A quantitative tool to establish magic number clusters, ε3, applied in small silicon clusters, Si2-11
The present work focuses on establishing a function to rank the stability of small silicon clusters to characterize their magic numbers. This function is composed by a thermodynamic descriptor, the atomization Gibbs free energy, and indirect kinetic descriptors, the highest occupied molecular orbital energy and the lowest excitation energy of each system. The silicon clusters geometries were optimized using density functional theory within a hybrid meta-GGA approximation (M06), while the electronic energy was corrected by single-point calculation using CASPT2 level of theory to obtain the molecular properties. Both methodologies were combined with polarized diffused triple zeta, 6-311++G(3df,3pd), basis set for all atoms. Some molecular properties and their combinations were considered to create the aforementioned function to represent the clusters chemical stability and their magic numbers. The chosen stability ranking function, called ε3, presents results in agreement with the previous mass spectrometry experimental data identifying 4, 6, 7 and 10 as magic numbers for small silicon clusters. We believe this stability ranking function can be useful to study other intramolecular atomic and molecular clusters.
KeywordsStability ranking function Molecular properties Silicon clusters CASPT2
This work was supported by Brazilian agencies Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under grants 2017/07707-3 and 2017/01359-3, and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grants 307052/2016-8, 404337/2016-3, 309051/2016-9 and 406107/2016-5.
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