No abstract

We present self-consistent local-spin-density calculations of the static electric dipole polarizability tensor for several isomers of sodium clusters with up to nine atoms. We show how the comparison of the calculated polarizabilities with the experimental data can be used to identify which isomer is observed in the experiments. Our results indicate that sodium clusters with six atoms or less are planar and that the drop in the polarizability of Na7 is related to the change from two-dimensional to three-dimensional geometries. We also present an analysis of recent measurements of photoabsorption resonance frequencies.PACS numbers: 31.20.Sy, 36.40.+d The determination of the atomic geometrical arrangement is a fundamental problem in the study of very small metallic clusters, because a deep understanding of their electronic and chemical properties requires the knowledge of their atomic structure. Unfortunately, direct experimental evidence on the geometrical structure of small metal clusters is scarce and it is very difficult to obtain for unsupported clusters. Quantum calculations of the total energy of clusters can suggest plausible structures, but they often find isomers with similar energies, and therefore cannot predict with confidence which structure is the most stable because the accuracy of the calculations is limited. In this context, the measurements of the average static electric polarizability of clusters x are very interesting since the polarizability depends on both cluster shape and size. Furthermore, recent measurements of the total photoabsorption cross section of alkali clusters 2 " 4 have been fitted to a collective resonance model, which uses the principal values of the static polarizability tensor as fit parameters. The anisotropy of the polarizability tensor provides additional information on the shape of the cluster.The rotationally averaged static electric polarizabilities a of sodium clusters with less than forty atoms were measured by Knight et al. l using a mclecular-beam deflection technique. The experimental results indicate that the general trend of the average polarizability per atom normalized to the atomic value a/na\ is a slow decrease with increasing cluster size from the atomic value of unity to the bulk value of 0.4. They also found that clusters with a "magic number" of atoms corresponding to the closed electronic shells of spherical models have smaller relative polarizabilities. Finally, they observed a "fine structure" of the polarizability between two shell closings which was attributed to the deviation from sphericity of the geometry of the sodium clusters. 5 The classical electrostatic polarizability of a perfect conducting sphere of radius R is a -Ane^R 3 . Using a conducting sphere of radius R=n x^r s , where r s is the Wigner-Seitz radius, as a model for a Na" cluster, the predicted normalized polarizability a/n is 40% of the measured atomic value a\, a good ballpark figure. Including the effect of the charge "spill out" present at the surface leads to the predictio...

The static electric dipole polarizabilities of the aluminum atom and dimer have been measured by deflecting a molecular beam in an inhomogeneous electric field. Collimated aluminum-cluster beams are produced by a pulsed laser vaporization source. Deflections are determined by means of a novel position-sensitive time-of-flight mass spectrometer. The measured polarizabilities are o 3 6.8+0.3 and 19+2 A for the atom and dimer, respectively, in good agreement with the ah initio calculations presented here. The experimental techniques described here allow precise determination of the mean deflections and velocities of the particles in the beam and are generally applicable for beams produced by laser vaporization sources.

No abstract

We present the results of several calculations of the ground state of Cs2 and Cs+2 performed in the local-spin-density approximation of density functional theory, and using different approximations for the core electrons in the derivation of ab initio norm-conserving pseudopotentials. We investigate the influence of both core polarization and relativistic effects on the molecular bonding, which turns out to be of minor importance for the determination of the equilibrium characteristics. We find that in order to guarantee an accurate description within the one-electron scheme, one must avoid the usual ‘‘linear’’ approximation of the exchange-correlation functional in the derivation of the pseudopotentials. This introduces significant errors for Cs and most probably for all one-electron systems.

No abstract

The static dipole polarizabilities and other ground-state properties of H, H2, He, Na, and Na2 are calculated using five different self-consistent schemes: Hartree–Fock, local spin density approximation, Hartree–Fock plus local density correlation, self-interaction-corrected local spin density approximation, and Hartree–Fock plus self-interaction-corrected local density correlation. The inclusion of the self-interaction corrected local spin density approximation in the Hartree–Fock method improves dramatically the calculated dissociation energies of molecules but has a small effect on the calculated polarizabilities. Correcting the local spin density calculations for self-interaction effects improves the calculated polarizability in the cases where the local spin density results are mediocre, and has only a small effect in the cases where the local spin density values are in reasonable agreement with experiment.

We present pseudopotential local-spin-density calculations of the static electric polarizability of sodium dimers and trimers and their respective cations. The electronic polarizabilities are obtained from self-consistent calculations in the presence of an external electric field, which is kept sufficiently small to avoid non-linear effects. The calculated polarizability tensor has a strong anisotropy directly related to the geometric and electronic structures of the molecules, the anisotropy being larger for the neutral clusters. The polarizabilities are averaged over the vibrational motion and rotations of the aggregates in order to be compared with the experimental measurements. The obtained values show an improvement in the agreement with experiment with respect to the values calculated in the spherical approximation.