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Notizen: In this paper we report on quantum mechanical calculations for the ground and the excited electronic surface states of an excess electron on (He)N clusters (N=3.5×105–6×1023), exploring the cluster size dependence of the excess electron localization and the bridging between the properties of the electron on cluster microsurfaces and on flat macrosurfaces. Representing the e-(He)N potential by a short-range repulsive model potential or by a pseudopotential, together with a long-range attractive dielectric image potential, we have shown that the electronic energies are relatively insensitive (i.e., within 20% for N=106 and within 6% for N≥107) to the details of the short-range repulsive interactions. The model potential results in a "critical'' radius R(1,0)c=148 A(ring) with a number of constituents N(1,0)c=3.0×105 for electron localization in the ground n=1, l=0 electronic state, while with a further increase of the cluster radius R above R(1,0)c, higher n,l states become localized at cluster radii R(n,l)c, with Rc(n,l') (approximately-greater-than) Rc(n,l) for l'(approximately-greater-than)l and Rc(n',l') (approximately-greater-than) Rc(n,l) for n'(approximately-greater-than)n and for all values of l and l'.The energies En,l of the n,l electronic states above the localization threshold are characterized by the scaling relations En,l(R)∝(R−R(n,l)c)η(l) with η(l)=2 for l=0 and η(l)=1 for l≠0. The charge distribution in this size domain for l=0 is characterized by the moments 〈rJ〉∝(R−R(n,0)c)−J, while for l=1, 〈r〉∝(R−R(n,1)c)−1/2. The "critical'' cluster radii for localization obey algebraic relations, which result in the cluster size dependence of the number of bound electronic states. Cluster surface size equations were obtained for R→∞ providing a quantitative description of the convergence of the electronic energies to those for a flat surface. Information on electronic spectroscopy was inferred from the cluster size dependence of the transition energies and oscillator strengths for the 1,0(1s)→n,1(np) electronic excitations. The 1s→1p electronic transition is characterized by a transition energy and an oscillator strength which both decrease as R−2, manifesting the onset of l degeneracy for macrosurfaces. Finally, electric field effects provide information on field-induced ionization and huge polarizabilities αc(approximately-equal-to) (109–1011)αH (where αH is the polarizability of the hydrogen atom) of these giant excess electron states. © 1994 American Institute of Physics.