave basis set with the Projector Augmented Wave (PAW) 48,49 pseudopotential method as implemented in the Vienna ab initio Simulation Package (VASP) 50,51 . Generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) 52 functional was adopted to treat the electron exchange correlation. The GGA-PBE method has been previously utilized to treat Li-decorated fullerenes and heterofullerenes for hydrogen storage 19,53 which is thus a suitable choice for our current system. The dispersion corrected DFT (DFT-D) scheme [54][55][56] was used to describe the van der Waals (vdW) interaction. The supercell approach was used, where the B 40 -based systems were placed at the center of a 25 × 25 × 25 Å 3 vacuum space. And only the Γ point was used to sample the Brillouin zone. The energy cutoff for the plane-wave basis set was set to 500 eV. All structures were fully relaxed until the force acting on each atom was less than 10 −2 eV/Å and a tolerance in total energy was at least 10 −4 eV.
The binding energies (BEs) for the Li-decorated B 40 are defined as E b = −(E Li-B40 −E B40 − mE Li )/m, where E Li-B40 is the total energy of Li-decorated B 40 , E B40 and E Li are the total energies of an isolated B 40 and a Li atom, respectively, and m is the number of Li atoms. Similarly, the average AE for H 2 is defined as E a = − (E Li-B40-nH2 − E Li-B40 − nE H2 )/n and the consecutive AE is defined as Δ E = − (E Li-B40-nH2 − E Li-B40-(n-1)H2 − E H2 ), where E Li-B40-nH2 and E Li-B40-(n-1)H2 are the total energies of n and (n-1) H 2 adsorbed on the Li-decorated B 40 , respectively. E Li-B40 also represents the total energy of Li-decorated B 40 , E H2 is the total energy of isolated H 2 molecule, and n stands for the number of adsorbed H 2 molecules.
We note that for comparison with D 2d B 40 in our previous work (ref. 36), the HOMO-LUMO energy gaps of 1, 2, and 3 were calculated using the Gaussian 09 package 57 , which is usually used for calculations on the isolated molecules. And the corresponding structures were optimized at the PBE0 levels with the 6-311 + G* basis set 58,59 , which has been benchmarked in prior works as a reliable method for boron clusters.