Comparative study on the spectral properties of boron clusters Bn0/−1(n = 38–40)

The all-boron fullerenes B40−1 and B39−1 discovered in recent experiments are characterized and revealed using photoelectron spectroscopy. Except for the photoelectron spectroscopy, one may identify such boron clusters with other spectroscopic techniques, such as infrared spectra and Raman spectra. Insight into the spectral properties of boron clusters is important to understand the boron clusters and find their potential applications. In this work, density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations are carried out to comparatively study the vibrational frequencies, infrared spectra, Raman spectra and electronic absorption spectra of boron clusters Bn0/−1(n = 38–40). The numerical simulations show that such boron clusters have different and meaningful spectral features. These spectral features are readily compared with future spectroscopy measurements and can be used as fingerprints to distinguish the boron clusters Bn0/−1 with different structures (cage structure or quasi-planar structure) and with different sizes (n = 38–40).

Scientific RepoRts | 6:25020 | DOI: 10.1038/srep25020 M&B 40 (M = Na, Be, Mg) [27][28][29] and optical spectra of neutral B 40 clusters 30 . As the discovery of C 60 , the observation of the all-boron fullerene will lead to a new beginning for the study of boron fullerenes, both experiment and theory, which may lead to new boron-based nanomaterials.
Optical properties of nanoclusters have dependency on size and structure 31 , due to the quantum confinement effect, size and structure of materials can influence the energy gap between highest occupied orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). It is necessary to study the spectral characteristics of medium-sized boron clusters, especially the boron fullerenes, current work is therefore to provide a comparative theoretical study on the infrared, Raman and electronic absorption spectra of boron clusters B n 0/−1 (n = 38-40) based on the DFT method and TD-DFT method. Although the spectra of neutral B 40 were reported 30 , we are unaware of such a study on other boron clusters, especially a detailed theoretical study. Our current study can provide valuable results to assist further experimental measurements on these boron clusters and derivatives, and also may provide theoretical guidance for the application of these boron clusters in the future.
All ground-state geometries and frequency calculations of these boron clusters are performed based on the density functional method PBE0 with 6-311 + G * basis set. These optimized structures are used in the calculations of electronic absorption spectra based on the time-dependent DFT formalism at the same level. The method used in our work has been used in previous papers 23,24,32 , it is reliable for boron clusters. In the previous papers, ground state geometries and relevant calculations of B n 0/−1 (n = 38-40) were performed using different methods with different basis sets. The initial structures of B n 0/−1 (n = 38-40) in our work are derived from the corresponding papers 21,23,24 . Although ground state geometries of the B 40 and B 39 −1 were optimized using density functional method PBE0 with the basis set 6-311 + G*, to obtain the relative comparison, all ground state geometries of B n 0/−1 (n = 38-40) are also re-optimized using the same method. All computations are carried out with the Gaussian09 software package 33 .

Results and Discussion
Optimized structures of boron clusters B n 0/−1 (n = 38-40) are depicted in Fig. S1 (Supplementary Information). Both B 40 and B 40 −1 cages contain two hexagonal and four heptagonal rings, B 38 and B 38 −1 cages contain four hexagonal rings. Cage clusters B 39 0/−1 with C 3 structure contain three hexagonal and three heptagonal rings, however, cage clusters B 39 0/−1 with C 2 structure contain two hexagonal and four heptagonal rings. Ground state parameters are summarized in Table 1, which are consistent with the previous literature 21, 23,24 . As given in Table 1, B 40 cage has the largest HOMO-LUMO energy gap of 3.13 eV among all boron clusters predicted here and it is larger than 3.01 eV of C 60 . In general, HOMO-LUMO energy gap reflects the ability for an electron to jump from the occupied orbital to the unoccupied orbital, which represents the intensity of chemical activity. A large HOMO-LUMO gap generally corresponds to a closed-shell electronic configuration with high stability. For the cage clusters with closed-shell electronic structure, B 40 has the largest energy gap, which indicates that its chemical activity is lowest. It is noticeable that energy gaps reduce from 3.13 eV of B 40 cage to 2.23 eV of B 38 cage, which verifies that the size of cage cluster has a great influence on the HOMO-LUMO energy gap. In addition, dipole moments of cage cluster B 38 0/−1 and B 40 0/−1 are zero among all the boron clusters because of the highly symmetric structures (D 2h and D 2d ), this indicates that they do not render far-infrared pure rotation spectrum.
Normal mode frequencies, infrared intensities and Raman activities of B n 0/−1 (n = 38-40) are calculated and depicted in Infrared spectra of boron clusters B n 0/−1 (n = 38-40) are given in Fig. 1, these infrared spectra peaks distribute in three regions: low frequency region (from 40 cm −1 to 600 cm −1 ), middle frequency region(from 600 cm −1 to 1000 cm −1 ) and high frequency region (from 1000 cm −1 to 1400 cm −1 ), the main characteristic peaks are located in the middle and high frequency regions (from 600 cm −1 to 1400 cm −1 ). Vibrational modes of these main peaks contain the stretching and bending vibration of boron atoms. These vibrational modes within the middle and high frequency regions are closely related to the molecular structure. This suggests that molecular with slightly difference can lead to the subtle differences of infrared absorption in these regions, namely, the infrared spectra of molecular show the characteristics of molecular, like fingerprints, known as the fingerprint region. Figure 1(a) presents the infrared spectra of B 40 cage, the major peaks appear at 382, 616, 712, 794, 822, 1103, 1153, 1252, 1264, 1274 and 1313 cm −1 . The sharpest peak occurs at 1274 cm −1 , this vibrational mode is doubly degenerate vibrational mode and formed by stretching vibration of boron atoms mainly located in the hexagonal rings. Figure 1(b) presents the infrared spectra of B 40 −1 cage, the main peaks appear at 289, 392, 402, 622, 662, 799, 1096, 1176, 1252 and 1287 cm −1 . The sharpest peak occurs at 1287 cm −1 , this vibrational mode is doubly degenerate and Raman active mode. Unlike the neutral B 40 cage, this vibrational mode is formed by stretching vibration of boron atoms mainly located in the heptagonal rings. As shown in Fig. 1(a,b) and Table 1, the addition of an   0  200  400  600  800  1000 1200 1400 electron does not change the symmetry and dipole moment, but lead to two other strong peaks (at 1096 cm −1 and 1176 cm −1 ) in the high frequency region and two other strong peaks (at 289 cm −1 and 662 cm −1 ), which will be useful to identify the anionic B 40 −1 cage and neutral B 40 cage. The infrared spectra of the B 40 −1 cage are quite similar to endohedral derivative Na@B 40 and exohedral derivatives Na&B 40 29 , the metal dopant Na in the B 40 cage changes the IR absorption peaks of B 40 , enhancing some peaks. As the analysis of M@B 40 (M = Ca, Sr) and M&B 40 (M = Be, Mg) 27 , metalloborospherenes (Na@B 40 and Na&B 40 ) are characterized as charge-transfer complexes (M + B 40 − ), where an metal atom donates one electron to the B 40 cage, resulting in similar features with anionic B 40 −1 . This indicates that the addition of an electron plays an important role in vibrational modes and infrared intensities. This also means that infrared spectra of anionic clusters B n −1 (n = 38-40) have the potential for the comparative analysis of metal-doped derivatives (M 1+ B n 1− ) in future experimental and theoretical researchs. In addition, at 289 cm −1 , the characteristic peak of B 40 −1 is strong, which is different from all other boron clusters. This strong peak is produced by bending vibration of boron atoms and it belongs to the far-infrared spectrum. Figure 1(c) presents the infrared spectra of quasi-planar B 40 , the main peaks appear at 396, 449, 781, 823, 870, 917, 1006, 1046, 1064, 1140, 1176, and 1289 cm −1 . The characteristic peaks of quasi-planar B 40 are consistent with the previous literature 30, 32 . The sharpest peak occurs at 1289 cm −1 , this vibrational mode is Raman active mode and formed by stretching vibration of boron atoms mainly located in the edge of the quasi-planar molecular.  Figure 1(e,f) show that three strong peaks with similar characteristics are located in high frequency region, but the addition of an electron shifts the three peaks from 1228, 1189 and 1130 cm −1 for B 38 to 1218, 1174, and 1098 cm −1 for B 38 −1 , respectively. In addition, the vibrational mode at 1015 cm −1 is strong in D 2h B 38 , but D 2h B 38 −1 dose not exhibit vibrational mode, the situation at 806 cm −1 is just the opposite. Figure 1(g) presents the infrared spectra of the quasi-planar B 38 , the main peaks appear at 705, 784, 873, 988, 1105, 1137, 1153, 1162, 1166 and 1350 cm −1 . The sharpest peak occurs at 1350 cm −1 , this vibrational mode is Raman active mode and formed by stretching vibration of boron atoms mainly located in the edge of the quasi-planar molecular. Figure 1(h) presents the infrared spectra of the quasi-planar B 38 −1 , the main peaks appear at 688, 851, 867, 900, 1002, 1013, 1120, 1192, 1304, and 1336 cm −1 . The sharpest peak occurs at 1120 cm −1 . The quasi-planar B 38 −1 has three strong characteristic peaks at 1120, 1002 and 867 cm −1 , other peaks are relatively weak. However, the main peaks of quasi-planar B 38 show the nearly same intensities. The addition of an electron weakens some strong vibrational modes and leads to three strong characteristic peaks. Figure 1(i,j) indicate that the two enantiomers C 3 B 39 −1 have the same infrared spectra, the main peaks appear at 382, 536, 586, 726, 837, 985, 1232, 1237, 1241, 1256, 1261 and 1309 cm −1 . The sharpest peak occurs at 1261 cm −1 , this vibrational mode is formed by stretching vibration of boron atoms. Figure 1(k,l) indicate that the two enantiomers C 3 B 39 also have the same infrared spectra, the main peaks appear at 346, 586, 730, 773, 1107, 1126, 1216, 1236, 1241 and 1265 cm −1 , and sharpest peak occurs at 1265 cm −1 . It's worth noting that neutral B 39 cage and anionic B 39 −1 cage with C 3 symmetry can be identified through the characteristic peaks at 1107 cm −1 , 1126 cm −1 , and 1309 cm −1 . Figure 1(m,n) show that the two enantiomers C 2 B 39 −1 have the almost same infrared spectra. The sharpest peak occurs at 1353 cm −1 for C 2 (1) B 39 −1 and 1352 cm −1 for C 2 (2) B 39 −1 , the two vibrational modes are formed by stretching vibration of a boron atom located in the adjacent heptagonal rings. Figure 1(o,p) show that the two enantiomers C 2 B 39 have the same infrared spectra, the sharpest peak occurs at 1264 cm −1 . It's worth noting that neutral B 39 cage and anionic B 39 −1 cage with C 2 symmetry can be identified through the characteristic peaks at 1311 cm −1 and 1352 cm −1 . Figure 1(i-p) show that the main characteristic peaks of B 39 0/−1 distribute in high-frequency region (from 1000 to 1400 cm −1 ), and other peaks are relatively weak. The addition of an electron enhance or weaken these characteristic peaks, lead to significative infrared spectra, such notable differences in infrared spectra of B 39 0/−1 can be used as the fingerprint of their existence. As mentioned before, the sharpest peak of each boron cluster is formed by stretching vibration of boron atoms. One can also observe that the main strong peaks of these boron clusters almost in the mid-infrared region. Except for the relatively strong main peaks mentioned here, these boron clusters have many different relatively weak characteristic peaks. The predicted infrared spectra in Fig. 1 show that boron clusters have different spectral features and characteristic peaks, the predicted infrared spectra provide some information in the future experimental characterization. If the infrared spectra of boron clusters are obtained in experiments, these different characteristic peaks can be used as a basis for the identification of these boron clusters. Due to the wide wavelength range of spectrograph means low wavelength resolution, the predicted frequency regions provide a theoretical basis for the selection of the spectrograph in the future experiments. As mentioned before, the main characteristic peaks are located in high frequency region (from 800 cm −1 to 1400 cm −1 ), especially, the characteristic peaks of B 39 0/−1 are located in high frequency (from 1000 cm −1 to 1400 cm −1 ). This indicates that we should concentrate on the high frequency region in experiments to identify these boron clusters and the wavelength range of spectrograph can be further reduced, it will improve the spectral measurement precision. The vibrational modes with lower intensity is difficult to be obtained in experiments, the calculated results may provide an effective data in the vibrational frequency analysis. The calculated results may be used for the analysis of one component of a mixture (for example, boron isomers) combined with other spectral analysis technology.
Scientific RepoRts | 6:25020 | DOI: 10.1038/srep25020   Table 1, the dipole moments of cage clusters B 38 0/−1 and B 40 0/−1 are zero and these clusters are highly symmetric structures, which may lead to the infrared inactive and Raman inactive vibrational modes. The calculated results indicate that all vibrational modes of quasi-planar B 38 0/−1 and B 40 0/−1 are infrared active and Raman active. Figure 3 depicts the Raman spectra of B 39 An interesting phenomenon is that the Raman spectra of B 39 0/−1 with C 3 symmetry are far stronger than that of B 39 0/−1 with C 2 symmetry. Figure 3(a,b) present the Raman spectra of the axially chiral B 39 −1 with C 3 symmetry, unlike the infrared spectra of axially chiral C 3 B 39 −1 , the two enantiomers have the different Raman spectra features. Figure 3(a) presents the Raman spectra of the C 3 (1) B 39 −1 , the main peaks appear at 231, 280, 307, 431, 526, 625, 726, 773, 813, 865, 985, 1137, 1256 and 1309 cm −1 . The sharpest peak occurs at 773 cm −1 , this vibrational mode is located in the middle frequency region. Figure 3 Figure 3(c,d) indicate that the axially chiral B 39 cages with C 3 symmetry have the similar Raman spectra instead of same Raman spectra. The sharpest peak occurs at 1126 cm −1 for C 3 (1) B 39 and 1140 cm −1 for C 3 (2) B 39 . Among the Raman active modes of C 3 B 39 , the vibration at 446 cm −1 belongs to typical radial breathing mode. Figure 3(e,f) depict the Raman spectra of the axially chiral C 2 B 39 −1 . Like the infrared spectra of C 2 B 39 −1 , the two enantiomers have the almost same Raman spectra. The sharpest peak occurs at 1320 cm −1 . Among the Raman active modes, the vibrations at 459 cm −1 for C 2 (1) B 39 −1 and 456 cm −1 for C 2 (2) B 39 −1 can be viewed as breathing mode. Figure 3(g,h) indicate that the two enantiomers C 2 B 39 have the almost same Raman spectra, the sharpest peak occurs at 1117 cm −1 . Among the Raman active modes, the vibrations at 446 cm −1 for C 2 35 : for small fullerenes, its vibrational frequency is relatively large, for larger fullerenes, its value is small. Dependence of frequency of radial breathing mode on the number of atoms in a fullerene is very interesting finding, which can be compared in nature to very well-known relationship between the diameter of a carbon nanotube and the location of its breathing mode in Raman spectra. As the discovery of carbon nanotube, Raman spectra of cage boron clusters can be useful for the analysis of boron nanotube in future studies.
The predicted Raman spectra in Figs 2 and 3 provide some information for future experimental characterization. Raman spectra, as the supplement of infrared spectra, can also be used for the basis of identification of boron clusters. From the infrared and Raman spectra of each boron cluster, we can find, at some frequencies, the boron cluster has strong infrared absorption, but the Raman peaks is very weak (or Raman inactive). However, at some frequencies, the relation is just the 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 experiment measurement.
To provide some information for future experimental characterization, we have calculated electronic absorption spectra (the first 36 exited states) of boron clusters B n 0/−1 (n = 38-40) with closed-shell electronic structure, as shown in Fig. 4. Figure 4(a) presents the electronic absorption spectra of D 2d B 40 , the strongest absorption peak occurs at 397 nm and the largest excitation wavelength is 535 nm. Figure 4(b) presents the electronic absorption spectra of quasi-planar B 40 , the strongest absorption peak occurs at 433 nm and the largest excitation wavelength is 1215 nm. Figure 4(a,b) indicate that electronic absorption spectra of quasi-planar B 40 are apparently red-shifted comparing with B 40 cage. Figure 4(c) presents the electronic absorption spectra of the C 3 B 39 −1 . The computed results show that the two enantiomers have the same electronic absorption spectra. The strongest absorption peak occurs at 476 nm and the largest excitation wavelength is 618 nm. Figure 4(d) presents the electronic absorption spectra of the C 2 B 39 −1 , the two enantiomers also have the same electronic absorption spectra. The strongest absorption peak occurs at 399 nm and the largest excitation wavelength is 666 nm. Figure 4(e) presents the electronic absorption spectra of the D 2h B 38 cage. The strongest absorption peak occurs at 437 nm amd the largest excitation wavelength is 949 nm. Note that the oscillator strength of this largest excitation wavelength is zero, and  Scientific RepoRts | 6:25020 | DOI: 10.1038/srep25020 the largest excitation wavelength (with nonzero oscillator strength) is 812 nm. Figure 4(f) presents the electronic absorption spectra of the quasi-planar B 38 . The strongest absorption peak occurs at 434 nm and the largest excitation wavelength is 2588 nm. Similar to B 40 , Fig. 4(e,f) indicate that electronic absorption spectra of quasi-planar B 38 are apparently red-shifted comparing with B 38 cage. Figure 4 indicates that the largest excitation wavelengths of B 40 (C s ) and B 38 are in the near infrared region. One can observe several near infrared (NIR) absorption peaks of the quasi-planar B 40 and B 38 . The B 40 (D 2d ) and B 39 −1 have only UV-vis spectra. 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 quasi-planar and cage-like B 40 with obvious different absorption peaks. The minimum excitation energy (the largest excitation wavelength) mainly comes from the electron transition from HOMO to LUMO. HOMO-LUMO energy gap reflects the probability of the molecules jumping from ground state to excited state. Generally speaking, the larger energy gap can lead to the larger electron excitation energy, i.e., the smaller the probability of electronic transition. On the contrary, the molecule with smaller energy gap is easier to jump to the excited state. According to the previous results, the HOMO-LUMO energy gaps are 3.13, 2.89, 2.73, 2.3, 1.82, 1.33 eV for B 40 (D 2d ), B 39 −1 (C 3 ), B 39 −1 (C 2 ), B 38 (D 2h ), B 40 (C s ), B 38 (C 1 ), respectively. Although the energy gap of ground state does not represent the minimum excitation energy, the decreasing HOMO-LUMO energy gaps just reflect the increasing largest excitation wavelength 535 nm , 618 nm, 666 nm, 949 nm, 1215 nm, and 2588 nm for B 40 (D 2d ), B 39 −1 (C 3 ), B 39 −1 (C 2 ), B 38 (D 2h ), B 40 (C s ), and B 38 (C 1 ), respectively. The new discovery of all-boron fullerene has provided an important clue for the development of new boron-based materials. In view of the remarkable structure and property, it is possible to have a potential application in energy, environment, optoelectronic materials and pharmaceutical chemistry. Here the infrared spectra, Raman spectra, and electronic absorption spectra of boron clusters B n 0/−1 (n = 38-40) were simulated at the level of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) with 6-311 + G* basis set, these spectra display a large variety of shapes and patterns. Comparative calculations show that size, symmetry, and charge state strongly affect the infrared and Raman spectra, which suggests that infrared and Raman spectra may play a key role in identifying these boron clusters. In addition, the calculated electronic absorption spectra indicate that quasi-planar boron clusters have obvious near-IR absorption peaks. These spectral features provide a theoretical basis in the future experimental measurements and confirmations. Our calculated results also provide much insight into the new doped boron clusters (such as MB n (M = Li, Na, K, Rb, n = 38-40)) and boron nanotubes.