Ab Initio Prediction of Boron Compounds Arising from Borozene: Structural and Electronic Properties
© to the authors 2009
Received: 15 September 2009
Accepted: 2 October 2009
Published: 21 October 2009
Structure and electronic properties of two unusual boron clusters obtained by fusion of borozene rings have been studied by means of first principles calculations based on the generalized-gradient approximation of the density functional theory. Moreover, a semiempirical tight-binding model has been appropriately calibrated for transport calculations on these clusters. Results show that the pure boron clusters are topologically planar and characterized by (3c–2e) bonds, which can explain, together with the aromaticity (estimated by means of NICS), the remarkable cohesive energy values obtained. Such feature makes these systems competitive with the most stable boron clusters to date. The energy gap values indicate that these clusters possess a semiconducting character, while when the larger system is considered, zero-values of the density of states are found exclusively within the HOMO–LUMO gap. Electron transport calculations within the Landauer formalism confirm these indications, showing semiconductor-like low bias differential conductance for these structures. Differences and similarities with carbon clusters are highlighted in the discussion.
KeywordsBoron clusters Borozene DFT NICS Transport
Boron is the first element in group IIIA of the periodic table, presents the external electronic configuration s 2 p 1 and possesses a variety of compounds second only to carbon. In several boron compounds [1, 2] the existence of multicenter bonds has been discovered, which arise from the electron deficiency of this element. Moreover, boron has a special place among the elements of the periodic table because of the wide variety of crystalline structure forms, i.e., polymorphism, which include nanotubes , nanoribbons , and nanoclusters [5, 6].
The interest in boron-based nanostructures has recently increased due to new studies of both the synthesis of single walled boron nanotubes (SWBNTs) and the prediction of ballistic conduction in SWBNTs [3, 6]; these findings, together with the properties that all boron nanotubes (a) are predicted to be metallic  and (b) are superconducting at low temperatures [8, 9], promoted their prospective applications in fabrication of novel electronic devices. The most stable boron structure is the α-rhombohedral bulk where boron icosahedra are centered on the edges of a rhombohedral unit cell .
Unlike the bulk boron compounds, boron clusters B n (n < 20) are quasiplanar, or even planar, with a symmetrical bond distribution, aromatic [11–13] and their existence is confirmed by the experiment . From the Aufbau principle postulated by Boustani  it follows that these quasiplanar isomers are more stable than their icosahedral counterparts. Recently Szwacki et al.  have predicted the existence of a planar and aromatic boron compound, named borozene, which has strong similitudes with benzene.
The molecule B60H12 here considered was built by fusing six borozene rings, for this reason it can be considered as the boron counterpart of coronene, whereas the structure of B228H24 was obtained by surrounding B60H12 with one series of borozene rings, therefore this cluster is constituted by a total of 24 borozene rings. A first optimization energy procedure was performed in the framework of the molecular mechanics approximation applying the CVFF Force Field [16, 17] which is enclosed in the Materials Studio package . The geometries obtained were fully optimized at a B3LYP/STO-3G [19–23] and B3LYP/6-311G [24, 25] level by using the quadratically convergent Self Consistent Field procedure .
In detail, due to the large size, the optimizations of B228H24 were carried out by means of the minimal basis set STO-3G whereas the more extended Pople basis set 6-311G was used in the optimizations of B60H12. In order to estimate the degree of aromaticity, the calculation of Nuclear Independent Chemical Shifts  on the plane of the aromatic system (NICS0) was computed using the Gaussian 03 package , applying the GIAO method [29, 30]. To obtain the contour plot of NICS, ghost atoms were placed on the plane of the molecule with a step size of about 1 Å.
Finally, electronic transport has been evaluated in the framework of the Nonequilibrium Green’s Function theory using a Landauer expression for the calculation of the current–voltage (I–V) characteristics . Consistently to the electron structure findings we assume that only p z orbitals contribute to the low bias transport along the molecules and that the Fermi energy is at the center of HOMO–LUMO gap. The molecular device configuration considered consists of two vertical gold leads in contact with the horizontal molecules forming ideal bonds with the boron atoms indicated in Fig. 1.
The analysis of the smaller cluster, henceforth named B6, was performed by using both basis sets mentioned above in order to make a consistent comparison with B228H24, henceforth named B24, analyzed only with the minimal basis set. We point out that the results obtained in the two cases are qualitatively equivalent, for this reason, unless specified, the data shown below are referred to the minimal basis set. As far as the boron–boron bond length is concerned, a shorter value has been found in the STO-3G optimized structure, in particular, taking into account cluster B6, the average value of this parameter is calculated to be, respectively, 1.649 and 1.638 Å for 6-311G and STO-3G basis set, while a bond length average of 1.629 Å is obtained for the cluster B24.
In the expressions above n is the number of boron atoms and the value of the B–H bond energy is calculated in the first approximation as 1/3 of the binding energy value of BH3. Structural parameters evaluated are competitive, in terms of stability, with the more stable flat two-dimensional structures considered up to date [32, 33]. It is well known that Boron has a variety of compounds containing multicenter bonds, in particular the three-center, two-electron (3c, 2e) bond is present in molecules such diborane , boron clusters  and boron sheets .
Previous works have shown that (3c, 2e) bonds preclude the formation of boron rings in boron clusters [6, 36], whereas, on the other hand, more recently the three-center bonding has been proposed to explain the stability of boron fullerenes [34, 37]. This peculiar feature is also seen for B6 and B24, while it is not present in Coronene and its larger clusters such Coronene 19, Coronene 37 and Coronene 61. Hence it is logical to assume that, as for boron fullerenes, it plays a pivotal role in maintaining a two-dimensional stable planar structure.
Energies and percentual contributes of p z orbitals to the composition of HOMO, LUMO and their nearest MOs
HOMO − 3
HOMO − 2
HOMO − 1
LUMO + 1
LUMO + 2
LUMO + 3
The symmetry of the plots reflects the assumed symmetry in the device configuration. A semiconductor-like behavior is evidenced in both structures. However, the zero bias differential conductance is one order of magnitude higher for the B24 cluster, this is due not only to the lower HOMO–LUMO gap but also to the larger value of the DOS. Delocalized (along the cluster) p z molecular orbitals allow an efficient charge transport through the cluster for larger bias (of the order of the gap) and a diode-like characteristic can be observed.
In this work first principles and semiempirical calculations were carried out to investigate both structural and electronic properties of two clusters obtained by condensation of 6 and 24 borozene molecules, considered as the analogs of Coronene and Coronene 19. Calculations predict a planar geometry for the pure clusters. Both (3c–2e) bonds and wide regions of aromaticity contribute to this stabilization, with cohesive energy values that are comparable with the most stable boron clusters considered to date.
Due to the high connectivity among boron atoms, we hypothesize that planar geometry could be compromised when impurities are introduced. Density of states spectra evidence a small gap, which decreases by increasing the cluster size, suggesting, at variance with carbon clusters, a semiconducting character in small sized clusters; furthermore the population analysis shows that the main contribution to the molecular orbitals near the GAP is due to π-bonds which derive from p z orbitals. Calculated low bias differential conductance for these structures confirms this semiconductor-like character.
G. Forte wishes to thank the Consorzio Interuniversitario Cineca for the computational support.
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