Structures, stabilities and spectral properties of borospherene B44− and metalloborospherenes MB440/− (M = Li, Na, and K)

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations are carried out to study the stabilities, photoelectron, infrared, Raman and electronic absorption spectra of borospherene B44− and metalloborospherenes MB440/− (M = Li, Na, and K). It is found that all atoms can form stable exohedral metalloborospherenes M&B440/−, whereas only Na and K atoms can be stably encapsulated inside B440/− cage. In addition, relative energies of these metalloborospherenes suggest that Na and K atoms favor exohedral configuration. Importantly, doping of metal atom can modify the stabilities of B44 with different structures, which provides a possible route to produce stable boron clusters or metalloborospherenes. The calculated results suggest that B44 tends to get electrons from the doped metal. Metalloborospherenes MB44− are characterized as charge-transfer complexes (M2+B442−), where B44 tends to get two electrons from the extra electron and the doped metal, resulting in similar features with anionic B442−. In addition, doping of metal atom can change the spectral features, such as blueshift or redshift and weakening or strengthening of characteristic peaks, since the extra metal atom can modify the electronic structure. The calculated spectra are readily compared with future spectroscopy measurements and can be used as fingerprints to identify B44− and metalloborospherenes.

the borospherene has aroused interest in all-boron fullerenes and their derivatives such as dynamical behavior of B 40 31 , hydrogen storage capacity of Ti-decorated B 40 32 , experimental and theoretical studies of B 28 − and B 29 − borospherenes 33,34 , structures and electronic properties of metalloborospherenes (Ca@B 40 , Be&B 40 , Sc@B 40 , Li&B 40 , Na@B 40 , Ca@B 39 + , Ca@B 38 , Ca@B 37 − and Li 4 &B 36 ) [35][36][37][38][39][40][41] , and spectral properties of borospherenes 42,43 . Recently, a new borospherene B 44 was reported 44 , relevant theoretical simulations indicated that neutral cage cluster B 44 containing two nonagonal, two hexagonal and two heptagonal holes is the most stable structure among the isomers of B 44 . In addition, energies of first five lowest-lying isomers are close to each other, it is possible to expect that the five isomers may appear in the future experiments. It is necessary to study the structures and spectral characteristics of anionic B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K). The structure search algorithms and DFT combined approaches have been used and the low-lying structures of boron clusters have been reported by many authors 26,[28][29][30]44 . It is not our purpose in this work to carry out an extensive structure search for the global minimum of B 44 − cluster and metalloborospherenes MB 44 0/− (M = Li, Na, and K). Instead, we will collect the B 44 structures from the paper (Chem. Commun., 2016, 52, 1653-1656) and study the structures, stabilities of corresponding anionic B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K). Current works are therefore to provide a theoretical study on the stabilities, photoelectron spectra, infrared, Raman and electronic absorption spectra of B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K). Our works may provide valuable results to assist further experimental identifications on the borospherene B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K), and also may provide theoretical guidance for the applications and synthesis of them in the future.
To obtain the adiabatic detachment energy (ADE) and contrastive analysis, the five lowest-lying neutral isomers of B 44 reported by Tai et al. 44 were re-optimized using the density functional method PBE0 with 6-311 + G* basis set. The five corresponding anionic isomers were optimized using the DFT functionals TPSSh and PBE0 in conjunction with the 6-311 + G* basis set. To obtain more accurate relative energies, single-point electronic energies of the five anionic isomers were subsequently calculated using the coupled-cluster theory UCCSD(T)/3-21 G method at their PBE0/6-311 + G* optimized geometries. All ground-state geometries of the metalloborospherenes MB 44 0/− and frequency calculations were performed based on the density functional method PBE0 with 6-311 + G* basis set. These optimized structures were then used in the calculations of photoelectron spectra and electronic absorption spectra based on the time-dependent DFT formalism 45 at the same level. All computations were carried out using the Gaussian09 software package 46 .

Results and Discussion
Optimized structures of borospherenes B 44 0/− are depicted in Fig. 1. Ground-state parameters are summarized in Table 1. Frequency calculations confirm the stability of B 44 0/− by showing no imaginary frequencies. The relative energy values of neutral B 44 agree well with the results of Tai et al. 44 that isomer IV is the most stable form and isomer I is the third stable form. However, our TPSSh, PBE0 and UCCSD(T) energy values of anionic B 44 − indicate that isomer I is the most stable form of the five isomers. Although the neutral isomer II and isomer III have different structures 44 (isomer II includes two octagonal B 8 , two heptagonal B 7 and two hexagonal B 6 holes, isomer III includes two octagonal B 8 , three heptagonal B 7 and one hexagonal B 6 holes), optimized structures of anionic isomer II and III show that the two isomers have almost the same structure (two octagonal B 8 , two heptagonal B 7 and two hexagonal B 6 holes). It suggests that the two neutral isomers have the similar structures (only have a very small difference). In addition, for the sake of contrastive analysis, we also study the dianion B 44 2− (I and IV), ground-state parameters are summarized in Table S1. The relative energy values of dianion B 44 2− indicate that B 44 2− (I) is more stable than B 44 2− (IV). Interestingly, isomer I is quite similar to cage B 40 and includes two octagonal, four heptagonal and one hexagonal holes, it can be constructed by replacing two opposite heptagonal holes of the borospherene B 40 by two octagonal holes and splitting one hexagonal hole of the B 40 into two neighbouring heptagonal holes. We will focus on the two isomers (I and IV) and corresponding metalloborospherenes MB 44 0/− (M = Li, Na, and K). Optimized structures of metalloborospherenes MB 44 0/− (M = Li, Na, and K) are depicted in Figure S1 (Supplementary Information). Ground-state parameters are summarized in Table 2. Frequency calculations confirm the stability of these endohedral and exohedral metalloborospherenes (except for endohedral Li@B 44 0/− ) by showing no imaginary frequencies. Endohedral Li@B 44 0/− (I) and Li@B 44 0/− (IV) prove to be unstable with imaginary frequencies. The calculated results indicate that Na atoms in Na@B 44 − (I), Na@B 44 (I), Na@B 44 − (IV) and Na@B 44 (IV) are slightly off the molecular center by 0.14, 0.11, 1.28 and 1.18 Å, respectively, along the C 2 molecular axis. In addition, K atoms in K@B 44 − (I), K@B 44 (I), K@B 44 − (IV) and K@B 44 (IV) are slightly off the molecular center by 0.12, 0.11, 0.09 and 0.04 Å, respectively, along the C 2 molecular axis. Energies of these metalloborospherenes MB 44 0/− (M = Na and K) indicate that most endohedral metalloborospherenes M@B 44 0/− (M = Na and K) are less stable than corresponding exohedral metalloborospherenes M&B 44 0/− (M = Na and K), respectively, whereas only the exohedral Na&B 44 − (IV) is less stable than endohedral Na@B 44 − (IV). The results reveal that Li, Na and K atoms favor the exohedral configuration. It's worth noting that the energy differences between the endohedral metalloborospherenes M@B 44 0/− (M = Na, K) and corresponding exohedral metalloborospherenes M&B 44 0/− (M = Na, K) are small. Interestingly and encouragingly, although B 44 (I) is less stable than B 44 (IV), Table 2 shows that Li&B 44 (IV), Na&B 44 (IV), Na@B 44 (IV), K&B 44 (IV) and K@B 44 (IV) are less stable than corresponding Li&B 44 (I), Na&B 44 (I), Na@B 44 (I), K&B 44 (I) and K@B 44 (I), respectively, the addition of metal atom enhances the stability of isomer I compared with isomer IV. The results may provide a possible route (doping of metal atoms) to produce stable borospherenes or metalloborospherenes which have good properties and potential applications.
Photoelectron spectroscopy is powerful experimental technique to probe the electronic structure of cluster. It can be viewed as an electronic fingerprint for the underlying cluster. Photoelectron spectroscopy in combination with theoretical calculations has been used to understand and identify the structures of size-selected Scientific RepoRts | 7:40081 | DOI: 10.1038/srep40081 boron clusters 29,30 . To facilitate future identifications of B 44 − , the ADEs for B 44 − and metalloborospherenes MB 44 − (M = Li, Na, and K) were calculated at the PBE0 level, then we calculated the vertical detachment energies (VDEs) and simulated the photoelectron spectra for B 44 − and metalloborospherenes MB 44 − (M = Li, Na, and K), using the time-dependent DFT (TD-DFT) method 29,30,45 . Adiabatic detachment energy of B 44 − represents the electron affinity (EA) of corresponding neutral B 44 . The larger EA can lead to the stronger probability of capturing an electron, i.e., the neutral B 44 with larger EA is easier to capture an electron. The five isomers give the ground-state ADEs of 3.23(I), 3.02(II), 3.02(III), 2.78(IV) and 2.99(V) eV, respectively. Among the five isomers of B 44 − , isomer I has the largest ADE (3.23 eV), which is larger than the ADE (2.29 eV) 29 of cage B 40 − and less than the ADE (3.51 eV) 29  . Photoelectron spectra of five isomers are given in Fig. 2. The predicted photoelectron spectra show that isomer IV has the lowest first vertical detachment energy (VDE) and the largest energy gap (about 0.73 eV) between the first and second bands. The first several bands of photoelectron spectra were used to identify boron clusters 29,30 , so we will focus on the bands at the low binding energy side. The first peaks of five isomers come from the calculated ground-state VDEs at 3.34(I), 3.19(II), 3.19(III), 2.95(IV) and 3.38(V) eV, respectively. The calculated ground-state VDE of each isomer originates from the detachment of the electron from the singly occupied molecular orbital (α-SOMO). The second peaks of the five isomers come from the second calculated VDEs at 3.48(I), 3.56(II), 3.56(III), 3.68(IV) and 3.72(V) eV, respectively. The second calculated VDEs of five isomers originate from detaching the electron from β -HOMO-1 resulting in the first triplet state. Figure 2(b,c) indicate that isomer II and isomer III have the same photoelectron spectrum, which confirms that the two isomers have almost the same structure.

I) is set to be zero), energy gaps (E g ), dipole moments (μ) and states of borospherenes B 44
0/− optimized at PBE0/6-311 + G* level. The superscripts a and b denote the alpha electron and beta electron, respectively. The superscripts c and d denote the energies (E) of B 44 − at TPSSh/6-311 + G* and UCCSD(T)/3-21 G//PBE0/6-311 + G* levels. The square bracket and round bracket denote the relative energies of B 44 − at TPSSh/6-311 + G* and UCCSD(T)/3-21 G//PBE0/6-311 + G* levels.      Predicted spectral peaks distribute in three regions: low frequency region (from 0 to 600 cm −1 ), middle frequency region (from 600 to 1000 cm −1 ) and high frequency region (from 1000 to 1600 cm −1 ). These vibrational modes within high frequency region are closely related to molecular structure. This suggests that molecular with slightly difference can lead to the subtle differences of infrared absorption in this region, namely, the infrared spectra of molecular show the characteristics of molecular, like fingerprints, known as fingerprint region.
Infrared spectra of borospherenes B 44 0/− are given in Fig. 4. Figure 4(a) presents the infrared spectrum of B 44 (I), the sharpest peak occurs at 1295 cm −1 . In addition, at 143 and 262 cm −1 , the characteristic peaks are strong, which is different from other isomers. The two strong peaks are produced by bending vibration of boron atoms and they belong to the far-infrared region. It's worth noting that infrared spectrum of B 44 (I) is somewhat similar to that of borospherene B 40 except for the two peaks at 143 and 262 cm −1 . Figure 4(b) presents the infrared spectrum of B 44 − (I), the sharpest peak occurs at 1271 cm −1 . The computed IR spectra of B 44 0/− (I) indicate that there are some IR inactive modes and only a few of IR active modes have strong absorption. As shown in Fig. 4(a,b), the addition of an electron does not change the symmetry, but leads to an other strong peaks (at 1217 cm −1 ) in the high frequency region and redshifts the three main peaks from 1295, 262 and 143 cm −1 for B 44 Figure 4(d,f) show that B 44 − (II) and B 44 − (III) have almost the same infrared spectrum, however, Fig. 4(c,e) show that B 44 (II) and B 44 (III) have the similar infrared spectra, which further indicates that the two neutral isomers have the similar structures, instead of same structure. The B 44 (IV) has two strong characteristic peaks at 1262 and 1301 cm −1 , whereas the addition of an electron weakens the two strong vibrational modes and leads to another strong characteristic peak at 1287 cm −1 . These features can be used to distinguish the B 44 (IV) and B 44 − (IV). Figure 4(a,b,g,h) show      (IV). It suggests that B 44 (IV) tends to get one electron from the doped metal. The predicted infrared spectra also provide some information for the identification of B 44 − and metalloborospherenes MB 44 − (M = Li, Na, and K), these different characteristic peaks provide a theoretical basis for the identification and confirmation of B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K). Figure 6 depicts the Raman spectra of B 44 0/− . Figure 6(a) depicts the Raman spectrum of B 44 (I), the sharpest peak occurs at 1312 cm −1 . Among the Raman active modes, the vibration at 144 cm −1 belongs to typical radial breathing mode, which is similar to the typical radial breathing mode of B 40 47 at 170 cm −1 . The breathing modes are used to identify the hollow structures in nanotubes. Figure 6(b) depicts the Raman spectrum of B 44 − (I), the sharpest peak occurs at 1307 cm −1 . Similar to B 44 (I), the vibration at 139 cm −1 belongs to typical radial breathing mode, which is similar to the typical radial breathing mode of B 40 − 43 at 176 cm −1 . Figure 6 Figure 6(d,f) show that B 44 − (II) and B 44 − (III) have almost the same Raman spectrum, however, Fig. 6(c,e) show that B 44 (II) and B 44 (III) have the similar Raman spectra. It further indicates that the two neutral isomers have the similar structures and the two anionic isomers have almost the same structure. Figure 6 indicates that the addition of an electron leads to the redshift of sharpest peak for each isomer. In addition, the calculated results indicate that all vibrational modes of B   Figure 7(a,c,g) show that exohedral M&B 44 (I, M = Li, Na, and K) have almost the same Raman spectrum, and Fig. 7(b,d,h) show that exohedral M&B 44 − (I, M = Li, Na, and K) have almost the same Raman spectrum. Interestingly, the addition of an electron blueshifts the first two strong peaks and reverses the intensity of first two strong peaks. Figure 7(e,i) show that endohedral Na@B 44 (I) and K@B 44 (I) have the similar Raman spectra, and Fig. 7(f,j) show that endohedral Na@B 44 − (I) and K@B 44 − (I) have the similar Raman spectra. Figure 7(e,f, i,j) show that the addition of an electron weakens some strong characteristic peaks.  spectra of each borospherene or metalloborospherene, we can find, at some frequencies, infrared absorption peaks are strong, but the Raman peaks are very weak. However, at some frequencies, the relation is just opposite.
In addition, at some frequencies, both the infrared and Raman peaks are strong. A vibrational mode of molecular with no change of dipole moment is infrared inactive, we can't obtain the normal mode frequency from the infrared spectral data in experiments. However, this vibrational mode may lead to the change of polarizability, this indicates that the vibrational mode is Raman active. The calculated Raman spectra can be useful for analytical purposes and contribute significantly to spectral interpretation and vibrational assignments, also can provide technical guidance for future synthesis. Finally, we calculated electronic absorption spectra of B 44 and metalloborospherenes MB 44 − (M = Li, Na, K) with closed-shell electronic structure, as shown in Fig. 8. Figure 8 Tables 1-2). It's worth noting that the electronic absorption spectra of exohedral M&B 44 − (I, M = Li, Na, and K) and endohedral M@B 44 − (I, M = Na, and K) are similar to that of dianion B 44 2− (I) ( Figure S4). Similarly, the electronic absorption spectra of exohedral M&B 44 − (IV, M = Li, Na, and K) and endohedral M@B 44 − (IV, M = Na, and K) are similar to that of dianion B 44 2− (IV) ( Figure S4). It further suggests that B 44 (I, IV) tend to get two electrons from the extra electron and the doped metal, respectively. The electronic absorption spectra may be used for the structural analysis in conjunction with other techniques. In addition, UV-Vis spectroscopy can be used to distinguish isomers, such as the five isomers of B 44 with obvious different absorption peaks.
In a summary, the structures, stabilities, photoelectron spectra, infrared spectra, Raman spectra, and electronic absorption spectra of B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K) were studied at the level of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) with 6-311 + G* basis set. The calculated results suggest that Li, Na and K atoms can form stable exohedral M&B 44 0/− (M = Li, Na, and K), whereas only Na and K atoms can be stably encapsulated inside the B 44 0/− cage. In addition, relative energies of these metalloborospherenes reveal that the Na and K atoms favor the exohedral configuration. More importantly, the addition of metal atom can modify the stability of B 44 with different structures, which provides a possible route (doping of metal atoms) to produce stable boron clusters or metalloborospherenes. The calculated results suggest that B 44 tends to get electrons from the doped metal. Metalloborospherenes MB 44 − are characterized as charge-transfer complexes (M 2+ B 44 2− ), where B 44 tends to get two electrons from the extra electron and the doped metal, resulting in similar features with anionic B 44 2− . The calculated results show that B 44 − and metalloborospherenes MB 44 0/− (M = Li, Na, and K) have different and meaningful spectral features, insight into the spectral properties is important to understand them and find their potential applications. In addition, the calculated electronic absorption spectra indicate that B 44 and metalloborospherenes MB 44 − (M = Li, Na, and K) have obvious near-IR absorption peaks. These spectral features can be used as fingerprints to identify and distinguish the borospherenes B 44 0/− and metalloborospherenes MB 44 0/− (M = Li, Na, and K). The all-boron fullerenes and metalloborospherenes have provided an important clue for the development of new boron-based materials. In view of the remarkable structures and properties, it is possible that borospherenes and metalloborospherenes have potential applications in energy, environment, optoelectronic materials and pharmaceutical chemistry.