Michael Seidl

Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit

We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R)=W+(12+c)/R+O(R−2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive ΔSCF expressions. We find c≈−0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution.

How correlation suppresses density fluctuations in the uniform electron gas of one, two, or three dimensions

The particle number N fluctuates in a spherical volume fragment Ω of a uniform electron gas. In an ideal classical-gas or “Hartree” model, the fluctuation is strong, with (ΔNΩ)2=NΩ. We show in detail how this fluctuation is reduced by exchange in the ideal Fermi gas and further reduced by Coulomb correlation in the interacting Fermi gas. Besides the mean particle number NΩ and mean square fluctuation (ΔNΩ)2=(N2)Ω−(NΩ)2, we also examine the full probability distribution PΩ(N). The latter is approximately Gaussian, and exactly Gaussian for . More precisely, for any NΩ it is a Poisson distribution for the ideal classical gas and a modified Poisson distribution for the ideal or interacting Fermi gases. While most of our results are for nonzero densities and three dimensions, we also consider fluctuations in the low-density or strictly correlated limit and in the electron gas of one or two dimensions. In one dimension, the electrons may be strictly correlated at all finite densities. Fuldes fluctuation-based index of correlation strength applies to the uniform gas in any number of dimensions.

Derivative Discontinuity in the Strong-Interaction Limit of Density-Functional Theory

We generalize the exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory to open systems with fluctuating particle numbers. When used in the self-consistent Kohn-Sham procedure on strongly interacting systems, this functional yields exact features crucial for important applications such as quantum transport. In particular, the steplike structure of the highest-occupied Kohn-Sham eigenvalue is very well captured, with accurate quantitative agreement with exact many-body chemical potentials. While it can be shown that a sharp derivative discontinuity is present only in the infinitely strongly correlated limit, at finite correlation regimes we observe a slightly smoothened discontinuity, with qualitative and quantitative features that improve with increasing correlation. From the fundamental point of view, our results obtain the derivative discontinuity without making the assumptions used in its standard derivation, offering independent support for its existence.

The Fermionic Density-functional at Feshbach Resonance

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature. The atoms interact via a short-range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second-order perturbation theory, has the same density dependence as the first-order exchange energy, and the two almost exactly cancel each other at a Feshbach resonance irrespective of the shape of the potential, provided ({mu}r{sub s})>>1. Here ({mu}){sup -1} is the range of the two-body potential, and r{sub s} is defined through the number density, n=3/(4{pi}r{sub s}{sup 3}). The implications of this result for universality are discussed.