Quantum fluid-dynamics from density functional theory

A partial differential eigenvalue equation for the density displacement fields associated with electronic excitations is derived in the framework of density functional theory. Our quantum fluid-dynamical approach is based on a variational principle and the Kohn-Sham ground-state energy functional, using only the occupied Kohn-Sham orbitals. It allows for an intuitive interpretation of electronic excitations in terms of intrinsic local currents that obey a continuity equation. We demonstrate the capabilities of this non-empirical approach by calculating the photoabsorption spectra of small sodium clusters. The quantitative agreement between theoretical and experimental spectra shows that even for the smallest clusters, the resonances observed experimentally at low temperatures can be interpreted in terms of density vibrations.Comment: RevTeX file with 2 figures. Update on April 17 2001: Typos corrected, references updated, larger axes labels on Fig. 1. Accepted for publication in Phys. Rev.

Collectivity in the optical response of small metal clusters

The question whether the linear absorption spectra of metal clusters can be interpreted as density oscillations (collective ``plasmons'') or can only be understood as transitions between distinct molecular states is still a matter of debate for clusters with only a few electrons. We calculate the photoabsorption spectra of Na2 and Na5+ comparing two different methods: quantum fluid-dynamics and time-dependent density functional theory. The changes in the electronic structure associated with particular excitations are visualized in ``snapshots'' via transition densities. Our analysis shows that even for the smallest clusters, the observed excitations can be interpreted as intuitively understandable density oscillations. For Na5+, the importance of self-interaction corrections to the adiabatic local density approximation is demonstrated.Comment: 6 pages, 3 figures. To appear in special issue of Applied Physics B, "Optical properties of Nanoparticles

On the challenge to improve the density response with unusual gradient approximations

Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations would require an exchange-correlation response differing substantially from the usual (semi-)local one. It has recently been shown that functionals of the generalized gradient approximation (GGA) type can yield unusual potentials, mimicking features of the exact exchange derivative discontinuity and showing divergences on orbital nodal surfaces. We here investigate whether these unusual potential properties translate into beneficial response properties. Using the Sternheimer formalism we closely investigate the response obtained with the 2013 exchange approximation by Armiento and K\"ummel (AK13) and the 1988 exchange approximation by Becke (B88), both of which show divergences on orbital nodal planes. Numerical calculations for Na2 as well as analytical and numerical calculations for the hydrogen atom show that the response of AK13 behaves qualitatively different from usual semi local functionals. However, the AK13 functional leads to fundamental instabilities in the asymptotic region that prevent its practical application in TDDFT. Our findings may help the development of future improved functionals, and corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations

Static Electric Dipole Polarizabilities of Na Clusters

The static electric dipole polarizability of $\mathrm{Na_N}$ clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for $2\le N \le 20$, including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments.Comment: 7 pages, 3 figures, accepted for publication in the European Physical Journal

Electrical response of molecular systems: the power of self-interaction corrected Kohn-Sham theory

The accurate prediction of electronic response properties of extended molecular systems has been a challenge for conventional, explicit density functionals. We demonstrate that a self-interaction correction implemented rigorously within Kohn-Sham theory via the Optimized Effective Potential (OEP) yields polarizabilities close to the ones from highly accurate wavefunction-based calculations and exceeding the quality of exact-exchange-OEP. The orbital structure obtained with the OEP-SIC functional and approximations to it are discussed.Comment: accepted for publication in Physical Review Letter

Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V_{\mathrm{xc}\sigma}(\re) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals like exact exchange. We demonstrate that the OEP can be obtained iteratively by solving a system of partial differential equations instead of an integral equation. This amounts to calculating the orbital shifts that exactify the Krieger-Li-Iafrate (KLI) approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact exchange energy. Counter-intuitive asymptotic limits of the exact OEP, not accessible from previous constructions, are presented.Comment: Physical Review Letters, accepted for publication. 4 pages, 1 figur

Dynamics of conversion of supercurrents into normal currents, and vice versa

The generation and destruction of the supercurrent in a superconductor (S) between two resistive normal (N) current leads connected to a current source is computed from the source equation for the supercurrent density. This equation relates the gradient of the pair potential's phase to electron and hole wavepackets that create and destroy Cooper pairs in the N/S interfaces. Total Andreev reflection and supercurrent transmission of electrons and holes are coupled together by the phase rigidity of the non-bosonic Cooper-pair condensate. The calculations are illustrated by snapshots from a computer film.Comment: 8 pages, 1 figure, accepted by Phys. Rev.

Measurement properties of the German version of the IKDC subjective knee form (IKDC-SKF).

PURPOSE: To examine the measurement properties of the German International Knee Documentation Committee Subjective Knee Form (IKDC-SKF) in knee disorder patients. METHODS: Three hundred twelve consecutive patients undergoing surgery for anterior cruciate ligament, meniscus and/or cartilage injuries completed the IKDC-SKF, Lysholm Score, Tegner Activity Scale, and Short Form-12 Health Survey before and 6 months post-surgery. IKDC-SKF measurement properties were calculated and patients were also asked to rate the relevance/comprehensibility of the questionnaire items. RESULTS: Reliability was good with high Cronbach's alpha and intraclass correlation coefficients, and standard error of measurement values of 4.4 to 6.0. The smallest detectable change (SDC) ranged from 12.3 to 16.7 points. Validity was good with 90% of all hypotheses confirmed. Confirmatory factor analysis did not show adequate fitting indices within the model. Over half of the items were rated as essential, and all were well comprehended. The majority of hypotheses for responsiveness were confirmed. No floor and ceiling effects were observed. The area under the curve ranged from 0.82 to 0.89 and the minimal important difference was smaller than the SDC. CONCLUSIONS: The German IKDC-SKF is a reliable outcome measure with good hypotheses testing and responsiveness, but its MIC and structural/content validity need further analysis