Excess electron states on the microsurfaces of Ne and H2 clusters

Abstract

In this paper we report on the ground and excited electronic states of localized excess electron surface states of (Ne)−N (N=1.1×104–6×1023) and (H2)−N (N=4.6×103–6×1023) clusters. We used an electron-cluster model potential, which consists of a short-range repulsive interaction with a strength V̄0 [with a lower limit V̄0 (≳0) corresponding to the energy of the quasifree electron in the macroscopic condensed material], and a long-range attractive polarization potential, to explore cluster size effects on the energetics and on the charge distribution of these excess electron clusters. The onset of the cluster size for excess electron localization in the ground (n=1, l=0) electronic state was inferred from a near-threshold scaling analysis, being characterized by a ‘‘critical’’ cluster radius R(1,0)c≂2(1−Q)a0/Q, where Q=(ε−1)/4(ε+1) is the effective cluster charge (for the cluster dielectric constant ε), R(1,0)c=39 Å for Ne(s), R(1,0)c=46 Å for Ne(l), R(1,0)c=35 Å for H2(s) and R(1,0)c=41 Å for H2(l), where (s) and (l) denote rigid and nonrigid cluster structures, respectively. With a further increase in the cluster radius R≳R(1,0)c, higher nl electronic states become localized. Moving up in the cluster size above the localization threshold, the energy levels Enl can be expressed (for low values of ε≤1.5) in terms of a ‘‘universal’’ scaling relation Enl/Ef=Φnl(rf/R), where Ef=(e2/2a0)Q2, rf=a0/Q and the scaling function Φnl is independent of ε. This scaling relation allows for the determination of isotope effects and the state of aggregation of the cluster on the energetics of electron localization. In order to make contact with experiment, we have studied electric field-induced ionization and the electronic spectroscopy of these excess electron clusters. The threshold dc electric field F(nl)c for field-induced ionization from the n,l state (over a broad range of R, i.e., R<320 Å for the 1s and 1p states and R<900 Å for the 2p state) is of the form F(nl)c∝‖Enl‖5/4 (ε−1)−1/4R−3. Information on electronic spectroscopy was inferred from the cluster size dependence of the transition energies and oscillator strengths for the 1s(n=1,l=0)→n′p(n′=1,2,...,l=1) transitions. The cluster size dependence of the spectroscopic data for the 1s→1p transition reveals that both the transition energy ΔE(1s→1p) and the oscillator strength f(1s→1p) are proportional to (1/R)2, with ΔE(1s→1p)→0 and f(1s→1p)→0 for R→∞, exhibiting the l degeneracy of the flat surface. On the other hand, for the 1s→2p transition, the energy ΔE(1s→2p) and the oscillator strength f(1s→2p) increase with increasing R, reaching the flat macrosurface value for R→∞.