Skip to main content
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1992 Feb 1;89(3):1036–1039. doi: 10.1073/pnas.89.3.1036

Magic numbers for metallic clusters and the principle of maximum hardness.

M K Harbola 1
PMCID: PMC48380  PMID: 11607276

Abstract

It is shown that for relatively more stable metallic clusters (those with magic number of atoms) the chemical hardness (I-A) too is relatively larger. Thus the occurrence of magic numbers for metal clusters whose stability is determined by their electronic shell structure can be understood as a manifestation of the principle of maximum hardness. This may also represent a possible way of delineating clusters with stability dominated by their electronic shell structure from those for which the magic numbers occur as a result of their geometric structure.

Full text

PDF
1036

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Engel E, Perdew JP. Theory of metallic clusters: Asymptotic size dependence of electronic properties. Phys Rev B Condens Matter. 1991 Jan 15;43(2):1331–1337. doi: 10.1103/physrevb.43.1331. [DOI] [PubMed] [Google Scholar]
  2. Harbola MK, Sahni V., V Quantum-mechanical interpretation of the exchange-correlation potential of Kohn-Sham density-functional theory. Phys Rev Lett. 1989 Jan 30;62(5):489–492. doi: 10.1103/PhysRevLett.62.489. [DOI] [PubMed] [Google Scholar]
  3. Li Y, Harbola MK, Krieger JB, Sahni V., V Ground-state energies and highest occupied eigenvalues of atoms in exchange-only density-functional theory. Phys Rev A Gen Phys. 1989 Nov 15;40(10):6084–6087. doi: 10.1103/physreva.40.6084. [DOI] [PubMed] [Google Scholar]
  4. Perdew JP. Energetics of charged metallic particles: From atom to bulk solid. Phys Rev B Condens Matter. 1988 Apr 15;37(11):6175–6180. doi: 10.1103/physrevb.37.6175. [DOI] [PubMed] [Google Scholar]
  5. Sahni V, V, Levy M. Exchange and correlation energies in density-functional theory: Bounds from available data. Phys Rev B Condens Matter. 1986 Mar 15;33(6):3869–3872. doi: 10.1103/physrevb.33.3869. [DOI] [PubMed] [Google Scholar]
  6. Yang W., Parr R. G. Hardness, softness, and the fukui function in the electronic theory of metals and catalysis. Proc Natl Acad Sci U S A. 1985 Oct;82(20):6723–6726. doi: 10.1073/pnas.82.20.6723. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. van Staveren MP, Brom HB, de Jongh LJ, Ishii Y. Energetics of charged small metal particles. Phys Rev B Condens Matter. 1987 May 15;35(14):7749–7751. doi: 10.1103/physrevb.35.7749. [DOI] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES