Sea-shell-like B₃₁⁺ and B₃₂: two new axially chiral members of the borospherene family

Abstract

Since the discovery of the cage-like borospherenes D_2d B₄₀^−/0 and the first axially chiral borospherenes C₃/C₂ B₃₉⁻, a series of fullerene-like boron clusters in different charge states have been reported in theory. Based on extensive global minimum searches and first-principles theory calculations, we present herein two new axially chiral members C₂ B₃₁⁺ (I) and C₂ B₃₂ (VI) to the borospherene family. B₃₁⁺ (I) features two equivalent heptagons on the top and one octagon at the bottom on the cage surface, while B₃₂ (VI) possesses two equivalent heptagons on top and two equivalent heptagons at the bottom. Detailed bonding analyses show that both sea-shell-like B₃₁⁺ (I) and B₃₂ (VI) follow the universal σ + π double delocalization bonding pattern of the borospherene family, with ten delocalized π bonds over a σ skeleton, rendering spherical aromaticity to the systems. Extensive molecular dynamics simulations show that these novel borospherenes are kinetically stable below 1000 K. The IR, Raman, and UV-vis spectra of B₃₁⁺ (I) and B₃₂ (VI) are computationally simulated to facilitate their future experimental characterizations.

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1. Introduction

As the lighter neighbour of carbon in the periodic table, boron is a typical electron-deficient element which shares with carbon the rare ability to form stable covalently bonded molecular frameworks with multicentre–two-electron bonds (mc–2e bonds) in both polyhedral molecules and bulk allotropes.^1,2 Persistent joint photoelectron spectroscopy (PES) experimental and first-principles theory investigations by Lai-Sheng Wang and co-workers in the past two decades on size-selected negatively-charged boron clusters B_n⁻ (n = 3–42) have revealed a rich landscape for boron nanoclusters from planar or quasi-planar (2D) structures (n = 3–38, 41, and 42) to cage-like borospherenes (n = 39, 40).^3–8 The first all-boron fullerenes D_2d B₄₀^−/0, dubbed borospherenes, were discovered in 2014, marking the onset of borospherene chemistry.⁵ The spherically aromatic borospherene D_2d B₄₀ is found to be composed of twelve interwoven boron double chains with two hexagons at the top and bottom and four heptagons on the waist. It features a unique bonding pattern of σ + π double delocalization, with twelve delocalized π bonds spherically distributed over a σ skeleton. The axially chiral B₃₉⁻ appears to be the only boron cluster monoanion observed in experiments to date which has a cage-like global minimum (GM).⁴ The spherically aromatic borospherene family has been expanded by our group at first-principles theory level to the cage-like B_n^q series (n = 36–42, q = n − 40) in different charge states which are all composed of twelve interwoven double chains with a σ + π double delocalization bonding pattern.^4,5,9–12 Two lowest-lying cage-like C_s B₃₉⁺ isomers in the same bonding pattern were also predicted in theory.¹³ Sea-shell-like C₂ B₂₈^−/0 and C_s B₂₉⁻ with nine delocalized π bonds over a σ-skeleton were later observed as minor isomers in PES experiments.^14,15 Following the same structural motif, our group predicted the possibility of sea-shell-like C_s B₂₉⁺, B₃₄, and B₃₅⁺ at first-principles theory levels^16,17 which also appear to follow the σ + π double delocalization bonding pattern of the borospherene family. Ion mobility measurements in combination with density-functional theory (DFT) calculations, on the other hand, indicate that B_n⁺ monocations possess double-ring tubular structures in the size-range between n = 16–25, showing another important structural domain for boron.¹⁸ However, the geometrical and electronic structures of B_n⁺ monocations in the size range between n = 30–38 has remained unknown to date, except the sea-shell-like B₃₅⁺ previously predicted by our group.¹⁷

In this work, we perform a theoretical investigation on the structures and bonding patterns of B₃₁⁺ and B₃₂ via extensive global minimum searches and first-principles theory calculations. Sea-shell-like C₂ B₃₁⁺ (I) and C₂ B₃₂ (VI) are found to be the well-defined GMs of B₃₁⁺ and B₃₂, respectively, presenting two new axially chiral members to the borospherene family. Both B₃₁⁺ (I) and C₂ B₃₂ (VI) appear to follow the universal σ + π double delocalization bonding pattern of the borospherene family, with ten delocalized π bonds over a σ skeleton, rendering spherical aromaticity to these novel borospherenes.

2. Theoretical procedure

Extensive GM searches were performed on B₃₁⁺ and B₃₂ using the TGmin program,^19–21 in conjunction with manual structural constructions based on the previously reported low-lying isomers of B₃₁^−/0 and B₃₂^−/0.²² About 5500 and 4500 trial points were generated on the potential energy surface for B₃₁⁺ and B₃₂ at the PBE/TZP level of theory. Frozen core approximation was used for the inner shells of [1s²] for B. The low-lying isomers for B₃₁⁺ and B₃₂ were then fully optimized at PBE0 and TPSSh levels^23,24 with the 6-311+G(d) basis set,²⁵ with vibrational frequencies checked to make sure all the low-lying isomers obtained were true minima. All these calculations were implemented using the Gaussian 16 program.²⁶ To obtain more accurate relative energies, the top five lowest-lying isomers of B₃₁⁺ and B₃₂ were further refined at the single-point CCSD(T)/6-311G(d) level^27,28 at their PBE0/6-311+G(d) geometries with the zero-point energy (ZPE) corrections included at PBE0. The obtained GMs C₂ B₃₁⁺ (I) and C₂ B₃₂ (VI) and their degenerated enantiomers C₂ B₃₁⁺ (I′) and C₂ B₃₂ (VI′) are shown in Fig. 1 and more low-lying isomers are listed in Fig. S1 (ESI).† Chemical bonding analyses on B₃₁⁺ (I) and B₃₂ (VI) (Fig. 1) were conducted using the Adaptive Natural Density Partitioning (AdNDP) method^29,30 at the PBE0/6-31G level. Nucleus-independent chemical shifts (NICS)^31,32 were calculated at the cage centres to assess the spherical aromaticity of B₃₁⁺ (I) and B₃₂ (VI). The IR and Raman spectra of B₃₁⁺ (I) and B₃₂ (VI) were simulated at PBE0/6-311+G(d) level and UV-vis absorption spectra calculated using the time-dependent DFT approach (TD-PBE0)^33,34 implemented in Gaussian 16. Extensive Born–Oppenheimer molecular dynamics (BOMD) simulations were performed for B₃₁⁺ (I) and B₃₂ (VI) at 500 K, 700 K, and 1000 K for 30 ps (Fig. S2, ESI†) using the CP2K software,³⁵ with the GTH-PBE pseudopotential and the DZVP-MOLOPT-SR-GTH basis set adopted.

Fig. 1 Optimized global minimum structures of the axially chiral borospherenes (a) C₂ B₃₁⁺ (I) and (b) C₂ B₃₂ (VI) and their degenerate enantiomers C₂ B₃₁⁺ (I′) and C₂ B₃₂ (VI′), with the B₇ heptagons and B₈ octagons on the cage surfaces highlighted in pink.

3. Results and discussion

3.1. Structures and stabilities

As shown in the configurational energy spectrum of B₃₁⁺ at the CCSD(T)/6-311G(d) level in Fig. 2a, the axially chiral sea-shell-like C₂ B₃₁⁺ (I) is the well-defined GM of B₃₁⁺ with the lowest vibrational frequency of 66.2 cm⁻¹. It consists of twenty-six triangles and eight quadrilaterals on the cage surface, two equivalent B₇ heptagons on the waist, and one B₈ octagon at the bottom (shaded in pink in Fig. 1a), following the Euler's rule in this case which reads: E (66 edges) = F (26 triangular + 8 quadrilaterals + 2 heptagonal + 1 octagonal faces) + V (31 vertices) − 2. The second, third, fourth, and fifth lowest-lying cage-like C₁ B₃₁⁺ (II), C₁ B₃₁⁺ (III), C_s B₃₁⁺ (IV), and C_s B₃₁⁺(V) lie 0.22, 0.24, 0.34, and 0.36 eV higher in energy than C₂ GM at CCSD(T) level, respectively (Fig. 2a), though B₃₁⁺ (III) lying 0.04 eV lower than the C₂ GM at the less accurate PBE0 level (Fig. S1a, ESI†). The sea-shell-like low-symmetry C₁ B₃₁⁺ (II) possesses three heptagons on the surface, while C₁ B₃₁⁺ (III) contains two hexagons and one heptagon. We notice that most of the low-lying B₃₁⁺ isomers are cage-like, whereas the first close-packed quasi-planar isomer C₁ B₃₁⁺ lies much higher (by 0.38 eV) than the GM at PBE0 (Fig. S1a, ESI†). The quasi-planar C₁ B₃₁⁺ with a hexagonal hole at the centre which corresponds to the GM of quasi-planar B₃₁⁻ appears to be 0.63 eV higher than C₂ GM at PBE0, well illustrating the charge-induced structural transition from planar B₃₁⁻ reported in ref. 22 to cage-like B₃₁⁺ obtained in this work due to two valence electrons' difference (Fig. S1a, ESI†).

Fig. 2 Configurational energy spectra of (a) B₃₁⁺ and (b) B₃₂ at CCSD(T)/6-311G(d)//PBE0/6-311+G(d) level, with the relative energies indicated in eV. Black, red and blue horizontal lines represent cage-like, quasi-planar and tubular structures, respectively.

C₂ B₃₂ (VI), the well-defined GM of neutral B₃₂ at CCSD(T) level, also possesses an axially chiral sea-shell-like structure with the lowest vibrational frequency of 141 cm⁻¹. It contains two equivalent heptagons on the top and two equivalent heptagons at the bottom on the cage surface (shaded in pink in Fig. 1b) and follows the Euler's rule which in this case reads: E (72 edges) = F (36 triangular + 2 quadrilaterals + 4 heptagonal faces) +V (32 vertices) − 2. The second lowest-lying C_s B₃₂ (VII) possesses two hexagons on the waist and one octagon at the bottom (Fig. S1b, ESI†). It is worth noticing that the quasi-planar C_s B₃₂ (VIII) predicted by Nguyen et al.³⁶ and the double-ring tubular D_16d B₃₂ (IX) proposed by Zhao's group³⁷ in Fig. 2b turned out to be the third and fourth lowest-lying isomers of neutral B₃₂ lying 0.25 eV and 0.32 eV higher in energy than our C₂ GM (VI) at CCSD(T), respectively (Fig. 2b). B₃₂ (VI) thus has the lowest energy in all the structures obtained to date for neutral B₃₂. The much-concerned quasi-planar C₂ B₃₂ (X) with a B₆ hexagon at the center which corresponds to the experimentally observed third isomer of C₂ B₃₂⁻ (ref. 22) appears to be 0.33 eV less stable than B₃₂ (VI) at CCSD(T) (Fig. 2b).

Extensive molecular dynamics (MD) simulations were performed on B₃₁⁺ (I) and B₃₂ (VI) to check the dynamical stabilities of these axially chiral borospherenes. As shown in Fig. S2 (ESI),† both B₃₁⁺ (I) and B₃₂ (VI) appear to be dynamically stable between 500–1000 K. The calculated average root-mean-square-deviations (RMSD) and maximum bond length deviations (MAXD) of B₃₁⁺ (I) are RMSD = 0.07, 0.11, and 0.13 Å and MAXD = 0.28, 0.46 and 0.58 Å at 500 K, 700 K, and 1000 K, respectively. The corresponding values of B₃₂ (VI) turn out to be RMSD = 0.07, 0.08 and 0.10 Å and MAXD = 0.21, 0.27 and 0.36 Å at 500 K, 700 K, and 1000 K, respectively. No high energy isomers are observed in these MD simulation processes.

3.2. Bonding pattern analyses

The high thermodynamic and dynamic stabilities of these axially chiral borospherenes originate from their unique electronic structures and bonding patterns. We choose to use the widely used AdNDP approach developed by Boldyrev and co-workers to analyse both the localized and delocalized bonding interactions in these novel species.^29,30 Detailed AdNDP analyses indicate that B₃₁⁺ (I) possesses 8×2c–2e σ bonds, 24×3c–2e σ bonds and 4×4c–2e σ bonds on the cage surface with the occupation numbers of ON = 1.80–1.94 |e|, 1.72–1.96 |e|, and 1.79–1.81 |e|, respectively. The remaining 20 valence electrons form 10 delocalized π bonds spherically distributed over the σ-skeleton, including 6×4c–2e π bonds and 4×5c–2e π bonds with ON = 1.68–1.83 |e|, in an overall bonding symmetry of C₂ (Fig. 3a). B₃₂ (VI) possesses a similar bonding pattern with B₃₁⁺ (I) (Fig. 3b). It contains 2×2c–2e σ bonds, 32×3c–2e σ bonds, and 4×4c–2e σ bonds on the cage surface. There exist 10 delocalized π bonds spherically distributed over the σ-skeleton, including 6×4c–2e π bonds and 4×5c–2e π bonds with ON = 1.78–1.90 |e|, in an overall symmetry of C₂. Both B₃₁⁺ (I) and B₃₂ (VI) thus possess 10 delocalized π bonds over a σ-skeleton and follow the universal σ + π double delocalization bonding pattern of the borospherene family.^4,5,9–16 Detailed bonding analyses further indicate that C_s B₃₂ (VII), the second lowest-lying isomer of B₃₂, also matches the σ + π double delocalization bonding pattern, with 10 delocalized π bonds over a σ skeleton (Fig. S3, ESI†).

Fig. 3 σ and π AdNDP bonding patterns of (a) C₂ B₃₁⁺ (I) and (b) C₂ B₃₂ (VI), with the occupation numbers (ONs) indicated.

The 10 delocalized π bonds on the cage surfaces renders spherical aromaticity to sea-shell-like B₃₁⁺ (I) and B₃₂ (VI), as evidenced by their calculated negative NICS values of NICS = −29 ppm and −24 ppm at the cage centers. We tabulate the numbers of σ bonds, π bonds, and calculated NICS values of the borospherene family reported so far in Table 1. It can be seen that the numbers of σ bonds increase monotonously with the number of valence electrons of the systems, while the numbers of π bonds increase in a stepwise pattern, with C₂ B₂₈, C_s B₂₉⁺, and C_s B₂₉⁻ possessing 9 delocalized π bonds, C₂ B₃₁⁺ and C₂ B₃₂ having 10 delocalized π bonds, C₂ B₃₄ and C₂ B₃₅⁺ containing 11 delocalized π bonds, and T_h B₃₆⁴⁻, C_s B₃₇³⁻, C_s B₃₈²⁻, C_s B₃₉⁺, C₃ B₃₉⁻, C₂ B₃₉⁻, D_2d B₄₀, C₁ B₄₁⁺, and C₂ B₄₂²⁺ in different charge states possessing 12 delocalized π bonds, respectively. These borospherenes all appear to be spherically aromatic with the negative calculated NICS values of NICS = −21 to −43 ppm. It is these delocalized π bonds that help to maintain the cage-like structures of the borospherene family and render spherical aromaticity to the systems.

Table 1 The numbers of σ bonds (n_σ), π bonds (n_π), and calculated NICS (ppm) values of the borospherene family reported to date

	nσ	nπ	NICS/ppm
C2 B28 (ref. 14)	33	9	−40
Cs B29^+ (ref. 16)	34	9	−34
Cs B29^− (ref. 15)	35	9	−21
C2 B31^+	36	10	−29
C2 B32	38	10	−24
C2 B34 (ref. 17)	40	11	−40
C2 B35^+ (ref. 17)	41	11	−38
Th B36^4− (ref. 12)	44	12	−36
Cs B37^3− (ref. 10)	45	12	−33
Cs B38^2− (ref. 11)	46	12	−37
Cs B39^+ (ref. 13)	46	12	−40
C3 B39^− (ref. 4)	47	12	−38
C2 B39^− (ref. 4)	47	12	−39
D2d B40 (ref. 5)	48	12	−43
C1 B41^+ (ref. 9)	49	12	−41
C2 B42^2+ (ref. 9)	50	12	−40

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3.3. Spectral simulations

Infrared photodissociation (IR-PD) spectra in combination with first-principles theory calculations have proven to be an effective approach in characterizing novel clusters.³⁸ B₃₁⁺ (I) and B₃₂ (VI) possess 87(43a + 44b) and 90(46a + 44b) vibrational modes, respectively. The simulated IR, Raman and UV-vis spectra of B₃₁⁺ (I) and B₃₂ (VI) are shown in Fig. 4. The major IR peaks of the two borospherenes appear to lie between 1100 and 1400 cm⁻¹, with two major IR active peaks at 1254 cm⁻¹ (b) and 1298 cm⁻¹ (b) in B₃₁⁺ (I) and two major peaks at 1277 cm⁻¹ (b) and 1315 cm⁻¹ (b) in B₃₂ (VI). All the other IR vibrational modes appear to have much lower intensities. The major Raman active peaks occur at 374 cm⁻¹ (a), 669 cm⁻¹ (a) and 1394 cm⁻¹ (a) in B₃₁⁺ (I) and 491 cm⁻¹ (a), 1181 cm⁻¹ (a) and 1308 cm⁻¹ (a) in B₃₂ (VI), with main contributions originating from the symmetric vibrational modes. The Raman vibrational modes at 374 cm⁻¹ (a) in B₃₁⁺ (I) and 491 cm⁻¹ (a) in B₃₂ (VI) correspond to the typical “radial breathing modes” (RBMs) of the two borospherenes which can be used to characterize the hollow structures of single-walled boron nanoclusters in experiments.³⁹

Fig. 4 Simulated IR, Raman, and UV-vis absorption spectra of (a) C₂ B₃₁⁺ (I) and (b) C₂ B₃₂ (VI) at PBE0/6-311+G(d) level.

The simulated UV-vis spectra of B₃₁⁺(I) and B₃₂ (VI) lie between 200–550 nm, with the main absorption peaks lying at 238 nm, 276 nm, 333 nm, 412 nm, 454 nm, and 534 nm in B₃₁⁺(I) and at 263 nm, 287 nm, 373 nm, 404 nm, 473 nm, and 540 nm in B₃₂ (VI), respectively (Fig. 4). The strong UV-vis peaks originate from electronic excitations from the deep inner shells to the high-lying unoccupied molecular orbitals of the systems, while the weak absorption bands above 500 nm are attributed to electronic excitations from the occupied frontier orbitals (HOMO and HOMO−1) to the unoccupied frontier orbitals (LUMO, LUMO+1, and LUMO+2).

4. Summary

We have performed in this work an extensive first-principles theory investigation on sea-shell-like C₂ B₃₁⁺ (I) and C₂ B₃₂ (VI), presenting two new axially chiral members to the borospherene family. These novel borospherenes follow the universal σ + π double delocalization bonding pattern of the borospherene family, with 10 delocalized π bonds over an σ skeleton on the cage surface, rendering spherical aromaticity to these borospherene species. B₃₁⁺ (I) may be characterized in gas-phases IR-PD spectral measurements, while B₃₂ (VI) may be detected in matrix isolation infrared spectroscopy.⁴⁰ More investigations on cage-like B_n^+/0 clusters are currently in progresses to further expand the borospherene family and enrich borospherene chemistry.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21720102006 to S.-D. Li).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ra01087a

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