Theoretical study of isomerism of carbonand silicon-substituted aluminum clusters M6Al38 and M12Al32

More than twenty M6Al38 isomers and several M12Al32 isomers of carbon- and silicon-substituted aluminum clusters with six and twelve dopant atoms of general formula MnAl44–n(M = C and Si, n = 6 and 12) have been studied by the density functional theory method. Calculations predict that, in the lowest-lying M6Al38, isomer, all substitutions of C atoms for Al are localized in one outer surface layer of the aluminum cage. In the course of optimization, the C atoms with a negative charge of about 1e are incorporated into positions of the intermediate layer to transform it into a 12-atom face composed of three adjacent vertex-sharing six-membered rings with short C–Al bonds. In the favorable isomer of M6Al38, the dopants are scattered as individual Si atoms located in both outer layers or in the subsurface space between the outer layers and the inner core of the cluster. Optimization of low-lying isomers with twelve starting substitutions of C and Si for Al in both outer layers has localized two preferable C12Al32 isomers. One of them contains three covalently bonded diatomic C2 anions, which are combined through bridging aluminum atoms in the three-dimensional [C6Al7] cluster inside the severely distorted outer cage. In the second, most favorable, isomer, the dopants are distributed as isolated C anions; together with the bridging Al atoms, they form the [M12Al32] inner cage with an unusual dumbbell-like structure. For M12Al32, the aluminum cage undergoes moderate distortions. The silicon atoms remain in the outer layers and form five-membered ring subclusters [Si5] and [Si2Al3] bound to the neighboring intermediate layers through elongated and weakened Si–Al bonds. Evaluation of the energies of the model exchange reactions Al44 + M6 → M6Al38 + Al6 and Al44 + 2M6 → M12Al32 + 2Al6 shows that for M= C both reaction are exothermic, whereas for M = Si the former reaction is nearly isothermal and the second reaction is endothermic and requires significant energy inputs. The differences between the equilibrium structures and the relative positions on the energy scale of the isomers of the C6Al38–Si6Al38 and C12Al38–Si12Al38 clusters are examined.