The symmetry of the boron buckyball and a related boron nanotube

doi:10.1016/j.cplett.2010.05.086

Chemical Physics Letters

Volume 494, Issues 1–3, 9 July 2010, Pages 80-83

https://doi.org/10.1016/j.cplett.2010.05.086 Get rights and content

Abstract

We investigate the symmetry of the boron buckyball and a related boron nanotube. Using large-scale ab initio calculations up to second-order Møller–Plesset perturbation theory, we have determined unambiguously the equilibrium geometry/symmetry of two structurally related boron clusters: the B₈₀ fullerene and the finite-length (5 0) boron nanotube. The B₈₀ cluster was found to have the same symmetry, I_h, as the C₆₀ molecule since its 20 additional boron atoms are located exactly at the centers of the 20 hexagons. Additionally, we also show that the (5 0) boron nanotube does not suffer from atomic buckling and its symmetry is D_5d instead of C_5v as has been described by previous calculations. Therefore, we predict that all the boron nanotubes rolled from the α-sheet will be free from structural distortions, which has a significant impact on their electronic properties.

Graphical abstract

Research highlights

► As reported from density functional calculations the minimum energy structure of the boron fullerene is T_h ► Extensive calculation using MP2 show that the boron fullerene ground state structure is I_h, the soccer ball symmetry ► Additional calculations using MP2 on a (5 0) boron nanotube also show that the central atom buckling does not exist ► This will have significant impact on the gap of the boron nano-tubes which will have an effect on the electronic properties (metal or semiconductor).

Introduction

Only recently the most energetically stable boron sheet, the so called α-sheet [1], has been theoretically described. This sheet is closely related to the very stable boron fullerene, B₈₀, which is predicted to be the boron analog of the famous C₆₀ fullerene [2], [3]. The α-sheet is also a precursor of boron nanotubes [4] whose theoretical study is very important in the light of the recent experimental verification [5]. The boron nanotubes had been investigated theoretically (see Refs. [6], [7], [8] and references therein) previous to the first boron tubular forms being synthesized. Additionally, small planar and quasi-planar boron clusters have also been extensively studied both experimentally and theoretically [9]. Together, these efforts have made possible the deeper understanding of the most likely stable structure of all-boron nanotubes, fullerenes and sheets, but more work still needs to be done.

The structural analogy between the B₈₀ and the boron nanotubes has been demonstrated in Refs. [10], [11]. Furthermore, Zope et al. have shown the link between B₈₀ and the α-sheet [12]. Despite all the success of the theoretical description of the B₈₀ cluster, whose structure ‘inspired’ many other investigations, the description of its symmetry is still controversial. The B₈₀ cluster was originally predicted to have the full icosahedral symmetry [2]. These calculations were done using the DFT-GGA approach. In a later publication, Gopakumar et al. have shown that the symmetry of the boron structure is not I_h, but instead, the cluster slightly distorts into the T_h symmetry [13] where two such structural distortions, called A and B, have been identified at both Hartree–Fock (HF) and hybrid B3LYP levels of theory. In comparison to our results, Gopakumar et al. have shown that the energy difference between the T_h and I_h isomers at the B3LYP/6-31G(d) level of theory is 0.50 kcal/mol. Our result is 0.15 kcal/mol at a very similar level of theory (please see Table 1 for B3LYP/cc-pVDZ). Additionally, Gopakumar et al. have calculated the energy difference of 17.08 kcal/mol at the HF/6-31G(d) level of theory whereas we have calculated the energy difference of 14.87 kcal/mol at the HF/cc-pVDZ levels of theory. The symmetry of B₈₀ was also addressed in several other later papers [14], [15], [16]. For instance, Sadrzadeh et al. demonstrated that in fact there is not one but three isomers, of C₁, T_h, and I_h symmetries, which are close in energy and have almost identical structures [15].

The ambiguity in the description of the symmetry of the B₈₀ fullerene using pure DFT or hybrid approaches motivated us to investigate the structure of this cluster using the abinitio second-order Møller–Plesset perturbation method (MP2). This method, although computationally expensive, is characterized by a much more accurate description of electron correlation effects than the DFT or hybrid HF/DFT methods can achieve. Additionally, we have extended our investigation to the finite-length boron (5 0) nanotube using the MP2 approach.

Section snippets

Computational details

The calculations have been carried out using both symmetry restricted and unrestricted methodologies. The computations with restricted symmetry have been done using the NWChem code suite [17]. We have done pure DFT (BLYP), hybrid DFT (B3LYP), HF, and MP2 calculations. The vibrational analysis and IR spectrum where obtained using tight convergence criteria. The symmetry unrestricted calculations have been done using the FreeON code suite [18]. The PBE, PBE0, and X3LYP functionals [19] have been

Boron buckyball

Several tests for the structure and symmetry of B₈₀ have been performed at the MP2/STO-3G level of theory. First, we did several computations at the B3LYP/STO-3G level of theory. At this level, the total energy difference between clusters confined to I_h and T_h (isomer A from Ref. [13]) symmetries is ΔE = 36.41 kcal/mol (see Table 1), with the structure with T_h symmetry being energetically more favorable. The 20 atoms that are located above or below the hexagonal rings of the B₆₀ frame are divided

Conclusions

In conclusion, we have done extensive calculations at various levels of theory to determine the equilibrium geometry of the B₈₀ cage and a related boron nanotube. We have determined that the equilibrium geometry of B₈₀ is I_h, the same as for C₆₀, and of the boron nanotube is D_5d. From these results, we have asserted that a high level description of the correlation effects is essential for the correct description of the structure of these and other hollow boron nanostructures.

Acknowledgment

We would like to thank the Robert A. Welch Foundation (Grant J-1675) for their support of this project. The authors would also like to acknowledge the High Performance Computing Center (URL: http://hpcc.tsu.edu/) at Texas Southern University for providing resources that have contributed to the research results reported within this paper.

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The symmetry of the boron buckyball and a related boron nanotube

Abstract

Graphical abstract

Research highlights

Introduction

Section snippets

Computational details

Boron buckyball

Conclusions

Acknowledgment

Chem. Phys. Lett.

Coord. Chem. Rev.

Coord. Chem. Rev.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. B

J. Phys. Chem. B

Inorg. Chem.

ChemPhysChem

Boron and boron carbide materials: nanostructures and crystalline solids

Nanoscale Res. Lett.