## Abstract

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=3.5×10^{5}-6×10^{23}), 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≥10^{7}) 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)}=3.0×10^{5} 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}≃ (10_{9}-10^{11})α_{H} (where α_{H} is the polarizability of the hydrogen atom) of these giant excess electron states.

Original language | English |
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Pages (from-to) | 9982-9996 |

Number of pages | 15 |

Journal | Journal of Chemical Physics |

Volume | 101 |

Issue number | 11 |

DOIs | |

State | Published - 1 Jan 1994 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Physics and Astronomy
- Physical and Theoretical Chemistry