Collective excitations in open-shell metal clusters: The time-dependent local-density approximation applied to the self-consistent spheroidal jellium particle

The self-consistent and microscopic time-dependent local-density-approximation (TDLDA) formalism for the calculation of the dynamical electronic response properties of open-shell, axially deformed small metal clusters is presented in detail. The model is based on the self-consistent ground-state calculation of the spheroidal jellium model, giving the optimized cluster shape, driven by its open-valence-shell electronic structure. First results on the static and dynamical electronic polarizability of the strongly axially deformed Na10 cluster are reported and compared with the experimental polarizability and photoabsorption cross-section results. The variety of the future applications of the model is outlined, as well as the possible improvement of the formalism

Photoabsorption cross section of negatively charged alkali-metal clusters

The optical response of anionic clusters of sodium and potassium with up to 40 valence electrons is calculated making use of a self-interaction-corrected linear-response formalism recently developed by the authors. It is found that, for these systems, the surface plasmon is excited systematically above the ionization threshold and is strongly Landau damped, with its strength distribution spread over an energy interval of typically ≈1 eV, reflecting the shorter lifetime of these systems with respect to the neutral and cationic clusters. Furthermore, it is found that temperature-dependent broadening mechanisms are able to wash out the fine structure in the line shapes of the cross sections

Comparative study of model potentials for the calculation of dielectric properties of small metal particles

Quite recently the dielectric electronic-response properties of small metal particles were investigated within a strictly self-consistent spherical jellium model. The bottleneck of this kind of calculation for a larger cluster is the self-consistent solution of the single-electron Kohn-Sham equations. Therefore, in this work simple model potentials are investigated and compared with the Kohn-Sham barrier. The result of this comparison is that the widely used model potentials such as finite- or infinite-step potentials are not able to mimic the complex dynamical behavior of a fully self-consistently responding surface

The Effective Particle-Hole Interaction and the Optical Response of Simple Metal Clusters

Following Sham and Rice [L. J. Sham, T. M. Rice, Phys. Rev. 144 (1966) 708] the correlated motion of particle-hole pairs is studied, starting from the general two-particle Greens function. In this way we derive a matrix equation for eigenvalues and wave functions, respectively, of the general type of collective excitation of a N-particle system. The interplay between excitons and plasmons is fully described by this new set of equations. As a by-product we obtain - at least a-posteriori - a justification for the use of the TDLDA for simple-metal clusters.Comment: RevTeX, 15 pages, 5 figures in uufiles format, 1 figure avaible from [email protected]

Role of Self-Interaction Effects in the Geometry Optimization of Small Metal Clusters

By combining the Self-Interaction Correction (SIC) with pseudopotential perturbation theory, the role of self-interaction errors inherent to the Local Density Approximation (LDA) to Density Functional Theory is estimated in the determination of ground state and low energy isomeric structures of small metallic clusters. Its application to neutral sodium clusters with 8 and 20 atoms shows that the SIC provides sizeable effects in Na_8, leading to a different ordering of the low lying isomeric states compared with ab-initio LDA predictions, whereas for Na_20, the SIC effects are less pronounced, such that a quantitative agreement is achieved between the present method and ab-initio LDA calculations.Comment: RevTeX, 4 pages, 1 figure available from [email protected]

Calculated lifetimes of hot electrons in aluminum and copper using a plane-wave basis set

We report about the lifetimes of hot electrons in crystalline aluminum and copper. For aluminum the results agree quantitatively with the experimental results. For copper we get good agreement for quasiparticle energies in the (110) direction above 2 eV which shows that the lifetimes for quasiparticle states above 2 eV are determined by sp bands, explaining the puzzling fact that simple Fermi liquid theory describes Cu in this direction quite well. The calculations were performed within the shielded interaction approximation using a plane-wave basis expansion for the wave functions. We show that for Cu this basis leads to equally good results as the more demanding linearized augmented plane-wave basis

Nonradiative Electronic Deexcitation Time Scales in Metal Clusters

The life-times due to Auger-electron emission for a hole on a deep electronic shell of neutral and charged sodium clusters are studied for different sizes. We consider spherical clusters and calculate the Auger-transition probabilities using the energy levels and wave functions calculated in the Local-Density-Approximation (LDA). We obtain that Auger emission processes are energetically not allowed for neutral and positively charged sodium clusters. In general, the Auger probabilities in small Na$_N^-$ clusters are remarkably different from the atomic ones and exhibit a rich size dependence. The Auger decay times of most of the cluster sizes studied are orders of magnitude larger than in atoms and might be comparable with typical fragmentation times.Comment: 11 pages, 4 figures. Accepted for publication in Phys. Rev.

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron \textit{ab-initio} time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_{6}$ of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C_{6} and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient and find that to a very high degree of correlation C_{6} scales as square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N_{2} molecule interactions.Comment: 22 pages including 6 figures. To be published in Journal of Chemical Physic

Time-dependent screening of a positive charge distribution in metals: Excitons on an ultra-short time scale

Experiments determining the lifetime of excited electrons in crystalline copper reveal states which cannot be interpreted as Bloch states [S. Ogawa {\it et al.}, Phys. Rev. B {\bf 55}, 10869 (1997)]. In this article we propose a model which explains these states as transient excitonic states in metals. The physical background of transient excitons is the finite time a system needs to react to an external perturbation, in other words, the time which is needed to build up a polarization cloud. This process can be probed with modern ultra-short laser pulses. We calculate the time-dependent density-response function within the jellium model and for real Cu. From this knowledge it is possible within linear response theory to calculate the time needed to screen a positive charge distribution and -- on top of this -- to determine excitonic binding energies. Our results lead to the interpretation of the experimentally detected states as transient excitonic states.Comment: 24 pages, 9 figures, to appear in Phys. Rev. B, Nov. 15, 2000, issue 2