Magic Number Behaviour and Structures of Silicon Dioxide-Based Clusters

The lowest energy structures of (SiO₂)_nO₂ cluster skeletons with size from n=2 to 12 is investigated theoretically by genetic algorithm. The calculations based on the Tsuneyuki--Tsukada--Aoki--Matsui (TTAM) and Flikkema--Bromley (FB) potentials give the same result: n=4 and n=8 are the magic numbers in the virtual (SiO₂)_nO₂ cluster sequence. This conclusion is in agreement with the experimental observation on the (SiO₂)_nO₂H₃^- cluster sequence. The comparison of the present results with those from the density-functional-theory calculations on (SiO₂)_nO₂H₄ shows that addition of H atoms to the O terminals of (SiO₂)_nO₂ clusters to form the complex (SiO₂)_nO₂H₄ clusters has only minor influence on the relative energies and the structures of different isomers. This means that the magic behaviour of the clusters (SiO₂)_nO₂H₃^- (n=4, 8) observed in our previous experiment is originated from the stability of the cluster skeletons (SiO₂)_n0₂ (n=4, 8).