A quantitative tool to establish magic number clusters, ε3, applied in small silicon clusters, Si2-11

  • Gabriel F. S. Fernandes
  • Francisco B. C. Machado
  • Luiz F. A. FerrãoEmail author
Original Paper
Part of the following topical collections:
  1. XIX - Brazilian Symposium of Theoretical Chemistry (SBQT2017)


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.

Graphical abstract

Stability ranking function, ε31, applied on Sin (n = 2 - 11) clusters showing Fukui’s functions for the Sin (n = 2 – 11) obtained by the electronic density difference through CASPT2//M06/6-311++G(3df,3pd) with an isosurface value equal to 0.003


Stability 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.

Supplementary material

894_2018_3748_MOESM1_ESM.docx (167 kb)
ESM 1 (DOCX 167 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de QuímicaInstituto Tecnológico de AeronáuticaSão José dos CamposBrazil

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