Supersymmetry approaches to the radial bound states of the hydrogen‐like atoms

Various structural possibilities for Al_nN and Al_nN₂ (n = 1–7) neutral and cationic isomers are investigated, using the density functional method of Becke's three‐parameter hybrid exchange functional with the Lee–Yang–Parr nonlocal correlation. Structural optimization and frequency analyses are performed with the basis of 6‐311+G(d) for both the neutrals and cations. The calculations predicted the existence of a number of previously unknown isomers (i.e., Al₅N₂ and Al₆N₂). The resulting geometries show that the nitrogen atom prefers to be trapped and not to be on the periphery. Frequency analyses indicate that the 3‐D Al₅N, which was previous proposed as the ground‐state structure, is in fact a first‐order stationary point with an imaginary frequency at 45i (a₂). The optimized ground‐state structure of Al₅N obtained in this work is a planar configuration with the symmetry of C_2v. The calculated adiabatic ionization potentials in their ground states showed that AlN, Al₂N, Al₃N, and Al₄N₂ clusters are more stable than any others in Al_nN and Al_nN₂ (n = 1–7) species, being consistent with the observed time‐of‐flight (TOF) signal intensities. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005