The Perdew-Burkle-Ernzerhof form generalized gradient approximation corrections are adopted for the exchange-correction potential [36]. The atomic orbital set employed throughout is a double-ζ plus polarization function. The numerical

integrals are performed and projected on a real space grid with an equivalent cutoff of 120 Ry for calculating the self-consistent Hamiltonian matrix elements. For boron nanowires under study, periodic boundary condition along the wire axis is employed with a lateral vacuum region larger than 25 Å to avoid the image interactions. The supercell of boron nanowires respectively contains one unit cell of α-B and β-B as translational unit growing along different directions. To determine the equilibrium configurations of these boron nanowires, we relax all atomic coordinates involved using a conjugate gradient buy BAY 73-4506 algorithm until the maximum atomic force of less than 0.02 eV/Å is achieved. In the calculations of the total energies and the energy band selleck inhibitor structures, we use four k sampling points along the tube axis according to the Monkhorst-Pack approximation. Cohesive energy (E c ) is calculated according to the expression, E c   = (E total  − n × E B ) / n, where E total is the total energy of the considered

boron nanowire, n is the number of B atoms, and E B is the energy of an isolated B atom. Results and discussion Firstly, we construct the stable configurations of the bulk α-B and β-B. The optimized configurations in the present study keep the same perfect structure as previously proposed [28, 29]. Also, according to the structural characteristic of the bulk α-B and β-B, in the following study, six possible representative nanowires are considered. Three were obtained

from the unit cell of α-B, growing along three base vectors, respectively. The other three were from the unit cell of β-B, also growing respectively Epothilone B (EPO906, Patupilone) along the base vectors. The corresponding boron nanowires are denoted according to the based bulk boron and their growth direction, named by α-a [100], α-b [010], α-c [001], β-a [100], β-b [010], and β-c [001]. For all these constructed boron nanowires, we perform a complete geometry optimization including spin polarization. Their equilibrium configurations are respectively shown in Figure 1a,b,c,d,e,f, where the left and right are respectively the side and top views for the same configuration. These results thus reveal that the optimized configurations of the six under-considered boron nanowires still keep the same perfect B-B bond structure as those in the bulk boron. To evaluate the stability of these boron nanowires, we calculate their cohesive energies by determining the cohesive energies according to the definition discussed previously. The calculated cohesive energies are listed in the first find more column of Table 1. For comparison, in Table 1, we also give the cohesive energies calculated at the same theoretical level of the bulk α-B and β-B.