- Nano Express
- Open Access
B12H n and B12F n : planar vs icosahedral structures
© Szwacki and Tymczak; licensee Springer. 2012
- Received: 16 January 2012
- Accepted: 30 April 2012
- Published: 30 April 2012
Using density functional theory and quantum Monte Carlo calculations, we show that B12H n and B12F n (n = 0 to 4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters. Moreover, we show that the fully planar B12F6 cluster is more stable than the three-dimensional counterpart. These results open up the possibility of designing larger boron-based nanostructures starting from quasi-planar or fully planar building blocks.
- Nucleus Independent Chemical Shift
- Trial Wave Function
- Icosahedral Structure
- Boron Hydride
- Diffusion Monte Carlo
The icosahedral B12H122- cluster is the most stable molecule among the number of polyhedral boranes synthesized so far . A large-scale and efficient synthesis of fully fluorinated boron hydrides, e.g., icosahedral B12F122-, has been also reported . On the other hand, the all-boron C3v-B12 cluster is quasi-planar, and it was reported to be one of the most stable all-boron clusters. It was also established by extensive computations that the quasi-planar B12 cluster is much lower in energy than the all-boron icosahedral B12 cluster. This was reported not only for the neutral clusters , but also for the charged ones . It is then interesting to investigate what happens with the relative stability of the two (quasi-planar and three-dimensional (3D)) all-boron structures upon addition of hydrogen or fluorine atoms. This is the purpose of this study.
Quasi-planar and 3D boron clusters with the number of hydrogen atoms smaller than the number of boron atoms have been studied both theoretically [5–11] and experimentally [12–14]. Ohishi et al.  reported the formation of B12H n + (n = 0 to 12) cationic clusters through ion-molecule reactions of the decaborane ions (B10H n +, n = 6 to 14) with diborane molecules (B2H6) in an external quadrupole static attraction ion trap. The mass spectrum analysis revealed that among the B12H n + clusters with different hydrogen content n, the B12H8+ molecule was the main product. In the same study, using first principle calculations with the Becke 3-parameter Lee-Yang-Parr (B3LYP) hybrid functional and the 6-31G(d) basis set, the authors compared the relative energies of quasi-planar and 3D B12H n + clusters with n varying from 0 to 12. According to that study, two-dimensional (2D) clusters with n = 0 to 5 are energetically preferred over the 3D structures, whereas 3D clusters are energetically favored for n ≥ 6. In a more recent combined experimental/theoretical study, Ohishi et al.  suggested that quasi-planar B12H n + with n = 0 to 3 clusters can be obtained by further removal of H atoms from the decaborane ions. This opens up the possibility of changing the structure of the B12H n + cluster by controlling the number of hydrogen atoms in the cluster.
To our knowledge, there are no previous studies on the structure and properties of quasi-planar B12F m clusters. However, the structures of two polyboron fluorides, B8F12 and B10F12, revealing unusual open structures were recently determined .
The initial search for the most stable structures of the boron hydrides B12H n and boron fluorides B12F n was done at the B3LYP/6-31G(d) level of theory using the FreeON code  with no symmetry restrictions. For clusters with an even number of hydrogen or fluorine atoms (even number of electrons), the computations were performed for the singlet multiplicity only, whereas doublet and quartet multiplicities were considered for clusters with an odd number of hydrogen or fluorine atoms (odd number of electrons). In the later case, structures with lower multiplicity were energetically more favorable. For the charged structures, a similar analysis has been done, and the ground state was found to have the lowest multiplicity. Next, the low-lying isomers of B12H n and B12F n have been re-optimized using the GAMESS-US code  at the B3LYP/6-311++G(d, p) level of theory, and for the resulting structures, the vibrational analysis has been done to identify true local minima. It is important to mention that the 'bare' B12 icosahedron undergoes distortions after structural optimization and that its symmetry is S2, not Ih. However, we will refer to that structure and its derivatives as icosahedral or 3D. The quasi-planar or fully planar clusters, for a change, will be often labeled as 2D structures.
The nucleus independent chemical shift (NICS) values and magnetic susceptibility tensors were calculated using the Gaussian 03 package  at the B3LYP/6-311++G(d, p) level of theory. To obtain the NICS values, we have used the gauge-independent atomic orbital method, and the magnetic susceptibility tensors were calculated using the continuous set of gauge transformations method.
The quantum Monte Carlo calculations have been done using the QWalk  package in two steps. The first step involved optimizing the trial many-body wave function by doing variational Monte Carlo calculations. The trial wave function was of the Slater-Jastrow form. The Slater determinants were constructed using B3LYP orbitals, generated using the GAMESS-US code with the previously optimized geometries within the B3LYP/6-311++G(d, p) level of theory. For the calculations, we have used Gaussian basis sets with effective core potentials . In the second step, we have done fixed-node diffusion Monte Carlo (DMC) calculations with the previously optimized trial wave functions. In the computations, we have used a time step of 0.005 a.u. The DMC error bars are about 0.1 eV.
Planar vs icosahedral structures
Similar results to those presented in Figure 3 were reported for the icosahedral and quasi-planar B12H n + structures . However, in their recent work, Ohishi et al.  have used the PBE0 functional instead of the B3LYP functional to determine the energies of the B12H n + clusters. The authors' choice was motivated by the fact that the B3LYP functional may overestimate the energy difference between 2D and 3D structures. To address this problem, we calculated the energy difference between the 2D and 3D structures of B12, B12H6, and B12F6 using the very accurate DMC approach. The DMC E2D - E3D values are -5.13, 0.79, and -0.47 eV for B12, B12H6, and B12F6, respectively, whereas the corresponding B3LYP values are -5.34, 0.41, and -0.63 eV, respectively (see Figure 3). This means that the DMC values are shifted up by a value not larger than about 0.4 eV with respect to the B3LYP values. This, however, does not affect the conclusions that are drawn from Figure 3, since even if we shift up the curves by 0.4 eV, the quasi-planar B12H n and B12F n (n = 0 to 4), and the fully planar B12F6 clusters still remain energetically favorable.
Fully planar clusters: B12H6 vs B12F6
As calculated here and also reported in , the fully planar B12H6 cluster corresponds to a local minimum of energy, whereas the D3h-B12F6 structure wins the competition with other 2D and 3D isomers and corresponds to a global minimum of energy. Many properties of the B12H6 cluster have been previously described in , but for consistency purposes, we have repeated some of those calculations at the B3LYP/6-311++G(d, p) level of theory. The highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of the planar B12H6 and B12F6 structures are 3.54 and 4.39 eV, respectively, whereas the HOMO-LUMO gaps of the corresponding 3D clusters are the same and equal to 2.73 eV. The B-H and B-F interatomic distances are 1.179 and 1.326 Å in B12H6 and B12F6, respectively. For comparison, the computed B-H and B-F bond lengths in borane (BH3) and boron trifluoride (BF3) are 1.190 and 1.318 Å, respectively.
While both 2D structures, B12H6 and B12F6, have similar shape and size, they exhibit quite different magnetic properties that are directly related to aromaticity. First, we have computed the anisotropy of magnetic susceptibility. The values for B12H6 and B12F6 are -208.1 and -125.8 cgs ppm, respectively. The isotropic values of the magnetic susceptibility are -91.9 and -118.2 cgs ppm for B12H6 and B12F6, respectively. These results suggest that the induced ring current is stronger for B12H6 than for B12F6. Similarly, as reported in  for B12H6, the central part of the B12F6 molecule has a paratropic current flowing inside the inner B3 triangle. The antiaromaticity of the inner triangle is, however, smaller for B12F6 than for B12H6 since the NICS(0) values are 3.9 and 13.3 ppm, respectively. A global aromatic current is dominant above the B12F6 (B12H6) molecule since the NICS values are negative, NICS(1) = -5.5 ppm (-3.6 ppm) and NICS(2) = -4.8 ppm (-5.0 ppm), 1 and 2 Å above and below the center of the cluster.
Our density functional theory and quantum Monte Carlo results show that the B12H n and B12F n (n = 0 to 4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters and that the fully planar B12F6 cluster is more stable than the 3D counterpart. We have also shown that negative or positive charge further stabilizes the 3D over the 2D B12X6 (X = H, F) clusters (except for B12X62+, where the opposite is observed). Our findings are potentially useful for designing larger boron-based nanostructures starting from quasi-planar or fully planar building blocks.
The authors would like to acknowledge the support given by the Robert A. Welch Foundation (grant J-1675), the NSF CREST CRCN center (grant HRD-1137732), and the Texas Southern University High Performance Computing Center (http://hpcc.tsu.edu/; grant PHY-1126251).
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