Journal of Cluster Science

, 22:525

Hydrogenation of B120/−: A Planar-to-Icosahedral Structural Transition in B12Hn0/− (n = 1–6) Boron Hydride Clusters


  • Hui Bai
    • Institute of Molecular SciencesShanxi University
    • Department of Chemistry, Institute of Materials ScienceXinzhou Teachers’ University
    • Institute of Molecular SciencesShanxi University
    • Department of Chemistry, Institute of Materials ScienceXinzhou Teachers’ University
Original Paper

DOI: 10.1007/s10876-011-0408-0

Cite this article as:
Bai, H. & Li, S. J Clust Sci (2011) 22: 525. doi:10.1007/s10876-011-0408-0


A systematic density functional theory and wave function theory investigation performed in this work reveals a planar-to-icosahedral structural transition between n = 4–5 in the partially hydrogenated B12Hn0/− clusters (n = 1–6) upon hydrogenation of all-boron B120/−. Coupled cluster calculations with triple excitations (CCSD(T)) indicate that a distorted icosahedral B12H6 cluster with C2 symmetry is overwhelmingly favored (by 35 kcal/mol) over the recently proposed perfectly planar borozene (D3h B12H6) (Szwacki et al., Nanoscale Res Lett 4:1085, 2009) which proves to be a high-lying local minimum. A similar 2D–3D structural transition occurs to the corresponding boron boronyl analogues of B12(BO)n with n –BO terminals. Detailed adaptive natural density partitioning (AdNDP) analyses reveal the bonding patterns of these quasi-planar or cage-like clusters which are characterized with delocalized σ and π molecular orbitals. The electron detachment energies of the concerned anions and excitation energies of the neutrals are also predicted to facilitate their future experimental characterizations.


BoronBoron hydridesDensity functional theoryStructuresAdaptive natural density partitioning


It is well-known that boron exhibits a variety of polymorphisms composed of icosahedral B12 cages [1]. In contrast, small boron clusters Bn−/0 in the size range between n = 3–20 have been confirmed to possess planar or quasi-planar structures by joint experimental and theoretical investigations in the past decade [28], with a 2D–3D transition at the double-ring tubular B20 [5]. Of special interests in these all-boron clusters, the quasi-planar C3v B12 in a triangular motif appears to be unique: it is an all-boron analogue of benzene with six delocalized π-electrons and possesses a large first excitation energy of 2.0 eV [24]. Upon hydrogenation of C3v B12 at the six corner positions, Szwacki and coworkers recently presented the possibility of the perfectly planar D3h B12H6 which they called borozene [9]. Borozene has aroused immediate attention since it was proposed [10, 11] and has been utilized as building blocks to form the nanoscale clusters of B60H12 and B228H24 [10] and boron fullerenes [12]. Typical perfectly planar boron hydride clusters reported also include C2v B7H2 [13], B4Hn (n = 1–3) [14], and D6h B6H66− [15].

However, B12Hn+ cations (n = 0–12) [16] generated in an external quadrupole static attraction ion trap were known to preferentially form planar structures in the size range between n = 0–5, whereas those with more hydrogen atoms (n = 6–12) preferentially formed icosahedral cages similar to the well-known 1:1 hydrogenated B12H122− dianion [1]. These results remind us that B12Hn neutrals and B12Hn anions may take similar geometries with the corresponding B12Hn+ cations, with a planar-to-icosahedral transition at certain size range. Keeping the inspiration in mind, at both density functional theory (DFT) and wave function theory levels in this work, we performed a systematical investigation on the effects of hydrogenation on both the geometrical and electronic structures of the quasi-planar C3v B12 and Cs B12 [24]. A planar-to-icosahedral structural transition was indeed identified at the coupled cluster level between n = 4–5 for both B12Hn neutrals and B12Hn anions and distorted icosahedral C2 B12H6 and C1 B12H6 cages were found to be overwhelmingly favored in energy (by 35 and 44 kcal/mol, respectively) over the perfectly planar D3h B12H6 and the corresponding quasi-planar C2 B12H6 anion [9]. A similar structural transition was obtained for the corresponding boron boronyls of B12(BO)n0/− with n –BO radicals (n = 1–6). Detailed adaptive natural density partitioning (AdNDP) [1719] analyses were performed on these partially hydrogenated species to reveal their bonding patterns which are characterized with delocalized σ and π bonds. The one-electron detachment energies of the anions and excitation energies of the neutrals were also predicted to facilitate their spectroscopic characterizations. This work on B12Hn0/− clusters parallels the results we recently reported for the partially hydrogenated B16Hn [20] and B18Hn [21]. These studies are expected to shed new insight into boron hydride intermediate species and advance the bonding patterns of boron-containing compounds in general.

Computational Details

Starting from initial structures constructed from the corresponding B12Hn+ cations (n = 0–12) [16] and B12Hn neutrals (n = 2, 4, 6, and 8) [9], we optimized the structures and analyzed the vibrational frequencies of B12Hn0/− (n = 0–6) clusters using the hybrid DFT method of B3LYP [22, 23] and the second-order Møller–Plesset approach (MP2) [24, 25] with the basis set of 6-311G(d,p). The two methods produced essentially the same geometries with slightly different bond parameters and, in some cases, generated different relative stability orders. The relative energies were further refined using the more accurate coupled cluster method including triple excitations (CCSD(T)) [2629] at both B3LYP and MP2 structures with zero-point corrections included (with the notations of CCSD(T)//B3LYP and CCSD(T)//MP2 hereafter, respectively). As shown in Figs. 1 and 2, CCSD(T)//B3LYP and CCSD(T)//MP2 methods produced the same stability orders with close relative energies for both the neutral and anion series. The adiabatic detachment energies (ADE) of the anions were calculated as the energy differences between the anions and the corresponding neutrals at their ground-state structures, whereas the vertical detachment energies (VDE) were calculated as the energy differences between the ground states of the anions and the ground states of neutrals at the anionic geometries. AdNDP [1719] bonding patterns shown in Figs. 3 and 4 were visualized using the MOLDEN 4.1 program [30]. To check the aromaticity of the distorted icosahedral clusters, the widely used nucleus independent chemical shifts (NICS) [31, 32] were calculated at the cage centers using the gauge-independent atomic orbital (GIAO) method [33]. The calculated ADE and VDE values for B12Hn (n = 0–6) anions are summarized in Table 1 and the ionization potentials (IP) and first excitation energies (Eex) of the neutrals are tabulated in Table 2. All the calculations in this work were performed using the Gaussian03 program [34].
Fig. 1

Planar and icosahedral isomers optimized for a B12Hn neutrals (n = 0–6) and b B12Hn anions (n = 0–6) at B3LYP/6-311G(d,p) level, with relative energies between the two isomers indicated in kcal/mol at CCSD(T)//B3LYP and CCSD(T)//MP2 (in parentheses)
Fig. 2

Energy differences between planar and icosahedral isomers for a B12Hn (n = 0–6) neutrals and b B12Hn (n = 0–6) anions at CCSD(T)//B3LYP (squares) and CCSD(T)//MP2 (round circles)
Fig. 3

AdNDP bonding patterns obtained for planar B12Hn neutrals (n = 0, 2, 4, and 6) with occupation numbers (ON) indicated. a π and σ bonds of D3h B12H6(1). b σ bonds of Cs B12H4(9), Cs B12H2(17), and D3h B12(25) (these neutrals also possess n similar B–H σ bonds and three similar 5c–2e π bonds with D3h B12H6(1))
Fig. 4

AdNDP bonding patterns of C2 B12H6 (2) with occupation numbers (ON) indicated

Table 1

Calculated ADE and VDE values of B12Hn (n = 0–6) anions at CCSD(T)//B3LYP and CCSD(T)//MP2 levels


ADE (eV)

VDE (eV)





4. C1 B12H6





8. Cs B12H5





12. Cs B12H4





15. C1 B12H3





19. C2 B12H2





23. C1 B12H





27. Cs B12





Table 2

Calculated first ionization potentials (IP) of B12Hn (n = 0–6) neutrals at CCSD(T)//B3LYP and CCSD(T)//MP2 and their excitation energies (Eex) at TD-B3LYP


IP (eV)

Eex (eV)




2. C2 B12H6




6. C1 B12H5




10. Cs B12H4




13. C1 B12H3




17. Cs B12H2




21. C1 B12H




25. C3v B12




Results and Discussion

Structures and Stabilities

We start from B12H6, the most concerned species in this work. As clearly shown in Fig. 1 at CCSD(T)//B3LYP level, the distorted icosahedral C2 B12H6(2, 1A) (denoted as C2 B12H6 hereafter) is overwhelmingly more stable (34.59 kcal/mol) than the perfect planar D3h B12H6(1, \( ^{1} {\text{A}}_{1}^{\prime } \)) previously reported in Ref. [9]. CCSD(T)//MP2 method produces essentially the same relative energy (−34.59 kcal/mol) as CCSD(T)//B3LYP, providing further evidence to support the reliability of the theoretical approaches used in this work. With one extra electron, the cage-like C1 B12H6(4, 2A) anion also turns out to be strongly favored in energy (by 43.58 kcal/mol) over the quasi-planar C2 B12H6(3, 2A) [9]. With such large energy differences, the high-lying planar D3h B12H6(1) and quasi-planar C2 B12H6(3) can be safely ruled out from experiments under normal conditions. As the ground states of the concerned systems, C2 B12H6(2) and C1 B12H6(4) are expected to be synthesized and characterized in future experiments. Thus, a 1:2 (H:B) hydrogenation of the quasi-planar B120/− leads to the formation of the distorted icosahedral C2 B12H6(2) and C1 B12H6(4).

A similar stability order exists in B12H50/− (though the relative energies become smaller than B12H60/−) for which the distorted icosahedral C1 B12H5(6, 2A) and Cs B12H5(8, 1A′) are 26.75(28.13) and 17.30(18.91) kcal/mol more stable than the corresponding quasi-planar C1 B12H5(5, 2A) and C1 B12H5(7, 1A) at CCSD(T)//B3LYP (CCSD(T)//MP2), respectively. B12H5 and B12H5 favor distorted icosahedral structures over planar geometries for the reason that they possess the same number of valence electrons as the known distorted icosahedral B12H6+ and B12H7+ [16], respectively.

However, as indicated in Figs. 1 and 2, icosahedral and planar isomers become energetically competitive for B12H40/− clusters, with the distorted Cs B12H4(10, 1A′) being only 5.30 (5.53) kcal/mol more stable than Cs B12H4(9, 1A′) at CCSD(T)//B3LYP (CCSD(T)//MP2), while Cs B12H4(12, 2A′) having the relative energies of −0.46 kcal/mol at CCSD(T)//B3LYP and +1.84 kcal/mol at CCSD(T)//MP2. Such small energy differences are within the accuracies of the theoretical methods used. The 2D and 3D isomers of B12H4 anion can be practically viewed iso-energetic isomers.

A stability conversion actually occurs at B12H30/−, with the quasi-planar C1 B12H3(13, 2A) and C1 B12H3(15, 1A) being 3.23 (7.61) and 12.45 (12.22) kcal/mol more stable than the icosahedral Cs B12H3(14, 2A′) and Cs B12H3(16, 1A′), respectively. Such a tendency develops as the content of the hydrogen atoms decreases, with the quasi-planar isomers (17, 19, 21, 23, 25, and 27) being overwhelmingly favored in energy over the distorted icosahedral ones (18, 20, 22, 24, 26, and 28) for B12H20/−, B12H0/−, and bared B120/− (convex B120/− were already characterized in previous photoelectron spectroscopy measurements (PES) [24]).

The overall stability variation of B12Hn neutrals can be clearly seen from Fig. 2a, where a planar-to-icosahedral transition occurs at n = 4, well in line with the reported structural transition at B12H5+ [16] which is iso-electronic with B12H4. A similar planar-to-icosahedral transition happens to B12Hn anions at n = 5 as shown in Fig. 2b, where the planar and icosahedral isomers of B12H4 are practically iso-energetic. We conclude that a planar-to-icosahedral structural transition occurs for B12Hn0/− clusters between n = 4–5. B12Hn0/− clusters maintain the quasi-planarity of the bared B120/− with n ≤ 3 (H:B ≤ 1:4), but they overwhelmingly favor distorted icosahedral structures when the number of hydrogen atoms reaches 5. We also tried B12H8 which contains two more hydrogen atoms than B12H6. At CCSD(T)//B3LYP (CCSD(T)//MP2) level, B12H8 proves to have a distorted icosahedral C2v B12H8 (1A1) ground state similar to the B12H8+ cation reported in Ref. [16], It turns out to be 112.53 (114.150) kcal/mol more stable than the quasi-planar Cs B12H8(1A′) proposed in Ref. [9].

Orbitals and Aromaticities

AdNDP analyses help to understand the structures and bonding patterns of various compounds [1719]. As shown in Fig. 3a, D3h B12H6(1) possesses six equivalent 2c–2e B–H σ bonds with the occupation number of ON = 1.97|e|, six periphery 2c–2e B–B σ bonds with ON = 1.75|e|, six in-plane 3c–2e σ bonds with ON = 1.87–1.95|e|, and three 5c–2e π bonds over the B12 plane with ON = 1.90|e|. Thus, it formally satisfies the 4n + 2 rule for π aromaticity and 4n rule for σ antiaromaticity in electron counts (similar situations were reported for B162− [6] and B19 [7]). However, the globally σ antiaromatic D3h B12H6 with six delocalized σ bonds covering six B3 triangles is expected to lead to the formation of islands of σ-aromaticity, as in the case of Li4 [1719]. It is true that the in-plane contour plot of NICS(x,y) for D3h B12H6 (Fig. 1c (left) in Ref. [9]) possesses six most negative NICS areas which exactly correspond to the six 3c–2e σ bonds of the molecule shown in Fig. 3a, indicating that the in-plane flow of the diatropic current mainly originates from the contribution of the six delocalized 3c–2e σ bonds. It is also interesting to notice that the central B3 triangle in D3h B12H6 is not covered by either the six 3c–2e σ bonds or the three 5c–2e π bonds in our AdNDP bonding pattern. This agrees with the observation that there exists a spatially localized antiaromatic region with positive NICS values at the center of D3h B12H6(1) [9]. This makes borozene (D3h B12H6(1)) fundamentally different from benzene which is globally aromatic without an antiaromatic area at the center.

Figure 3b compares the bonding patterns of the concerned hydrogenated B12 species. The three delocalized 5c–2e π bonds and the six delocalized 3c–2e σ bonds have been well maintained in D3h B12 (similar to C3v B12), Cs B12H2, Cs B12H4, and D3h B12H6. However, the numbers of 2c–2e B–B σ bonds along the periphery of the B12 core in these species decrease from 9, to 8, to 7, to 6, with one short B–B σ periphery bond at the corner broken as each pair of terminal hydrogen atoms added in. Thus, the size of the outer B9 ring increases from D3h B12, to Cs B12H2, to Cs B12H4, and finally, to D3h B12H6 which possesses the biggest outer B9 ring in this series to host the inner B3 ring in a perfect molecular plane. However, as demonstrated above, the overall stability of the planar structures with respect to their icosahedral counterparts decreases with increasing numbers of hydrogen atoms.

Now we turn to the bonding patterns (Fig. 4) of the distorted icosahedral C2 B12H6(2) which possesses six 2c–2e B–H σ bonds around the B12 cage in C2 symmetry, twelve 3c–2e σ bonds symmetrically distributed in pairs, one 4c–2e σ bond covering four unterminated boron atoms in a distorted rhombus matching the C2 symmetry of the molecule, and two 3c–2e π bonds covering three unterminated boron atoms each. The thirteen delocalized σ bonds are expected to make major contributions to make C2 B12H6(2) more table than D3h B12H6(1) which has six delocalized σ bonds. The six unterminated boron atoms covered by the two 3c–2e π bonds can be further hydrogenated in radial directions when the number of hydrogen atoms exceeds six (n > 6). We also notice that C2 B12H6(2) possesses a negative NICS value of −35.82 ppm at the center of the cage, indicating that it is 3D aromatic in nature.

Detachment and Excitation Energies

The calculated ADE values between 1.64 and 3.23 eV and VDE values between 1.68 and 3.43 eV for B12Hn anions (n = 0–6) tabulated in Table 1 may help to facilitate their PES characterizations. CCSD(T)//B3LYP and CCSD(T)//MP2 methods agree well in producing these one-electron detachment energies. There exist a clear even–odd alternation in both ADE and VDE values, with the open-shell B12Hn anions (n = 0, 2, 4, and 6) possessing systematically lower ADE and VDE values than their closed-shell B12Hn neighbors (n = 1, 3, and 5).

Table 2 indicates that B12Hn neutrals (n = 0–6) possess considerably high first ionization potentials (IP = 7.12–8.88 eV) at CCSD(T). These values also exhibit an even–odd alternation, with IP = 8.10–8.88 eV for the closed-shell B12Hn neutrals (n = 0, 2, 4, and 6) and IP = 7.12–7.62 eV for the open-shell ones (n = 1, 3, and 5).

As for the first excitation energies of the B12Hn neutrals at their ground states, Eex = 0.91, 0.67, and 0.55 eV for the distorted icosahedral C2 B12H6(2), C1 B12H5(6), and Cs B12H4(10), and Eex = 1.05, 1.67, 1.43, and 2.32 eV for the quasi-planar C1 B12H3(13), Cs B12H2(17), C1 B12H(21), and C3v B12(25), respectively. Planar isomers appear to have larger Eex values than their icosahedral counterparts, but icosahedral isomers prove to be the ground states of the B12Hn neutrals when the number of hydrogen atoms reaches four (n ≥ 4).

B12(BO)n Boron Boronyls (n = 2, 4, and 6)

The BO/H isolobal relationship recently established in a series of PES experiments [3537] has built a clear structural link between boron oxide clusters and their boron hydride counterparts. Here we substitute n hydrogen atoms in B12Hn (n = 6, 4, and 2) with n BO radicals to form the boron boronyls of B12(BO)6 (D329 and C230), B12(BO)4 (Cs31 and Cs32), and B12(BO)2 (Cs33 and D5d34). As shown in Fig. 5, these isomers are all true minima of the systems with similar symmetries and geometries with their parent boron hydride clusters. More importantly, these boron boronyls possess the same stability orders as their B12Hn counterparts with similar relative energies (compare Figs. 1 and 5). There exists a similar planar-to-icosahedral transition at n = 4 for B12(BO)n, with the distorted icosahedral C2 B12(BO)6(30) being overwhelmingly more stable than the quasi-planar D3 B12(BO)6(29). Detailed AdNDP analyses indicate that B12(BO)n neutrals also possess similar bonding patterns with their B12Hn counterparts, except the n B≡O triple bonds (two π and one σ) involved in n BO radicals. A similar situation exists for B12(BO)n anions.
Fig. 5

Planar and icosahedral isomers optimized for B12(BO)n boron boronyls (n = 2, 4, and 6) at B3LYP, with relative energies indicated in kcal/mol at CCSD(T)//B3LYP


Comprehensive theoretical investigations performed in this work indicate that there exists a planar-to-icosahedral structural transition between n = 4–5 in the partially hydrogenated B12Hn0/− (n = 1–6) clusters and their boron boronyl counterparts. The distorted icosahedral C2 B12H6(2) proves to be overwhelmingly more stable than the perfectly planar borozene (D3h B12H6(1)). Given the fact that α-sheet boron has proven to be the most stable boron sheet composed of a hybrid of triangular and hexagonal motifs [38, 39], it will be very unlikely that borozene may serve as building blocks to form stable planar boron nanostructures. Instead, icosahedral B12 cages at the centers of the B12Hn0/− clusters (n ≥ 5) discussed in this work may serve as the most possible building blocks of novel boron-based nanomaterials.


This work was jointly supported by the National Science Foundation of China (No. 20873117) and Shanxi Natural Science Foundation (No. 2010011012-3). The authors are grateful to Professor A. I. Boldyrev and Dr. T. Galeev and A. Sergeeva at Utah State University for their generous help in using the AdNDP program.

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