Skip to main content
SpringerLink
Log in

Glass-like energy and property landscape of Pt nanoclusters

  • Research Article
  • Published:
Nano Research Aims and scope Submit manuscript

Abstract

Pt nanoclusters play an important role in catalysis-related applications. Essential to their activities are their geometries and energy landscapes. In this work, we studied the energy landscapes of Pt clusters using a parallel differential evolution optimization algorithm and an accelerated ab initio atomic relaxation method, which allowed us to explore unprecedentedly large numbers of geometry local minima at ab initio level. We found many lower-energy isomers with low symmetry in their geometry. The energy landscapes were demonstrated to be glass-like with a large number of local minimum structures close to the global minimum. The electronic and magnetic properties of most glass-like local minima were dramatically different from the global minimum, and they should be observed in the experimental measurements. The connections between these local minima were further analyzed using data mining techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Vayssilov, G. N.; Lykhach, Y.; Migani, A.; Staudt, T.; Petrova, G. P.; Tsud, N.; Skála, T.; Bruix, A.; Illas, F.; Prince, K. C. et al. Support nanostructure boosts oxygen transfer to catalytically active platinum nanoparticles. Nat. Mater. 2011, 10, 310–315.

    Article  Google Scholar 

  2. Allian, A. D.; Takanabe, K.; Fujdala, K. L.; Hao, X. H.; Truex, T. J.; Cai, J.; Buda, C.; Neurock, M.; Iglesia, E. Chemisorption of CO and mechanism of CO oxidation on supported platinum nanoclusters. J. Am. Chem. Soc. 2011, 133, 4498–4517.

    Article  Google Scholar 

  3. Chin, Y. H.; Buda, C.; Neurock, M.; Iglesia, E. Reactivity of chemisorbed oxygen atoms and their catalytic consequences during CH4-O2 catalysis on supported Pt clusters. J. Am. Chem. Soc. 2011, 133, 15958–15978.

    Article  Google Scholar 

  4. Vajda, S.; Pellin, M. J.; Greeley, J. P.; Marshall, C. L.; Curtiss, L. A.; Ballentine, G. A.; Elam, J. W.; Catillon-Mucherie, S.; Redfern, P. C.; Mehmood, F. et al. Subnanometre platinum clusters as highly active and selective catalysts for the oxidative dehydrogenation of propane. Nat. Mater. 2009, 8, 213–216.

    Article  Google Scholar 

  5. Viñes, F.; Gomes, J. R. B.; Illas, F. Understanding the reactivity of metallic nanoparticles: Beyond the extended surface model for catalysis. Chem. Soc. Rev. 2014, 43, 4922–4939.

    Article  Google Scholar 

  6. Baletto, F.; Ferrando, R. Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects. Rev. Mod. Phys. 2005, 77, 371–423.

    Article  Google Scholar 

  7. Ferrando, R.; Jellinek, J.; Johnston, R. L. Nanoalloys: From theory to applications of alloy clusters and nanoparticles. Chem. Rev. 2008, 108, 845–910.

    Article  Google Scholar 

  8. Johnston, R. L. Atomic and Molecular Clusters; Taylor and Francis: London, UK, 2002.

    Book  Google Scholar 

  9. Marks, L. D. Experimental studies of small particle structures. Rep. Prog. Phys. 1994, 57, 603–649.

    Article  Google Scholar 

  10. Wales, D. J.; Scheraga, H. A. Global optimization of clusters, crystals, and biomolecules. Science 1999, 285, 1368–1372.

    Article  Google Scholar 

  11. De, S.; Schaefer, B.; Sadeghi, A.; Sicher, M.; Kanhere, D. G.; Goedecker, S. Relation between the dynamics of glassy clusters and characteristic features of their energy landscape. Phys. Rev. Lett. 2014, 112, 083401.

    Article  Google Scholar 

  12. Schaefer, B.; Pal, R.; Khetrapal, N. S.; Amsler, M.; Sadeghi, A.; Blum, V.; Zeng, X. C.; Goedecker, S.; Wang, L. S. Isomerism and structural fluxionality in the Au26 and Au26 - nanoclusters. ACS Nano 2014, 8, 7413–7422.

    Article  Google Scholar 

  13. Gerber, T.; Knudsen, J.; Feibelman, P. J.; Gránä s, E.; Stratmann, P.; Schulte, K.; Andersen, J. N.; Michely, T. Co-induced smoluchowski ripening of Pt cluster arrays on the graphene/Ir(111) moiré. ACS Nano 2013, 7, 2020–2031.

    Article  Google Scholar 

  14. Kumar, V.; Kawazoe, Y. Evolution of atomic and electronic structure of Pt clusters: Planar, layered, pyramidal, cage, cubic, and octahedral growth. Phys. Rev. B 2008, 77, 205418.

    Article  Google Scholar 

  15. Xiao, L.; Wang, L. C. Structures of platinum clusters: Planar or spherical? J. Phys. Chem. A 2004, 108, 8605–8614.

    Article  Google Scholar 

  16. Wang, X. L.; Tian, D. X. Structures and structural evolution of Ptn (n = 15–24) clusters with combined density functional and genetic algorithm methods. Comput. Mater. Sci. 2009, 46, 239–244.

    Article  Google Scholar 

  17. Chen, Z. H.; Jiang, X. W.; Li, J. B.; Li, S. S.; Wang, L. W. PDECO: Parallel differential evolution for clusters optimization. J. Comp. Chem. 2013, 34, 1046–1059.

    Article  Google Scholar 

  18. Doye, J. P. K.; Wales, D. J. Global minima for transition metal clusters described by Sutton–Chen potentials. New J. Chem. 1998, 22, 733–744.

    Article  Google Scholar 

  19. Pavan, L.; Di Paola, C.; Baletto, F. Sampling the energy landscape of Pt13 with metadynamics. Eur. Phys. J. D 2013, 67, 24.

    Article  Google Scholar 

  20. Chaves, A. S.; Rondina, G. G.; Piotrowski, M. J.; Tereshchuk, P.; Da Silva, J. L. F. The role of charge states in the atomic structure of Cun and Ptn (n = 2–14 atoms) clusters: A DFT investigation. J. Phys. Chem. A 2014, 118, 10813–10821.

    Article  Google Scholar 

  21. Goedecker, S.; Hellmann, W.; Lenosky, T. Global minimum determination of the Born–Oppenheimer surface within density functional theory. Phys. Rev. Lett. 2005, 95, 055501.

    Article  Google Scholar 

  22. Bhattacharyya, K.; Majumder, C. Growth pattern and bonding trends in Ptn (n = 2–13) clusters: Theoretical investigation based on first principle calculations. Chem. Phys. Lett. 2007, 446, 374–379.

    Article  Google Scholar 

  23. Lai, X. J.; Xu, R. C.; Huang, W. Q. Geometry optimization of bimetallic clusters using an efficient heuristic method. J. Chem. Phys. 2011, 135, 164109.

    Article  Google Scholar 

  24. Zhai, H. C.; Ha, M. A.; Alexandrova, A. N. AFFCK: Adaptive force-field-assisted ab initio coalescence kick method for global minimum search. J. Chem. Theory Comput. 2015, 11, 2385–2393.

    Article  Google Scholar 

  25. Wei, G. F.; Liu, Z. P. Subnano Pt particles from a firstprinciples stochastic surface walking global search. J. Chem. Theory Comput. 2016, 12, 4698–4706.

    Article  Google Scholar 

  26. De, S.; Willand, A.; Amsler, M.; Pochet, P.; Genovese, L.; Goedecker, S. Energy landscape of fullerene materials: A comparison of boron to boron nitride and carbon. Phys. Rev. Lett. 2011, 106, 225502.

    Article  Google Scholar 

  27. Vilhelmsen, L. B.; Hammer, B. Systematic study of Au6 to Au12 gold clusters on MgO(100) F centers using densityfunctional theory. Phys. Rev. Lett. 2012, 108, 126101.

    Article  Google Scholar 

  28. Doye, J. P. K.; Meyer, L. Mapping the magic numbers in binary Lennard-Jones clusters. Phys. Rev. Lett. 2005, 95, 063401.

    Article  Google Scholar 

  29. Wales, D. J. A microscopic basis for the global appearance of energy landscapes. Science 2001, 293, 2067–2070.

  30. Ballard, A. J.; Martiniani, S.; Stevenson, J. D.; Somani, S.; Wales, D. J. Exploiting the potential energy landscape to sample free energy. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2015, 5, 273–289.

    Google Scholar 

  31. Wales, D. J.; Salamon, P. Observation time scale, free-energy landscapes, and molecular symmetry. Proc. Natl. Acad. Sci. USA 2014, 111, 617–622.

    Article  Google Scholar 

  32. Aprà, E.; Ferrando, R.; Fortunelli, A. Density-functional global optimization of gold nanoclusters. Phys. Rev. B 2006, 73, 205414.

    Article  Google Scholar 

  33. Doll, K.; Schön, J. C.; Jansen, M. Ab initio energy landscape of LiF clusters. J. Chem. Phys. 2010, 133, 024107.

    Article  Google Scholar 

  34. Santambrogio, G.; Brü mmer, M.; Wö ste, L.; Dö bler, J.; Sierka, M.; Sauer, J.; Meijer, G.; Asmis, K. R. Gas phase vibrational spectroscopy of mass-selected vanadium oxide anions. Phys. Chem. Chem. Phys. 2008, 10, 3992–4005.

    Article  Google Scholar 

  35. Al-Sunaidi, A. A.; Sokol, A. A.; Catlow, C. R. A.; Woodley, S. M. Structures of zinc oxide nanoclusters: As found by revolutionary algorithm techniques. J. Phys. Chem. C 2008, 112, 18860–18875.

    Article  Google Scholar 

  36. Hartke, B. Global geometry optimization of clusters guided by N-dependent model potentials. Chem. Phys. Lett. 1996, 258, 144–148.

    Article  Google Scholar 

  37. Wang, Y. C.; Lv, J.; Zhu, L.; Ma, Y. M. Crystal structure prediction via particle-swarm optimization. Phys. Rev. B 2010, 82, 094116.

    Article  Google Scholar 

  38. Roberts, C.; Johnston, R. L. Investigation of the structures of MgO clusters using a genetic algorithm. Phys. Chem. Chem. Phys. 2001, 3, 5024–5034.

    Article  Google Scholar 

  39. Flikkema, E.; Bromley, S. T. A new interatomic potential for nanoscale silica. Chem. Phys. Lett. 2003, 378, 622–629.

    Article  Google Scholar 

  40. Johnston, R. L. Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries. Dalton Trans. 2003, 4193–4207.

    Google Scholar 

  41. Catlow, C. R. A.; Bromley, S. T.; Hamad, S.; Mora-Fonz, M.; Sokol, A. A.; Woodley, S. M. Modelling nano-clusters and nucleation. Phys. Chem. Chem. Phys. 2010, 12, 786–811.

    Article  Google Scholar 

  42. Johnston, R. L. Applications of Evolutionary Computation in Chemistry; Springer: Berlin Heidelberg, 2004.

    Book  Google Scholar 

  43. Chen, Z. H.; Wang, L. W.; Li, J. B.; Li, S. S. A curved line search algorithm for atomic structure relaxation. arXiv:1506.04242.

  44. Ha, M. A.; Dadras, J.; Alexandrova, A. Rutile-deposited Pt–Pd clusters: A hypothesis regarding the stability at 50/50 ratio. ACS Catal. 2014, 4, 3570–3580.

    Article  Google Scholar 

  45. van Rijssel, J.; Erné, B. H.; Meeldijk, J. D.; Casavola, M.; Vanmaekelbergh, D.; Meijerink, A.; Philipse, A. P. Enthalpy and entropy of nanoparticle association from temperaturedependent cryo-TEM. Phys. Chem. Chem. Phys. 2011, 13, 12770–12774.

    Article  Google Scholar 

  46. Barron, H.; Barnard, A. S. Using structural diversity to tune the catalytic performance of Pt nanoparticle ensembles. Catal. Sci. Technol. 2015, 5, 2848–2855.

    Article  Google Scholar 

  47. Blöuml, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953–17979.

    Article  Google Scholar 

  48. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758–1775.

    Article  Google Scholar 

  49. Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 1993, 47, 558–561.

    Article  Google Scholar 

  50. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186.

    Article  Google Scholar 

  51. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865–3868.

    Article  Google Scholar 

  52. Yang, S. H.; Drabold, D. A.; Adams, J. B.; Ordejón, P.; Glassford, K. Density functional studies of small platinum clusters. J. Phys.: Condens. Matter. 1997, 9, L39.

    Google Scholar 

  53. Watari, N.; Ohnishi, S. Atomic and electronic structures of Pd13 and Pt13 clusters. Phys. Rev. B 1998, 58, 1665–1677.

    Article  Google Scholar 

  54. Aprà, E.; Fortunelli, A. Density-functional calculations on platinum nanoclusters: Pt13, Pt38, and Pt55. J. Phys. Chem. A 2003, 107, 2934–2942.

    Article  Google Scholar 

  55. Aprà, E.; Baletto, F.; Ferrando, R.; Fortunelli, A. Amorphization mechanism of icosahedral metal nanoclusters. Phys. Rev. Lett. 2004, 93, 065502.

    Article  Google Scholar 

  56. Wheeler, R. A.; Hoffmann, R. A new magic cluster electron count and metal-metal multiple bonding. J. Am. Chem. Soc. 1986, 108, 6605–6610.

    Article  Google Scholar 

  57. Krogman, J. P.; Thomas, C. M. Metal–metal multiple bonding in C3-symmetric bimetallic complexes of the first row transition metals. Chem. Commun. 2014, 50, 5115–5127.

    Article  Google Scholar 

  58. Liu, X.; Bauer, M.; Bertagnolli, H.; Roduner, E.; van Slageren, J.; Phillipp, F. Structure and magnetization of small monodisperse platinum clusters. Phys. Rev. Lett. 2006, 97, 253401.

    Article  Google Scholar 

  59. Walsh, A.; Woodley, S. M. Evolutionary structure prediction and electronic properties of indium oxide nanoclusters. Phys. Chem. Chem. Phys. 2010, 12, 8446–8453.

    Article  Google Scholar 

  60. Sadeghi, A.; Ghasemi, S. A.; Schaefer, B.; Mohr, S.; Lill, M. A.; Goedecker, S. Metrics for measuring distances in configuration spaces. J. Chem. Phys. 2013, 139, 184118.

    Article  Google Scholar 

  61. Eisen, M. B.; Spellman, P. T.; Brown, P. O.; Botstein, D. Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA 1998, 95, 14863–14868.

    Article  Google Scholar 

  62. Becker, O. M.; Karplus, M. The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics. J. Chem. Phys. 1997, 106, 1495–1517.

    Article  Google Scholar 

  63. Wales, D. J.; Miller, M. A.; Walsh, T. R. Archetypal energy landscapes. Nature 1998, 394, 758–760.

    Article  Google Scholar 

  64. D’agostino, G. Phonon properties of transition-metal clusters. Philos. Mag. Part B 1997, 76, 433–440.

    Article  Google Scholar 

Download references

Acknowledgements

We sincerely acknowledge Professor Dongxu Tian from Dalian University of Technology for providing the structures of Pt clusters of their calculations. The work is supported by the Material Theory program (KC2301) through the Director, Office of Science, Office of Basic Energy Sciences, Materials Science and Engineering Division, of the U.S. Department of Energy (DOE) under Contract No. DEAC02-05CH 11231. This research used the resources of the National Energy Research Scientific Computing Center (NERSC) and Oak Ridge Leadership Computing Facility (OLCF) with the computer time allocated by the ASCR Leadership Computing Challenge (ALCC) program.

Author information

Authors and Affiliations

  1. Materials Sciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 50F, Berkeley, California, 94720, USA

    Zhanghui Chen & Lin-Wang Wang

  2. State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing, 100083, China

    Zhanghui Chen, Jingbo Li & Shushen Li

Authors
  1. Zhanghui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingbo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shushen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lin-Wang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lin-Wang Wang.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Z., Li, J., Li, S. et al. Glass-like energy and property landscape of Pt nanoclusters. Nano Res. 10, 2721–2731 (2017). https://doi.org/10.1007/s12274-017-1475-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12274-017-1475-9

Keywords

Search

Navigation