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The stability, geometry and electronic structure of the title nanoclusters were compared by using density functional theory (DFT) calculations. Their electrical property analysis showed that the relative magnitude of the HOMO-LUMO gaps (eV) that are average values from the calculated results with five different DFT functionals is as follows: B12N12(7:02)>>Al12N12(4.09)>B12P12(3.80)>Al12P12(3.39). Computing the standard enthalpy and the Gibbs free energy of formation, it was found that the B(12)N(12) structure is thermodynamically stable at 298 K and 1 atmosphere of pressure, while the Al(12)N(12) structure may be stable at low temperatures. Due to positive values of change of enthalpy and entropy of formation for both the B(12)P(12) and Al(12)P(12) clusters, it seems that their formation from the consisting atoms is not spontaneous at any temperature.

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The NO2 molecule adsorption on B12N12 nano-cage was investigated using density functional theory calculations in terms of adsorption energy, HOMO/LUMO energy gap (Eg) changes, charge transfer, structural deformation, etc. Furthermore, some aspects of stability and properties of B12N12 including calculation of binding electronic and Gibbs free energies, density of states, and molecular electrostatic potential surfaces are investigated. Three possible configurations for NO2 adsorption on the B12N12 nano-cage are energetically found. Interestingly, the results reveals that the Eg of B12N12 cluster is very sensitive to the presence of NO2 molecules as its value reduces from 6.84 eV in free cluster to 3.23 eV in the most stable configuration of NO2/cluster complex. This phenomenon dramatically increases the electrical conductivity of the cluster, suggesting that the B12N12 nano-cluster may be potential sensor for NO2 gaseous molecule detection.

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