Electron bubbles in helium clusters. I. Structure and energetics

Abstract

In this paper we present a theoretical study of the structure, energetics, potential energy surfaces, and energetic stability of excess electron bubbles in ((4)He)(N) (N=6500-10(6)) clusters. The subsystem of the helium atoms was treated by the density functional method. The density profile was specified by a void (i.e., an empty bubble) at the cluster center, a rising profile towards a constant interior value (described by a power exponential), and a decreasing profile near the cluster surface (described in terms of a Gudermannian function). The cluster surface density profile width (approximately 6 A) weakly depends on the bubble radius R(b), while the interior surface profile widths (approximately 4-8 A) increase with increasing R(b). The cluster deformation energy E(d) accompanying the bubble formation originates from the bubble surface energy, the exterior cluster surface energy change, and the energy increase due to intracluster density changes, with the latter term providing the dominant contribution for N=6500-2 x 10(5). The excess electron energy E(e) was calculated at a fixed nuclear configuration using a pseudopotential method, with an effective (nonlocal) potential, which incorporates repulsion and polarization effects. Concurrently, the energy V(0) of the quasi-free-electron within the deformed cluster was calculated. The total electron bubble energies E(t)=E(e)+E(d), which represent the energetic configurational diagrams of E(t) vs R(b) (at fixed N), provide the equilibrium bubble radii R(b) (c) and the corresponding total equilibrium energies E(t) (e), with E(t) (e)(R(e)) decreasing (increasing) with increasing N (i.e., at N=6500, R(e)=13.5 A and E(t) (e)=0.86 eV, while at N=1.8 x 10(5), R(e)=16.6 A and E(t) (e)=0.39 eV). The cluster size dependence of the energy gap (V(0)-E(t) (e)) allows for the estimate of the minimal ((4)He)(N) cluster size of N approximately 5200 for which the electron bubble is energetically stable.

Ion formation upon electron collisions with valine embedded in helium nanodroplets

“…Anion formation at low electron energies is strongly suppressed for large HNDs in comparison to smaller droplets [39,47,50,51]. We explain this (i) by the low mobility of the electron bubble [43,[55][56][57] and (ii) by the reduced ejection probability of parent cluster anions of amino acids in case they are formed. Also, in the energy range of DEA that is typically assigned to core excited resonances, the fragmentation pattern differs strongly between doped HNDs and the gas phase.…”

On subthreshold ionization of helium droplets, ejection of He+, and the role of anions

“…In bulk helium the energy of the bubble lies about 0.1 eV above the vacuum level; its radius is 17 Å. 23 The smallest helium droplet that supports a bubble state has been computed to contain The resonance at 22 eV in the yield of these large helium cluster anions has been attributed to an electron that excites an atom in the droplet to the lowest triplet state which, in vacuum, has an energy of 19.82 eV and a lifetime of 8000 s. 17 The inelastically scattered electron is then self-trapped in a bubble while He * forms a separate bubble with a radius of about 10 Å. 17 The energy difference between the first and second resonance (i.e.…”

“…12,19 What is the local structure near a positive or negative charge in undoped helium droplets, and how does it compare to that in bulk helium or helium films? [20][21][22][23] Our present work addresses the formation and subsequent ejection of bare He + from undoped droplets. For ionizing radiation exceeding the ionization threshold of atomic He (24.59 eV) small Hen + cluster ions (n > 1) are thought to result from a two-step mechanism.…”

Helium anion formation inside helium droplets

“…Helium droplets offer an interesting and exclusive environment for the study of physical and chemical phenomena [1][2][3][4][5][6][7]. This is due to the low temperature of helium droplets (0.37 K), their superfluidity and their capacity of efficient doping with a wide variety of atoms and molecules.…”