© to the authors 2009
Received: 13 May 2009
Accepted: 26 May 2009
Published: 11 June 2009
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© to the authors 2009
Received: 13 May 2009
Accepted: 26 May 2009
Published: 11 June 2009
Based on our comprehensive theoretical investigation and known experimental results for small boron clusters, we predict the existence of a novel aromatic inorganic molecule, B12H6. This molecule, which we refer to as borozene, has remarkably similar properties to the well-known benzene. Borozene is planar, possesses a large first excitation energy, D3hsymmetry, and more importantly is aromatic. Furthermore, the calculated anisotropy of the magnetic susceptibility of borozene is three times larger in absolute value than for benzene. Finally, we show that borozene molecules may be fused together to give larger aromatic compounds with even larger anisotropic susceptibilities.
Why certain molecules are more stable than others is not always easy to understand. Nature’s diversity does not always permit a simple answer for the structure of all compounds. However, a very useful concept in structural stability is aromaticity [1, 2], which was first developed to account for the properties of organic compounds involving ring structures such as benzene (C6H6) and more recently extended to inorganic systems . However, the question arises whether aromatic hydrocarbons are the only structures where an “aromatic ring” acts as a building block and plays a key role in their stability. In this study, we predict the existence of a novel inorganic molecule, B12H6, that has remarkably similar properties to benzene. This molecule, which we call borozene for brevity, is planar, possesses a large first excitation energy, exhibits a highly aromatic character, and similar to benzene is a building block of possibly much larger aromatic compounds.
Small all-boron clusters, B n (n < 20) have been widely investigated both experimentally and theoretically [4–9]. All these studies indicate that small boron clusters assume in most cases quasi-planar structures and in some special cases even perfectly planar structures. In contrast, neutral and anionic boron hydrides, B n Hn+m, are all known to have three-dimensional deltahedral structures . There is yet little known about the structure of small boron hydrides where the number of hydrogen atoms is smaller than the number of boron atoms (see ref.  and references therein). One such example is the recently studied σ-aromatic and π-antiaromatic cluster, which is fully planar .
The structure and electronic properties of all clusters were obtained at the X3LYP/6-311G(d,p) level of theory using tight convergence criteria as implemented in FreeON (formerly known as MondoSCF), a suite of programs using Gaussian basis sets and all-electron Hartree–Fock, density functional theory or hybrid approach for self-consistent electronic structure calculations [12–17]. The initial search for the most stable structures of the boron hydride B12H n have been done at the X3LYP/6-31G(d,p) level of theory starting from the energy-minimum structure of B12Hn- 2 and the low-lying isomers in each case have been reoptimized using the 6-311G(d,p) basis set. The obtained local energy-minimum structures are well separated in energy from its higher isomers by at least 22 kcal/mol in the case of B12H n , where n ≤ 6, and 17 kcal/mol in the case of the B12H8 cluster. The B22H8 and B60H12 clusters, which result from the fusion of two and six B12H6 molecules, respectively, were fully optimized using symmetry-unrestricted calculations.
To ensure that the structures for the neutral and negatively charged B12H6molecules correspond to a local minima of energy, the nature of the stationary points where checked by vibrational frequency calculations. In addition, several tests have been done for neutral B12H6optimizing this molecule starting from structures with randomly displaced atoms. For all tested cases, the substructure of boron atoms became planar after optimization to within 0.012 and 0.014 Å at the X3LYP/6-311++G(d,p) and UHF-MP2/6-311++G(d,p) levels of theory, respectively. Precise calculations at the X3LYP/6-311G(d,p) level of theory and using very tight convergence criteria revel, however, that the fully planar B12H6molecule is the most energetically favorable structure. Similar tests were done for B22H8and B60H12, and after optimization at the X3LYP/6-311G(d,p) level of theory both substructures of boron atoms became planar to within 0.016 Å.
The first singlet excitation energy, nuclear magnetic resonance (NMR) shielding tensors, and magnetic susceptibility tensors were calculated using the Gaussian03 package . This package was also used to further optimize the B12H6 molecule using the 6-311++G(d,p) basis set. To obtain the nucleus independent chemical shift (NICS) values (from the NMR shielding tensors), we have used the GIAO (gauge-independent atomic orbital) method and the magnetic susceptibility tensors were calculated using the CSGT (continuous set of gauge transformations) method. All computations have been performed at the X3LYP/6-311++G(d,p) level of theory except for the B60H12 cluster, for which we have used the RHF/6-31G(d,p) level of theory. The anisotropy of magnetic susceptibility is defined as the difference between out-of-plane and the average in-plane components of the susceptibility tensor.
The MOs of B12H6 and C6H6 were calculated at the RHF/6-311++G(d,p) level of theory using the GAMESS-US package . The same package was used to calculate the π–π interaction between molecules in borozene and benzene dimmers at the RHF-MP2/6-311G(d,p) and RHF-MP2/6-311++G(d,p) levels of theory, respectively. The counterpoise correction was applied to account for the basis set superposition error.
The search for the stable structures of B12H n , with n ≤ 6 is simplified by the fact that the most energetically favorable configurations, as far as we can determine, are those where the hydrogen atoms are directly attached to the outer boron atoms of the molecule. We have established that the most likely stable configuration for B12H2 is when the hydrogen atoms are attached to one of the outer short-bonded boron pairs of the B12 cluster. The energetically preferred configuration for B12H4 is when the hydrogen atoms are attached to one of the two remaining outer short-bonded boron pairs in the B12H2. Finally, the B12H6 cluster has all short B–B pairs, from B12, with hydrogen atoms attached to them. Only B12H6 is a fully planar molecule, whereas B12H2 and B12H4 are quasi-planar with Cs symmetry. In Fig. 1a, we have shown the structure of B12H6. The hydrogenation energy, defined as ΔE = E(B12H n ) − E(B12Hn-2) − E(H2) where E is the total energy, is −44 kcal/mol for n = 2, −45 kcal/mol for n = 4, and −51 kcal/mol for n = 6. We have found, however, that if a fourth H2 molecule is attached to B12H6 the hydrogenation energy increases to −2 kcal/mol (i.e., the H2 molecule is weakly bound to B12H6). It is also important to mention that our ΔE values are about two times larger than the predicted energy of hydrogenation of the cluster , which is an additional indication of unusual stability of the B12 structure. The B12H8 molecule is shown in Fig. 1b and can be described as a distorted B12H6 cluster with two extra (one terminal and one bridging) hydrogen atoms attached to it. The B–H bond lengths are 1.36 and 1.21 Å for the bridging and terminal hydrogen atoms, respectively, whereas the remaining B–H distances in B12H8 and in all other described earlier B12H n (n ≤ 6) clusters are the same and equal to 1.18 Å. The last value is very close to the calculated bond lengths B–H = 1.19 Å in borane, BH3.
Molecular symmetry, HOMO–LUMO energy gaps, and the isotropic and anisotropic values of magnetic susceptibility for the studied planar boranes and hydrocarbons
HOMO–LUMO gap (eV)
Magnetic susceptibility (cgs-ppm)
To gain information about the individual contributions of the B3triangles to the overall aromaticity of the B12H6molecule, we have studied its two-dimensional NICS map. In Fig. 1c, we have shown the contour plot of NICS(x, y) in plane (left) and at 1 Å above the B12H6molecule (right). It is clearly seen from the left part of the figure that the NICS values are negative inside the twelve outer B3triangles of the molecule, suggesting a flow of a global diatropic current around the central triangle. The central part of the molecule has a paratropic current flowing inside the inner B3triangle which is not overwhelmed by a diatropic current due to an electron charge transfer from the center of the structure towards the outer boron triangles after hydrogenation. Also, this antiaromatic region is spatially localized since the NICS values are negative at 1 Å (see the right part of Fig. 1c) and 2 Å above and below the center of the B12H6molecule (NICS(1) = −3.9 ppm; NICS(2) = −5.2 ppm).
Vertical electron affinities and ionization energies for B12H6 and calculated using the 6-311++G(d,p) basis set
Electron affinity (eV)
Ionization energy (eV)
Although the specific route for the synthesis of the B12H6(or ) structure is not yet known, it is clear from our investigation that to some extent the chemistries of B12H6and benzene may be very similar, suggesting that similar methods could be employed to synthesize this and related compounds. Given the technological importance of benzene and its derivatives, we believe that the B12H6molecule will have a significant technological impact and deserves further extensive study.
We would like to thank Dr. Daniel Vrinceanu for his helpful discussion and Brad Mazock for computational support. This project was supported by the Robert A. Welch Foundation (Grant J-1675) and the NIH-RCMI Program (Grant RR03045).