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Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters
Author(s) -
Kotsos B. A.,
Grypeos M. E.
Publication year - 2001
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10026
Subject(s) - classification of discontinuities , harmonic oscillator , particle (ecology) , basis (linear algebra) , chemistry , atomic number , quantum , distribution (mathematics) , atomic physics , variation (astronomy) , physics , molecular physics , quantum mechanics , geometry , mathematics , mathematical analysis , oceanography , astrophysics , geology
The dependence of the harmonic oscillator (HO) energy level spacing ℏω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ℏω at the closed shells. These discontinuities diminish as N increases. For large N , ℏω becomes simply: ℏω≃ c 1 N −1/3 + c 2 N −1 . © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001