234 research outputs found

    Self-consistent iterative solution of the exchange-only OEP equations for simple metal clusters in jellium model

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    In this work, employing the exchange-only orbital-dependent functional, we have obtained the optimized effective potential using the simple iterative method proposed by K\"ummel and Perdew [S. K\"ummel and J. P. Perdew, Phys. Rev. Lett. {\bf 90}, 43004-1 (2003)]. Using this method, we have solved the self-consistent Kohn-Sham equations for closed-shell simple metal clusters of Al, Li, Na, K, and Cs in the context of jellium model. The results are in good agreement with those obtained by the different method of Engel and Vosko [E. Engel and S. H. Vosko, Phys. Rev. B {\bf 50}, 10498 (1994)].Comment: RevTex, 6 pages, 5 eps figures. To appear in Journal of Physics:Condensed Matter (2005

    Finite-size effects and the stabilized spin-polarized jellium model for metal clusters

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    In the framework of spherical geometry for jellium and local spin density approximation, we have obtained the equilibrium rsr_s values, rˉs(N,ζ)\bar{r}_s(N,\zeta), of neutral and singly ionized "generic" NN-electron clusters for their various spin polarizations, ζ\zeta. Our results reveal that rˉs(N,ζ)\bar{r}_s(N,\zeta) as a function of ζ\zeta behaves differently depending on whether NN corresponds to a closed-shell or an open-shell cluster. That is, for a closed-shell one, rˉs(N,ζ)\bar{r}_s(N,\zeta) is an increasing function of ζ\zeta over the whole range 0≤ζ≤10\le\zeta\le 1, and for an open-shell one, it has a decreasing part corresponding to the range 0<ζ≤ζ00<\zeta\le\zeta_0, where ζ0\zeta_0 is a polarization that the cluster assumes in a configuration consistent with Hund's first rule. In the context of the stabilized spin-polarized jellium model, our calculations based on these equilibrium rsr_s values, rˉs(N,ζ)\bar{r}_s(N,\zeta), show that instead of the maximum spin compensation (MSC) rule, Hund's first rule governs the minimum-energy configuration. We therefore conclude that the increasing behavior of the equilibrium rsr_s values over the whole range of ζ\zeta is a necessary condition for obtaining the MSC rule for the minimum-energy configuration; and the only way to end up with an increasing behavior over the whole range of ζ\zeta is to break the spherical geometry of the jellium background. This is the reason why the results based on simple jellium with spheroidal or ellipsoidal geometries show up MSC rule.Comment: 10 pages, RevTex, 8 PostScript figures. to appear in J. Chem. Phys., 111 (1999

    Stabilized Spin-Polarized Jellium Model and Odd-Even Alternations in Jellium Metal Clusters

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    In this paper, we have considered the mechanical stability of a jellium system in the presence of spin degrees of freedom and have generalized the stabilized jellium model, introduced by J. P. Perdew, H. Q. Tran, and E. D. Smith [Phys. Rev. B42, 11627 (1990)], to a spin-polarized case. By applying this generalization to metal clusters (Al, Ga, Li, Na, K, Cs), we gain additional insights about the odd-even alternations, seen in their ionization potentials. In this generalization, in addition to the electronic degrees of freedom, we allow the positive jellium background to expand as the clusters' polarization increases. In fact, our self-consistent calculations of the energetics of alkali metal clusters with spherical geometries, in the context of density functional theory and local spin density approximation, show that the energy of a cluster is minimized for a configuration with maximum spin compensation (MSC). That is, for clusters with even number of electrons, the energy minimization gives rise to complete compensation (N↑=N↓N_\uparrow=N_\downarrow), and for clusters with odd number of electrons, only one electron remains uncompensated (N↑−N↓=1N_\uparrow-N_\downarrow=1). It is this MSC-rule which gives rise to alternations in the ionization potentials. Aside from very few exceptions, the MSC-rule is also at work for other metal culsters (Al, Ga) of various sizes.Comment: 18 pages, Rev_Tex, 14 figures in PostScript, Extended and improved version of our recent article with the same titl

    Self-compressed inhomogeneous stabilized jellium model and surface relaxation of simple metal thin films

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    The interlayer spacings near the surface of a crystal are different from that of the bulk. As a result, the value of the ionic density in the normal direction and near to the surface shows some oscillations around the bulk value. To describe this behavior in a simple way, we have formulated the self-compressed inhomogeneous stabilized jellium model and have applied it to simple metal thin films. In this model, for a ν\nu-layered slab, each ionic layer is replaced by a jellium slice of constant density. The equilibrium densities of the slices can be determined by minimizing the total energy per electron of the slab with respect to the slice densities. To avoid the complications that arise due to the number of independent slice-density parameters for large-ν\nu slabs, we consider a simplified version of the model with three jellium slices: one inner bulk slice with density nˉ1\bar n_1 and two similar surface slices of densities nˉ2\bar n_2. In this simplified model, each slice may contain more than one ionic layer. Application of this model to the ν\nu-layered slabs (3≤ν≤103\le\nu\le 10) of Al, Na, and Cs shows that, in the equilibrium state, nˉ1\bar n_1 and nˉ2\bar n_2 assume different values, which is significant in the Al case, and the state is more stable than that predicted in the homogeneous model in which only one global jellium density is used for the whole system. In addition, we have calculated the overall relaxations, the work functions, and the surface energies, and compared with the results of the earlier works.Comment: 19 pages, 9 figures, in pdf forma

    Quantum size correction to the work function and the centroid of excess charge in positively ionized simple metal clusters

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    In this work, we have shown the important role of the finite-size correction to the work function in predicting the correct positions of the centroid of excess charge in positively charged simple metal clusters with different rsr_s values (2≤rs≤72\le r_s\le7). For this purpose, firstly we have calculated the self-consistent Kohn-Sham energies of neutral and singly-ionized clusters with sizes 2≤N≤1002\le N\le 100 in the framework of local spin-density approximation and stabilized jellium model (SJM) as well as simple jellium model (JM) with rigid jellium. Secondly, we have fitted our results to the asymptotic ionization formulas both with and without the size correction to the work function. The results of fittings show that the formula containing the size correction predict a correct position of the centroid inside the jellium while the other predicts a false position outside the jellium sphere.Comment: RevTex, 11 pages with 10 Postscript figure

    Exact exchange optimized effective potential and self-compression of stabilized jellium clusters

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    In this work, we have used the exchange-only optimized effective potential in the self-consistent calculations of the density functional Kohn-Sham equations for simple metal clusters in stabilized jellium model with self-compression. The results for the closed-shell clusters of Al, Li, Na, K, and Cs with N=N=2, 8, 18, 20, 34, and 40 show that the clusters are 3% more compressed here than in the local spin density approximation. On the other hand, in the LSDA, neglecting the correlation results in a contraction by 1.4%.Comment: 7 pages, RevTex, 5 eps figures, 2 table

    Volume change of bulk metals and metal clusters due to spin-polarization

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    The stabilized jellium model (SJM) provides us a method to calculate the volume changes of different simple metals as a function of the spin polarization, ζ\zeta, of the delocalized valence electrons. Our calculations show that for bulk metals, the equilibrium Wigner-Seitz (WS) radius, rˉs(ζ)\bar r_s(\zeta), is always a n increasing function of the polarization i.e., the volume of a bulk metal always increases as ζ\zeta increases, and the rate of increasing is higher for higher electron density metals. Using the SJM along with the local spin density approximation, we have also calculated the equilibrium WS radius, rˉs(N,ζ)\bar r_s(N,\zeta), of spherical jellium clusters, at which the pressure on the cluster with given numbers of total electrons, NN, and their spin configuration ζ\zeta vanishes. Our calculations f or Cs, Na, and Al clusters show that rˉs(N,ζ)\bar r_s(N,\zeta) as a function of ζ\zeta behaves differently depending on whether NN corresponds to a closed-shell or an open-shell cluster. For a closed-shell cluster, it is an increasing function of ζ\zeta over the whole range 0≤ζ≤10\le\zeta\le 1, whereas in open-shell clusters it has a decreasing behavior over the range 0≤ζ≤ζ00\le\zeta\le\zeta_0, where ζ0\zeta_0 is a polarization that the cluster has a configuration consistent with Hund's first rule. The resu lts show that for all neutral clusters with ground state spin configuration, ζ0\zeta_0, the inequality rˉs(N,ζ0)≤rˉs(0)\bar r_s(N,\zeta_0)\le\bar r_s(0) always holds (self-compression) but, at some polarization ζ1>ζ0\zeta_1>\zeta_0, the inequality changes the direction (self-expansion). However, the inequality rˉs(N,ζ)≤rˉs(ζ)\bar r_s(N,\zeta)\le\bar r_s(\zeta) always holds and the equality is achieved in the limit N→∞N\to\infty.Comment: 7 pages, RevTex, 10 figure
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