Modeling the core-hole screening in jellium clusters using density functional theory

Abstract

The screening of a 2p core-hole in Na clusters is investigated using density functional theory (DFT) applied to an extended jellium model with an all-electron atom in the center. The study is related to recent experiments at the free-electron laser at DESY in which photoelectron spectra from mass-selected, core-shell-ionized metal clusters have been recorded. Relaxed and unrelaxed binding energies as well as Kohn-Sham (KS) orbital energies are calculated in Perdew-Zunger self-interaction-corrected exchange-only local spin-density approximation for valence and 2p core electrons in Na clusters up to 58 atoms. The relaxed binding energies follow approximately the metal-sphere behavior. The same behavior is seen in the experiment for sufficiently big clusters, indicating perfect screening and that the relaxation energy due to screening goes to the photoelectron. Instead, calculating the kinetic energy of the photoelectrons using unrelaxed binding energies or KS orbital energies yields the wrong results for core-shell electrons. The screening dynamics are investigated using timedependent DFT. It is shown that screening occurs on two time scales, a coreshell-dependent inner-atomic and an inter-atomic valence electron time scale. In the case of Na 2p ionization the remaining electrons in the 2p shell screen within tens of attoseconds, while the screening due to cluster valence electrons occurs within several hundreds of attoseconds. The screening time scales may be compared with the photon energy and cluster size-dependent escape times of the photoelectron in order to estimate whether the photoelectron is capable of picking up the relaxation energy or whether the residual system is left in an excited state.Core-holes are created when matter is irradiated with energetic photons. The net binding energy is obtained from the kinetic energy of the photoelectron upon subtracting the photon energy. As the target size increases from the isolated atom via molecules and clusters to, ultimately, bulk matter, the shift of the net binding energy contains information about the screening capability of the other electrons in the system and allows us to investigate, e.g., metal-to-nonmetal transitions. In fact, x-ray photoelectron spectroscopy (XPS) is well established and extensive work has been devoted to the measurement of core-level binding energy shifts in solids and at surfaces [1]. However, the systematic study of core-level shifts as a function of the target size became possible only recently because of the necessity of having size-selected clusters and tunable, powerful x-ray sources such as free-electron lasers available.From the theoretical point of view, the calculation of core-level binding energies in manyelectron systems is nontrivial, both conceptually and computationally [1,2]. The study of atoms, clusters or bulk, in which suddenly a core-electron is removed by single-photon ionization, has a long history, starting probably from Slater's transition state theory [3,4] and various kinds of self-consistent field methods (...

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“…So far this ad-hoc model has not yet been backed by a thorough theoretical consideration. In the current Focus Issue of New Journal of Physics, an all-electron atom in jellium model for the study of core-shell ionization is introduced [40].…”

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