The European Physical Journal D

, Volume 57, Issue 1, pp 49–60 | Cite as

DFT and GEGA genetic algorithm optimized structures of Cun ν (ν=±1,0,2; n=3-13) clusters

  • G. Guzmán-RamírezEmail author
  • F. Aguilera-Granja
  • J. Robles
Clusters and Nanostructures


We report a study on small copper clusters \(\text{Cu}_n^{\nu}\) (ν= ±1,0,2; n=3-13) where the minimum energy structures were computed through a joint gradient embedded genetic algorithm (GEGA) technique, and further density functional theory (DFT) geometry reoptimization of the best GEGA cluster structures for each size and charge. Our results are compared to previous ab initio and DFT calculations, when available in the literature, and it is shown than a number of never reported structures for some clusters have been found. From an extensive calibration of some of the DFT commonly used approximate functionals and basis sets, a discussion on its performance and efficiency for Cu cluster calculations is provided. All GEGA found structures are subject to a second step DFT reoptimization process, at the final reported level of theory, BLYP/6-311+G(d), and it is observed that the symmetry found initially by GEGA for almost all of the 66 clusters studied is kept during the DFT reoptimization, which shows the reliability of the initial search algorithm employed. Several geometry-related-properties of these clusters are discussed and compared with some results available in the literature.


Density Functional Theory Potential Energy Surface Symmetry Point Group Lower Energy Structure Stable Isomer 
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  1. P.B. Balbuena, P.A. Derosa, J.M. Seminario, J. Phys. Chem. B 103, 2830 (1999) Google Scholar
  2. K. Jug, B. Zimmermann, P. Calaminici, A.M. Köster, J. Chem. Phys. 116, 4497 (2002) Google Scholar
  3. P. Jaque, A. Toro-Labbé, J. Chem. Phys. 117, 3208 (2002) Google Scholar
  4. V.E. Matulis, O.A. Ivashkevich, V.S. Gurin, J. Mol. Struct. Theochem 681, 169 (2004) Google Scholar
  5. E.M. Fernández, J.M. Soler, I.L. Garzón, L.C. Balbás, Phys. Rev. B 70, 165403 (2004) Google Scholar
  6. G.H. Guvelioglu, P. Ma, X. He, R.C. Forrey, H. Cheng, Phys. Rev. Lett. 94, 026103 (2005) Google Scholar
  7. M. Yang, K.A. Jackson, C. Koehler, T. Frauenheim, J. Jellinek, J. Chem. Phys. 124, 024308 (2006) Google Scholar
  8. P. Calaminici, A.M. Köster, Z. Gómez-Sandoval, J. Chem. Theory Comput. 3, 905 (2007) Google Scholar
  9. B. Assadollahzadeh, P.R. Bunker, P. Schwerdtfeger, Chem. Phys. Lett. 451, 262 (2008) Google Scholar
  10. C. Massobrio, A. Pasquarello, R. Car, Chem. Phys. Lett. 238, 215 (1995) Google Scholar
  11. R.C. Longo, L.J. Gallego, Phys. Rev. B 74, 193409 (2006) Google Scholar
  12. Ş. Erkoç, R. Shaltaf, Phys. Rev. A 60, 3053 (1999) Google Scholar
  13. M. Kabir, A. Mookerjee, A.K. Bhattacharya, Eur. Phys. J. D 31, 477 (2004) Google Scholar
  14. M. Böyükata, J.C. Belchior, J. Braz. Chem. Soc. 19, 884 (2008) Google Scholar
  15. S. Wang, Z.P. Liu, J. Lu, K.N. Fan, Acta Chimica Sinica 65, 1831 (2007) Google Scholar
  16. S. Darby, T.V. Mortimer-Jones, R.L. Johnstone, C. Roberts, J. Chem. Phys. 116, 1536 (2002) Google Scholar
  17. D.C. Young, Computational Chemistry (Wiley Interscience, New York, 2001) Google Scholar
  18. A.N. Alexandrova, A.I. Boldyrev, Y. Fu, X. Yang, X. Wang, L. Wang, J. Chem. Phys. 121, 5709 (2004) Google Scholar
  19. A.N. Alexandrova, A.I. Boldyrev, J. Chem. Theory Comput. 1, 566 (2005) Google Scholar
  20. M.J. Frisch et al., Gaussian 98, Revision A.7 (Gaussian Inc., Pittsburgh PA, 1998) Google Scholar
  21. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964) Google Scholar
  22. S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58, 1200 (1980) Google Scholar
  23. P.J. Hay, W.R. Wadt, J. Chem. Phys. 82, 270 (1985) Google Scholar
  24. D.M. Deaven, K.M. Ho, Phys. Rev. Lett. 75, 288 (1995) Google Scholar
  25. A.D. Becke, Phys. Rev. A 38, 3098 (1988) Google Scholar
  26. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988) Google Scholar
  27. Y. Wang, J.P. Perdew, Phys. Rev. B 43, 8911 (1991) Google Scholar
  28. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) Google Scholar
  29. J.M. Tao, J.P. Perdew, V.N. Staroverov, G.E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003) Google Scholar
  30. J.P. Perdew, Y. Wang, Phys. Rev. B 45, 13244 (1992) Google Scholar
  31. A.D. Becke, J. Chem. Phys. 98, 5648 (1993) Google Scholar
  32. K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand-Reinhold, New York, 1989), Vol. IV Google Scholar
  33. M.D. Morse, Chem. Rev. 86, 1049 (1986) Google Scholar
  34. J. Ho, K.M. Ervin, W.C. Lineberger, J. Chem. Phys. 93, 6987 (1990) Google Scholar
  35. A.M. James, G.W. Lemire, P.R.R. Langridge-Smith, Chem. Phys. Lett. 227, 503 (1994) Google Scholar
  36. M.J. Frisch et al., Gaussian 03, Revision D.02 (Gaussian Inc., Wallingford CT, 2004) Google Scholar
  37. H. Akeby, I. Panas, L.G.M. Pettersson, P. Siegbahn, U. Wahlgren, J. Phys. Chem. 94, 5471 (1990) Google Scholar
  38. S. Li, M.M.G. Alemany, J.R. Chelikowsky, J. Chem. Phys. 125, 034311 (2006) Google Scholar
  39. J. Oviedo, R.E. Palmer, J. Chem. Phys. 117, 9548 (2002) Google Scholar
  40. S. Krückeberg, L. Schweikhard, J. Ziegler, G. Dietrich, K. Lützenkirchen, C. Walther, J. Chem. Phys. 114, 2955 (2001) Google Scholar
  41. Y. Sun, M. Zhang, R. Fournier, Phys. Rev. B 77, 075435 (2008) Google Scholar
  42. M. Zhang, R. Fournier, Phys. Rev. A 79, 043203 (2009) Google Scholar
  43. C. Kittel, Introduction to Solid State Physics (Wiley, 2005) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • G. Guzmán-Ramírez
    • 1
    Email author
  • F. Aguilera-Granja
    • 2
  • J. Robles
    • 1
  1. 1.Posgrado en Química and Departmento de Farmacia, División de Ciencias Naturales y ExactasUniversidad of GuanajuatoGuanajuatoMexico
  2. 2.Instituto de Física, Universidad Autónoma de San Luis PotosíSan Luis PotosíMexico

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