Search strategy for stable isomers of silicon clusters encapsulating certainfourth-period transition metals
DOI:
https://doi.org/10.17308/kcmf.2026.28/13966Keywords:
Atomic clusters, Silicon clusters, Density functional theory, Electronic spectrumAbstract
Objectives: A modification of the Wade-Mingos rule is proposed to predict the stable isomers of silicon-metal clusters. According to this modification, stable isomers composed of n silicon atoms with 4n+4 and 4n+6 valence electrons are formed by removing one or two vertices, respectively, from the structures of stable isomers with 4n+2 valence electrons.
Computational method: To demonstrate the modified rule, the atomic structures and electronic spectra of MeSi15 – (Me = Sc, V) clusters calculated using four different DFT functionals are presented. The atomic structures of the most stable isomers are described. The influence of the choice of functional on the cluster geometry optimization results is investigated.
Conclusions: A comparison of the calculated electronic spectra of the stable isomers with the experimental photoelectron spectrum allowed for the determination of which isomers can be obtained experimentally
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1. Kroto H., Heath J., O’Brien S., Curl R. F., Smalley R. E. C60: Buckminsterfullerene. Nature. 1985;318: 162–163. https://doi.org/10.1038/318162a0
2. Honea E., Ogura A., Murray C., Raghavachari K., … Brown W. L. Raman spectra of size-selected silicon clusters and comparison with calculated structures. Nature. 1993;366: 42–44. https://doi.org/10.1038/366042a0
3. Röthlisberger U., Andreoni W., Parrinello M. Structure of nanoscale silicon clusters. Physical Review Letters. 1994;72: 665–668. https://doi.org/10.1103/PhysRevLett.72.665
4. Ho K.-M., Shvartsburg A. A., Pan B., … Jarrold M. F. Structures of medium-sized silicon clusters. Nature. 1998;392: 582–585. https://doi.org/10.1038/33369
5. Maus M., Ganteför G., Eberhardt W. The electronic structure and the band gap of nano-sized Si particles: competition between quantum confinement and surface reconstruction. Applied Physics A. 2000; 70: 535–539. https://doi.org/10.1007/s003390051075
6. Hiura H., Miyazaki T., Kanayama T. Formation of metal-encapsulating Si cage clusters. Physical Review Letters. 2001; 86: 1733–1736. https://doi.org/10.1103/PhysRevLett.86.1733
7. Ohara M., Koyasu K., Nakajima A., Kaya K. Geometric and electronic structures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo and W). Chemical Physics Letters. 2003;371(3–4): 490–497. https://doi.org/10.1016/S0009-2614(03)00299-9
8. Iwasa T., Nakajima A. Geometric, electronic, and optical properties of a superatomic heterodimer and trimer:Sc@Si16–V@Si16 and Sc@Si16–Ti@Si16–V@Si16. The Journal of Physical Chemistry C. 2012;116: 14071–14077. https://doi.org/10.1021/jp302752g
9. Lu S. J. Exploring the structural evolution and electronic properties of medium-sized Nb2Sin −/0 (n = 13–20) clusters by density functional theory calculations. Chemical Physics Letters. 2018;713: 58–64. https://doi.org/10.1016/j.cplett.2018.10.028
10. Dong C., Han L., Yang J., Cheng L. Study on structural evolution, thermochemistry and Eelectron affinity of neutral, mono- and di-anionic zirconium-doped silicon clusters ZrSin 0/-/2-(n = 6–16). International Journal of Molecular Sciences. 2019;20: 2933. https://doi.org/10.3390/ijms20122933
11. Lu S. J., Xu H. G., Xu X. L., Zheng W. J. Structural evolution and electronic properties of TaSin–/0 (n = 2–15) clusters: size-selected anion photoelectron spectroscopy and theoretical calculations. The Journal of Physical Chemistry A. 2020;124(47): 9818–9831. https://doi.org/10.1021/acs.jpca.0c09209
12. Dong C., Yang J., Lu J. Structural and electronic properties of nanosize semiconductor HfSin 0/−/2− (n = 6–16) material: a double-hybrid density functional theory investigation. Journal of Molecular Modeling. 2020;26: 85. https://doi.org/10.1007/s00894-020-04352-1
13. Koyasu K., Atobe J., Furuse S., Nakajima A. Anion photoelectron spectroscopy of transition metal- and lanthanide metal-silicon clusters: MSin − (n = 6–20). The Journal of Chemical Physics. 2008;129(21): 214301. https://doi.org/10.1063/1.3023080
14. Xu H. G., Zhang Z. G., Feng Y., Yuan J., Zhao Y., Zheng W. Vanadium-doped small silicon clusters: photoelectron spectroscopy and density-functional calculations. Chemical Physics Letters. 2010;487(4–6): 204–208. https://doi.org/10.1016/j.cplett.2010.01.050
15. Xu H. G., Wu M. M., Zhang Z. G., Yuan J., Qiang Sun Q., Zheng W. Photoelectron spectroscopy and density functional calculations of CuSin − (n = 4–18) clusters. The Journal of Chemical Physics. 2012;136(10): 104308. https://doi.org/10.1063/1.3692685
16. Yang B., Xu X. L., Zheng W. J., Xu H. G. Structural evolution and bonding properties of Cr2Sin– (n = 1–12) Clusters: mass-selected anion photoelectron spectroscopy and theoretical calculations. The Journal of Physical Chemistry A. 2022;126(7): 1182–1193. https://doi.org/10.1021/acs.jpca.1c10810
17. Wang K., Zhao H. Y., Miao L., … Ma L. Photoelectron spectroscopy and density functional investigation of the structural evolution, electronic, and magnetic properties of CrSin– (n = 14–18) clusters. The Journal of Physical Chemistry A. 2022;126(8): 1329–1335. https://doi.org/10.1021/acs.jpca.1c09557
18. Zhang Y., Yang J., Cheng, L. Probing structure, thermochemistry, electron affinity and magnetic moment of erbium-doped silicon clusters ErSin (n = 3–10) and their anions with density functional theory. Journal of Cluster Science. 2018;29: 301–311. https://doi.org/10.1007/s10876-018-1336-z
19. Lu J., Lu Q., Li X. Structures, simulated photoelectron spectroscopy, and electronic properties of CuASix (A = Sc, Cu, x ≤ 13) clusters: relatively stable neutral pentagonal bipyramid structures of CuASi5. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy. 2025;326: 125196. https://doi.org/10.1016/j.saa.2024.125196
20. Chen Y., Liu Y., Li S., Yang J. Theoretical study on the growth behavior and photoelectron spectroscopy of lanthanum-doped silicon clusters LaSi0/−n (n = 6–20). Journal of Cluster Science. 2019;30: 789–796. https://doi.org/10.1007/s10876-019-01541-8
21. Wade K. The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds. Journal of the Chemical Society D: Chemical Communications. 1971;15: 792–793. https://doi.org/10.1039/C29710000792
22. Mingos D. M. P. A general theory for cluster and ring compounds of the main group and transition elements. Nature Physics Science. 1972;236(68): 99–102. https://doi.org/10.1038/physci236099a0
23. Mingos D. M. P. Polyhedral skeletal electron pair approach. Accounts of Chemical Research. 1984;17: 311–319. https://doi.org/10.1021/ar00105a003
24. Becke A. D. Density-functional thermochemistry. III. The role of exact exchange. The Journal of Chemical Physics. 1993;98: 5648–5652. https://doi.org/10.1063/1.464913
25. Lee C., Yang W., Parr R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Physical Review B, Condensed Matter and Material Physics. 1988;37(2): 785–789. https://doi.org/10.1103/physrevb.37.785
26. Vosko S. H., Wilk L., Nusair M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Canadian Journal of Physics. 1980;58(8): 1200-1211. https://doi.org/10.1139/p80-159
27. Stephens P. J., Devlin F. J., Chabalowski C. F., Frisch M. J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. The Journal of Phyical Chemistry. 1994;98: 11623–11627. https://doi.org/10.1021/j100096a001
28. Becke A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Physical Review A, General Physics. 1988;38(6): 3098–3100. https://doi.org/10.1103/PhysRevA.38.3098
29. Perdew J. P., Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Physical Review B, Condensed Matter and Material Physics. 1992;45(23): 13244–13249. https://doi.org/10.1103/Phys-RevB.45.13244
30. Becke A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Physical Review A. 1988;38: 3098–3100. https://doi.org/10.1103/PhysRevA.38.3098
31. Perdew J. P., Burke K., Ernzerhof M. Generalized gradient approximation made simple. Physical Review Letters. 1996;77: 3865–3868. https://doi.org/10.1103/PhysRev-Lett.77.3865
32. Perdew J. P., Burke K., Ernzerhof M. Errata: generalized gradient approximation made simple. Physical Review Letters. 1997;78: 1396. https://doi.org/10.1103/PhysRev-Lett.78.1396
33. Rappoport D., Furche F. Property-optimized Gaussian basis sets for molecular response calculations. The Journal of Chemical Physics. 2010;133: 134105. https://doi.org/10.1063/1.3484283
34. Weigend F., Ahlrichs R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Physical Chemistry Chemical Physics. 2005;7: 3297–3305. https://doi.org/10.1039/b508541a
35. Gaussian 09, Revision D.01. Frisch M. J., Trucks G. W., Schlegel H. B., … Fox D. J. Gaussian, Inc., Wallingford CT, 2013. http://gaussian.com/g09citation 36. Pritchard B. P., Altarawy D., Didier B., Gibson T. D., Windus T. L. New basis set exchange: an open, up-to-date resource for the molecular sciences community. Journal of Chemical Information and Modeling. 2019;59: 4814–4820. https://doi.org/10.1021/acs.jcim.9b00725
37. Feller D. The role of databases in support of computational chemistry calculations. Journal of Computational Chemistry. 1996;17: 1571–1586. https://doi.org/10.1002/(sici)1096-987x(199610)17:13<1571::aid-jcc9>3.0.co;2-p
38. Schuchardt K. L., Didier B. T., Elsethagen T., … Windus T. L. Basis set exchange: a community database for computational sciences. Journal of Chemical Information and Modeling. 2007;47: 1045–1052. https://doi.org/10.1021/ci600510j
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