Simple Jellium Model Research Articles

First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

We propose a spatially and temporally nonlocal exchange-correlation (xc) kernel for the spin-unpolarized fluid phase of ground-state jellium, for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact xc kernel, to accurately describe the correlation energies of bulk jellium, and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel [A. Ruzsinszky, et al., Phys. Rev. B 101, 245135 (2020)] are maintained in the new revised MCP07 (rMCP07) kernel, while others are added. The revision $f_\mathrm{xc}^\mathrm{rMCP07}(q,\omega)$ differs from MCP07 only for non-zero frequencies $\omega$. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wavevector $q$ tends to zero, the kernel has a $-4\pi \alpha(\omega)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $\alpha(\omega)$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.}

First-row transition metal doped germanium clusters Ge16M: some remarkable superhalogens.

A theoretical study of geometric and electronic structures, stability and magnetic properties of both neutral and anionic Ge16M0/− clusters with M being a first-row 3d transition metal atom, is performed using quantum chemical approaches. Both the isoelectronic Ge16Sc− anion and neutral Ge16Ti that have a perfect Frank–Kasper tetrahedral Td shape and an electron shell filled with 68 valence electrons, emerge as magic clusters with an enhanced thermodynamic stability. The latter can be rationalized by the simple Jellium model. Geometric distortions from the Frank–Kasper tetrahedron of Ge16M having more or less than 68 valence electrons can be understood by a Jahn–Teller effect. Remarkably, DFT calculations reveal that both neutral Ge16Sc and Ge16Cu can be considered as superhalogens as their electron affinities (≥3.6 eV) exceed the value of the halogen atoms and even that of icosahedral Al13. A detailed view of the magnetic behavior of Ge16M0/− clusters shows that the magnetic moments of the atomic metals remain large even when they are quenched upon doping. When M goes from Sc to Zn, the total spin magnetic moment of Ge16M0/− increases steadily and reaches the maximum value of 3 μB with M = Mn before decreasing towards the end of the first-row 3d block metals. Furthermore, the IR spectra of some tetrahedral Ge16M are also predicted.

Valence photoionization of free, neutral, and size-varied alkali metal clusters

The valence photoelectron spectra of free, neutral, and size-varied K and Rb alkali metal clusters are studied. The experimental spectra are simulated with jellium model-based calculations with and without inclusion of dipole matrix elements and continuum wavefunctions. The simple jellium model used is found to provide good qualitative correspondence with the experimental results. It is shown that the dipole matrix elements provide a remarkable improvement to the standard density of states approach in understanding the photoelectron spectra of small to medium size metal clusters.

A jellium model analysis on quantum growth of metal nanowires and nanomesas

A simple jellium model is used to investigate the stability of a metal nanowire as a function of its size. The theoretical results from the model indicate the quantum selectivity of preferable radii of nanowires, in apparent agreement with the experimental observations. It is consequently suggested that a series of stable “magic numbers” and “instability gaps” observed in the synthesis experiments of Au nanowires is mainly attributed to the quantum-mechanical behavior. These stable radii can be achieved by rearranging atoms during the formation of nanowires. The model is also used to analyze the growth of Au nanomesas on a graphite surface, and the puzzling growth behavior of Au nanomesas can be reasonably explained.

Structure and stability of the Al14 halides Al14In− (n=1–11): Can we regard the Al14 core as an alkaline earthlike superatom?

We have studied the structures and stabilities of Al(14)I(n) (-) (n=1-11) clusters at the density functional level of theory. The experimentally observed Al(14)I(n) (-) (n=3, 5, 7, 9, and 11) [Bergeron et al., Science 307, 231 (2005)] are found to be stable both kinetically and thermodynamically. Al(14)I(3) (-), not Al(14)I(-), is the first member of the Al(14)I(n) (-) series in the mass spectrometric experiment, which is ascribable to the low kinetic stability of the Al(14)I(-) cluster. The Al(14) core in Al(14)I(3) (-) is close to neutral Al(14), both electronically and structurally. Population analysis shows that charge transfer occurs from the Al cluster to the I atoms, where the populations for Al(14) vary from -0.70(Al(14)I(-)) to +0.96(Al(14)I(11) (-)). The Al(14)I(5) (-) and Al(14)I(7) (-) clusters have the structure of Al(14)I(3) (-) as a core framework, but, for n=9 and 11, we found many more stable isomers than the isomers having the Al(14)I(3) (-) core. In particular, the shape of Al(14) in the Al(14)I(11) (-) cluster is a hexagonal wheel-shaped form, which was observed in the x-ray experiment for the metalloid complex [Al(14){N(SiMe(3))(2)}(6)I(6)Li(OEt(2))(2)](-)[Li(OEt(2))(4)](+)toluene [Kohnlein et al., Angew. Chem., Int. Ed. 39, 799 (2000)]. We have demonstrated that a simple jellium model cannot describe the structure and stability of the iodine-doped aluminum clusters, although it is successful for describing those of aluminum clusters. The electronic and geometric changes of the Al(14) (-) cluster due to the presence of iodines are very similar to the case of a magic cluster Al(13) (-). It can be concluded from our electronic and structural analysis that one cannot regard the Al(14) core as an alkaline earthlike superatom in the Al(14) iodide clusters.

First-principles investigations of the polarizability of small-sized and intermediate-sized copper clusters

Density functional theory calculations are used to compute the dipole polarizabilities of copper clusters. Structures for the clusters are taken from the literature for n = 2-32 and several isomers are used for each cluster size for n < or = 10. The calculated polarizabilities are in good agreement with the prediction of a simple jellium model, but much smaller than experimental observations for n = 9-32 [M. B. Knickelbein, J. Chem. Phys., 120, 10450 (2004)]. To investigate this difference, the calculated polarizabilities are tested for the effects of basis set, electron correlation, and equilibrium geometry for small-size clusters (n = 2-10). These effects are too small to account for the theory-experiment gap. Temperature effects are also studied. Thermal expansion of the clusters leads to very small changes in polarizability. On the other hand, the presence of permanent dipoles in the clusters could account for the experimental observations if the rotational temperature of the clusters were sufficiently low. The potential importance of the cluster dipole moments implies that reliable ground-state structures and experimental temperatures are needed to find quantitative agreement between calculated and observed polarizabilities.

Ab initioabsorption spectra ofAln (n=2–13)clusters

We investigate the optical absorption spectra of ${\mathrm{Al}}_{n}$ $(n=2--13)$ clusters using the time-dependent spin-polarized local-density approximation. The overall shapes of the calculated spectra strongly depend on cluster geometries. It is observed that a simple jellium model is not valid for these clusters. In the size range of $nl~5,$ the spectra show discrete, atomiclike transitions. For $n=6--12,$ the shape of the absorption spectra can be explained on the basis of an ellipsoidal shell model. A strong collective excitation peak is observed for ${\mathrm{Al}}_{13}$ cluster, which is due to its spherical symmetry.

Density-functional investigation of the size dependence of the electronic structure of mixed aluminum-sodium clusters

Equilibrium geometries and electronic-structure properties have been obtained for cationic, anionic, and neutral ${\mathrm{Al}}_{n}\mathrm{Na}$ and ${\mathrm{Al}}_{n}{\mathrm{Na}}_{2}$ $(n=1--12)$ clusters within the density-functional theory using the generalized gradient approximation for the exchange-correlation potential. The resulting geometries show that the sodium atom prefers to be on the periphery and does not get trapped. The stability has been investigated by analyzing the binding energy, the dissociation energy, and the second difference in energy. The results indicate that for neutral clusters, ${\mathrm{Al}}_{4}\mathrm{Na}$ and ${\mathrm{Al}}_{7}\mathrm{Na}$ are stable. Considerable enhanced stability is also seen for ${\mathrm{Al}}_{4}{\mathrm{Na}}_{2},$ ${\mathrm{Al}}_{6}{\mathrm{Na}}_{2},$ ${\mathrm{Al}}_{4}{\mathrm{Na}}^{\ensuremath{-}},$ and ${\mathrm{Al}}_{6}{\mathrm{Na}}^{\ensuremath{-}}$ clusters. The stability of these clusters cannot be explained on the basis of a simple jellium model. The calculated vertical ionization potentials are in good agreement with their experimental counterparts. No consistent signature of a monovalent nature for Al is observed in these systems. The addition of sodium atoms is found to quench the weak magnetic moment of pure Al clusters and all ${\mathrm{Al}}_{n}{\mathrm{Na}}_{2}$ clusters are found to be nonmagnetic.

Spherical averaged jellium model with norm-conserving pseudopotentials

The effect of non-local norm-conserving pseudo-potentials on the static and dynamic properties of Nan and Lin cluster with n=6,8 is investigated in the frame of self-consistent LDA calculations with spherically averaged ionic density (SAPS model). A comparison with previous calculations which use local pseudo-potentials as well with uniform averaged non-local pseudo-jellium calculation has been carried out. A better quantitative agreement with experiments has been found in the calculation of the photoresponse cross-section with respect to either simple jellium or pseudo-jellium model, even in very small clusters, where deviations from sphericity are not negligible.

Theoretical Models for the Optical Properties of Clusters and Nanostructures

Applications of the Time Dependent Density Functional Formalism to calculate the response of metallic and semiconducting nanostructures to static and time-dependent electric fields in the linear regime are reviewed. The paper focuses on the presentation of models of increasing sophistication for the cluster structure, ranging from the simple spherical jellium model to a fully ab initio description of the ionic structure. Simple models explain the main features of the spectrum. For instance the existence of a pronounced surface plasmon resonance in the absorption spectrum of alkali metal clusters, and its redshift with respect to the classical Mie resonance are well explained within the framework of the simple jellium model. However, the detailed understanding of the experimental optical spectra can only be achieved by complementary ab initio calculations. In fact, the optical spectrum appears to carry detailed information on the cluster structure. Details of the new theories and computational schemes to deal with the optical properties of complex systems are also presented: linear and nonlinear susceptibilities, quasiparticle excitations, core-polarization. These methods are of relevance in the physics of nanostructures and nanoscale technology.

Bromide Electrosorption on Liquid Gallium: A Typical Example of Halide Electrosorption from Aqueous Solutions and Its Modeling

The adsorption of bromide ion on liquid gallium from aqueous solutions of NaBr + HBr of concentrations ranging from 0.02 to 1.99 M was determined on the basis of capacitive charge measurements carried out by a computerized chronocoulometric technique. This adsorption is parametrized by the use of the virial isotherm corrected for the potential difference across the diffuse layer. The resulting adsorption behavior has several features in common with chloride, bromide, and iodide adsorption on mercury. These general features are interpreted on the basis of a molecular model that accounts for the local potential at the position of an adsorbed anion created by the surrounding anions as well as by the water dipoles. The fundamental role played by the mutual interactions among the adsorbed anions, the adsorbed water dipoles, and the inhomogeneous electron gas, the latter treated on the basis of a simple one-parameter jellium model, is pointed out.

Calculated ionization cross sections for proton-fullerene ion collisions

A simple jellium model is constructed in order to obtain one-electron wave functions for the valence electrons of the fullerene. With this jellium wave function we have calculated ionization cross sections for proton-C60+ collisions in the semiclassical approximation. For higher projectile velocities, for which the semiclassical approximation is valid also for electron impact, theoretical cross sections fit satisfactorily the experimental data of Volpel et al. [Phys. Rev. Lett.71 (1993) 3439].

Chemisorption of molecular oxygen on copper clusters studied by jellium and MO-LCAO models

Chemisorption of molecular oxygen on copper clusters is investigated within the local spin density approximation, using a self-consistent jellium approach and MO-LCAO calculations. The presented results show that the simple jellium model describes the chemisorption process in a satisfactory manner and is able to explain the main trends in the measured chemisorption properties of O 2 on copper clusters.

CO on Pt(335): Vibrational overtones and site dependence of the vibrational Stark effect

Electron energy loss spectroscopy is used to compare atop CO at two sites on Pt(335): on the flat (111) terrace and on the step edge. The cross section for the C–O stretch overtone of the terrace species is not significantly larger than that of the edge species. Previous experiments have shown that the vibrational frequency of terrace CO responds much less to applied electrostatic field than does edge CO, even though their ir cross sections are about the same. The present experiment shows that CO has similar molecular properties at the two sites: a chemical explanation for the different Stark tuning rates is ruled out. The difference could be due to spatial variation of the electric field. Local screening of almost all the static electric field at terrace sites is one possibility, but a simple jellium model is unable to explain the observed effect. Interaction of the molecular quadrupole moment with the spatially varying field near the surface is also important.

遷移金属とセラミックスとの界面における原子間結合状態に関する一考察

Results of valence AES analyses, which have been performed for transient-metal/ceramic interfaces by the authors, are surmarized in the present study. Atomic interactions at the interfaces are discussed by using thermo-chemical data. The data do not give a consistent full explanation of all. A simple jellium model is introduced to interpret them. The interactions are systematically discussed from views on two extremes of electronic property.

The nature of the interactions of poly(methyl methacrylate) oligomers with an aluminum surface

Polymer–metal interfaces are of increasing technological importance in a variety of applications. These interfaces are characterized by specific interactions between functional groups of the organic polymer and the metallic substrate. In order to study the structure of these interfaces at the molecular level, the energetics of the segment–surface interactions must be well characterized. We have used density functional theory to investigate the interactions of poly(methyl methacrylate) (PMMA) oligomers with aluminum surfaces. The aluminum surface is represented by the simple jellium model. The energetics of the interactions between the organic molecules and the aluminum surface are calculated as a function of the orientation with respect to the surface of the organic molecule and various internal degrees of freedom. The computed energy hypersurfaces exhibit a rich structure characterized by several energy minima and barriers. Implications of such an energy hypersurface for the architecture of long chain molecules at the interface are discussed. The energy hypersurfaces also show that the rotational conformational statistics of PMMA interacting with an aluminum surface should be quite different from that of bulk PMMA. The reported energy hypersurfaces have been used to construct an empirical force-field for future molecular simulations of long chains subject to the proper potentials.

Core-level shift at a jelliumlike surface: Al(001)

The shift of $2p$ core-level binding energies associated with surface atoms relative to bulk atoms for an Al(001) surface has been determined using photoemission partial-yield techniques. The observed shift is -57 meV. A possible mechanism for the core-level shift is discussed using a simple jellium model; i.e., the shift is related to the variation in the electrostatic potential associated with the conduction-electron response to the jelliumlike surface potential step.

Non-local-density based self-consistent surface calculations. II. Bimetal interfaces

For pt.I see ibid., vol.10, p.567 (1977). The effect of a non-local exchange correlation potential on the charge density profile and electrostatic potential near an interface is investigated in the case of a metal-metal junction. A simple jellium model is considered, in which an approximate exchange correlation potential is constructed from the self-energy formalism as modified for interfaces. An extension of the Thomas-Fermi model of the electron gas is used as a first approximation to the self-consistent solution of the problem and the results compared with a self-consistent local-density calculation and some exact results for jellium interfaces. The model gives the correct qualitative features of the interface and at higher metallic densities the quantitative agreement is good.

Charge distribution in heterovalent alloys

The selfconsistent charge density is calculated by means of the density functional formalism using a local exchange-correlation potential for a simple jellium model of a divalent impurity and a vacancy in a monovalent host. The resulting charge density around the impurity does not lend itself to an interpretation in terms of a surface dipole layer, though the dependence of the total charge transfer on the density is as predicted by the dipole model. The charge density inside a vacancy is found to be higher than that obtained by folding over a free surface; the calculated formation energy is an order of magnitude lower than typical experimental values. The validity of the Thomas-Fermi approximation for this model is discussed.