Liquid drop model for charged spherical metal clusters
- Institut fuer Theoretische Physik, Universitaet Regensburg, D-93040 Regensburg (Germany)
The average ground-state energy of a charged spherical metal cluster with {ital N} atoms and {ital z} excessive valence electrons, i.e., with net charge {ital Q}={minus}{ital ez} and radius {ital R}={ital r}{sub {ital sN}}{sup 1/3}, is presented in the liquid drop model (LDM) expansion {ital E}({ital N},{ital z})={ital a}{sub v}{ital N}+{ital a}{sub s}{ital N}{sup 2/3}+{ital a}{sub c}{ital N}{sup 1/3}+{ital a}{sub 0}({ital z})+{ital a}{sub {minus}1}({ital z}){ital N}{sup {minus}1/3}+{ital O}({ital N}{sup {minus}2/3}). We derive analytical expressions for the leading LDM coefficients {ital a}{sub v}, {ital a}{sub s}, {ital a}{sub c}, and, in particular, for the charge dependence of the further LDM coefficients {ital a}{sub 0} and {ital a}{sub {minus}1}, using the jellium model and density functional theory in the local density approximation. We obtain for the ionization energy {ital I}({ital R})={ital W}+{alpha}({ital e}{sup 2}/{ital R})+{ital O}({ital R}{sup {minus}2}), with the bulk work function {ital W}=[{Phi}(+{infinity}){minus}{Phi}(0)]{minus}{ital e}{sub b}, given first by Mahan and Schaich in terms of the electrostatic potential {Phi} and the bulk energy per electron {ital e}{sub b}, and a new analytical expression for the dimensionless coefficient {alpha}. We demonstrate that within classical theory {alpha}=1/2 but, in agreement with experimental information, {alpha} tends to {approximately}0.4 if quantum-mechanical contributions are included. In order to test and confirm our analytical expressions, we discuss the numerical results of semiclassical density variational calculations in the extended Thomas{endash}Fermi model. Copyright {copyright} 1996 Academic Press, Inc.
- OSTI ID:
- 279970
- Journal Information:
- Annals of Physics (New York), Vol. 245, Issue 2; Other Information: PBD: Feb 1996
- Country of Publication:
- United States
- Language:
- English
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