Title Dependence of the $\pi$-electron eigenvalue sum on the number of atoms in almost spherical C cagesDependence of the $\pi$-electron eigenvalue sum on the number of atoms in almost spherical C cages Author Amovilli, C. Howard, I.A. Klein, D.J. March, N.H. Faculty/Department Faculty of Sciences. Physics Research group Department of Physics Publication type article Publication 2002Lancaster, Pa, 2002 Subject Physics Source (journal) Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015 Volume/pages 66(2002):1, p. 1-5 ISSN 1094-1622 1050-2947 Article Reference 013210 Carrier E-only publicatie Target language English (eng) Full text (Publishers DOI) Affiliation University of Antwerp Abstract A free-electron-like model is first shown to lead to the eigenvalue sum of the pi electrons in almost spherical C cages, being proportional to N, where N is the number of C atoms. The model is also closely related to a tight-binding model, stemming from the Huckel theory of pi electrons. The equilibrium radius R-e of the C cages is assumed to be determined by the "rule" of constant surface area per C atom, and hence R(e)proportional toN(1/2). We then compare these models with a series of Hartree-Fock calculations on the fullerenes C-50, C-60, C-70, and C-84, from which more accurate energy scaling relations are obtained. Finally, the relation between the total energy of the four C cages at equilibrium and the all-electron eigenvalue sum is confirmed by the Hartree-Fock studies. Full text (open access) https://repository.uantwerpen.be/docman/irua/1eaacf/5988.pdf E-info http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000177200800076&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000177200800076&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000177200800076&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle