Theoretical study of isomerism in nitrogen- and phosphorus-substituted aluminum clusters M6Al38 and M12Al32 (M = N, P)

Аннотация

More than 20 М₆Al₃₈ isomers and several М₁₂Al₃₂ isomers for nitrogen- and phosphorus-substituted clusters with six and twelve dopant atoms M = N and P substituted for Al atoms in different positions at the surface of the aluminum cage and inside it have been studied by the density functional theory method. In the preferred N₆Al₃₈ isomer, all N atoms are substituted for Al atoms initially located in one outer layer of the cluster. In the course of geometry optimization, the nitrogen atoms are incorporated into positions in the neighboring intermediate layer, thus converting it into a 12-atom face consisting of three vertex-sharing adjacent six-membered rings with short N–Al bonds. For Р₆Al₃₈, a distribution of the dopant either in both surface layers or in the intermediate space between the surface layers and the inner core of the cluster is preferred. Optimization of alternative structures of the N₁₂Al₃₂ cluster with N atoms substituted for Al atoms in both outer layers is evidence in favor of the isomer in which the dopants are dispersed as separated monatomic anions N–. Together with their bridging Al atoms, these anions form the inner [N₁₂Al₁₄] cage with an unusual dumbbell-like structure in which the upper and lower halves are linked through N–Al bonds with the equatorial aluminum atoms. In the next low-lying isomer being ~23 kcal/mol higher on the energy scale, there is observed the “microclustering” of the dopant to form three covalently bonded diatomic dianions N₂^2-; the latter, together with the bridging Al atoms are combined into a [N₆Al₆] “subcluster” inside the severely distorted outer cage. In P₁₂Al₃₂, the aluminum cage is subjected only to moderate distortions: the phosphorus atoms remain in the outer layers and form two three-membered rings [Р₃]. The estimated energies of the model substitution reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ (1) and Al₄₄ + 2M₆ → M₁₂Al₃₈ + 2A_l6 (2) demonstrate that all these reactions are exothermic; however, for the nitrogen-containing clusters, the decrease in energy with increasing number of substitutions increases from 66 (1) to 113 (2) kcal/mol, while in the case of phosphorus, it decreases from 45 (1) to 4 (2) kcal/mol. The results obtained for N₆Al₃₈, N₁₂Al₃₂, Р₆Al₃₈, and Р₁₂Al₃₂ are compared with the previous calculations for the C₆Al₃₈, C₁₂Al₃₂, Si₆Al₃₈, and Si₁₂Al₃₂ clusters.