Excess electron surface states on helium clusters

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=10 ⁶ and within 6% for N≥10⁷) to the details of the short-range repulsive interactions. The model potential results in a "critical" radius R_c^(1,0)=148 Å with a number of constituents N_c^(1,0)=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_c^(1,0), higher n,l states become localized at cluster radii R_c ^(n,l), with R_c^(n,l′) > R _c^(n,l) for l′>1 and R_c ^(n′,l′) > R_c^(n,l) for n′>n and for all values of l and l′. The energies E_n,l of the _n,l electronic states above the localization threshold are characterized by the scaling relations E_n,l(R)∝(R-R _c^(n,l))^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 〈r_J〉∝(R-R _c^(n,0))^-J, while for l=1, 〈r〉∝ (R-R_c^(n,1))^-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 α_c≃ (10₉-10¹¹)α_H (where α_H is the polarizability of the hydrogen atom) of these giant excess electron states.