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Finite Size Effects in Chemical Bonding: From Small Clusters to Solids

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Abstract

We address the fundamental question of which size a metallic nano-particle needs to have before its surface chemical properties can be considered to be those of a solid, rather than those of a large molecule. Calculations of adsorption energies for carbon monoxide and oxygen on a series of gold nanoparticles ranging from 13 to 1,415 atoms, or 0.8–3.7 nm, have been made possible by exploiting massively parallel computing on up to 32,768 cores on the Blue Gene/P computer at Argonne National Laboratory. We show that bulk surface properties are obtained for clusters larger than ca. 560 atoms (2.7 nm). Below that critical size, finite-size effects can be observed, and we show those to be related to variations in the local atomic structure augmented by quantum size effects for the smallest clusters.

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Notes

  1. An estimate of the numerical errors in solving the Kohn–Sham equations can be obtained by noting that the variation of molecular atomization energies calculated by different codes (GPAW, VASP and Gaussian03) in Ref. [19] is found to be uncorrellated and of the order of 50 meV.

  2. The chosen contour of 0.001 e/Å3 ensures that the electrostatic energy of the density-difference distribution is converged to 10 meV compared to the electrostratic energy of the full density difference, and that the sum of the absolute value of the redistributed charge enclosed in these contours is at least 70% of the total redistributed charge.

References

  1. Thomas JM, Thomas WJ (1997) Principle and practice of heterogeneous catalysis. VCH, Weinheim

  2. Li Y, Somorjai GA (2010) Nano Lett 10:2289

    Article  CAS  Google Scholar 

  3. Valden M, Lai X, Goodman DW (1998) Science 281:1647

    Article  CAS  Google Scholar 

  4. Bond GC, Thompson DT (1994) Catal Rev Sci Eng 41:319

    Article  Google Scholar 

  5. Haruta M, Kobayashi T, Sano H, Yamada N (1987) Chem Lett 2:405

    Article  Google Scholar 

  6. Ertl G (2008) Angew Chem Int Ed 47:3524

    Article  CAS  Google Scholar 

  7. Somorjai GA, Park JY (2008) Chem Soc Rev 37:2155

    Article  CAS  Google Scholar 

  8. Honkala K, Hellman A, Remediakis IN, Logadottir A, Carlsson A, Dahl S et al (2005) Science 307:555

    Article  CAS  Google Scholar 

  9. Jiang T, Mowbray D, Dobrin S, Falsig H, Hvolbaek B, Bligaard T et al (2009) J Phys Chem C 113:10548

    Article  CAS  Google Scholar 

  10. Sanchez A, Abbet S, Heiz U, Schneider WD, Hakkinen H, Barnett RN et al (1999) J Phys Chem A. 103:9573

    Article  CAS  Google Scholar 

  11. Chretien S, Gordon MS, Metiu H (2004) J Chem Phys 121:3756

    Article  CAS  Google Scholar 

  12. Lopez-Acevedo O, Kacprzak KA, Akola J, Hakkinen H (2010) Nat Chem 2:329

    Article  CAS  Google Scholar 

  13. Pyykko P (2008) Chem Soc Rev 37:1967

    Article  Google Scholar 

  14. Mpourmpakis G, Andriotis AN, Vlachos DG (2010) Nano Lett 10:1041

    Article  CAS  Google Scholar 

  15. Xie Y-P, Gong X-G (2010) J Chem Phys 132:244302

    Article  Google Scholar 

  16. Roldan A, Manel Ricart J, Illas F, Pacchioni G (2010) Phys Chem Chem Phys 12:10723

    Article  CAS  Google Scholar 

  17. Yudanov I, Metzner M, Genest A, Rosch N (2008) J Phys Chem C 112:20269

    Article  CAS  Google Scholar 

  18. Martin TP (1996) Phys Rep 273:199

    Article  CAS  Google Scholar 

  19. Enkovaara J, Rostgaard C, Mortensen JJ, Chen J, Dulak M, Ferrighi L et al (2010) J Phys Condens Matter 22:1

    Article  Google Scholar 

  20. Mortensen JJ, Hansen LB, Jacobsen KW (2005) Phys Rev B 71:035109

    Article  Google Scholar 

  21. Blocl P (1994) Phys Rev B 50:17953

    Article  Google Scholar 

  22. Hammer B, Hansen LB, Norskov JK (1999) Phys Rev B 59:7413

    Article  Google Scholar 

  23. Boyen HG, Kastle G, Weigl F, Koslowski B, Dietrich C, Ziemann P et al (2002) Science 297:1533

    Article  CAS  Google Scholar 

  24. Bader RFW (1990) Atoms in molecules: a quantum Theory Oxford University Press, Oxford

  25. Kitchin JR, Norskov JK, Barteau MA, Chen JG (2004) Phys Rev Lett 93:156801

    Article  CAS  Google Scholar 

  26. Inoglu N, Kitchin JR (2010) Phys Rev B 82:045414

    Article  Google Scholar 

  27. von Issendorff B, Cheshnovsky O (2005) Annu Rev Phys Chem 56:549

    Article  Google Scholar 

Download references

Acknowledgement

This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357. The researchers’ use of Argonne's Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, also under contract No. DE-AC02-06CH11357. Additional support from the Office of Science of the U.S. Department of Energy to the SUNCAT Center for Interface Science and Catalysis at SLAC/Stanford, the NABIIT program under the Danish Strategic Research Council, and from the Lundbeck Foundation to the Center for Atomic-scale Materials Design at DTU is gratefully acknowledged.

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Correspondence to J. K. Nørskov or K. W. Jacobsen.

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Kleis, J., Greeley, J., Romero, N.A. et al. Finite Size Effects in Chemical Bonding: From Small Clusters to Solids. Catal Lett 141, 1067–1071 (2011). https://doi.org/10.1007/s10562-011-0632-0

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  • DOI: https://doi.org/10.1007/s10562-011-0632-0

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