Shell-Correction Methods for Clusters

Yannouleas, Constantine; Landman, Uzi

doi:10.1007/978-94-009-0211-4_6

Cited by 18 publications

(28 citation statements)

References 100 publications

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“…The above prediction of the occurrence of "magicnumber" cds's in nanowires, due to characteristics of electronic cohesion and atomic bonding in such structures of reduced dimensions, are directly correlated with the energetics of metal clusters, where magic-number sequences of cluster sizes, shapes and structural motifs due to electronic and/or geometric shell effects, have been long predicted and observed. [7][8][9] These results lead one directly to conclude that other properties of nanowires, derived from their energetics, may be described using methodologies developed previously in the context of clusters. Indeed, in a previous letter, 10 we showed that certain aspects of the mechanical response (i.e., elongation force) and electronic transport (e.g., quantized conductance) in metallic nanowires can be analyzed using the local-densityapproximation (LDA) -based shell correction method (SCM), developed and applied previously in studies of metal clusters.…”

Section: Introductionmentioning

confidence: 60%

Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires

1998

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Physical Review B 57, 4872 [1998]) Energetics and quantized conductance in jellium-modeled nanowires are investigated using the local-density-functionalbased shell correction method, extending our previous study of uniform-in-shape wires [C. Yannouleas and U. Landman, J. Phys. Chem. B 101, 5780 (1997)] to wires containing a variable-shaped constricted region. The energetics of the wire (sodium) as a function of the length of the volumeconserving, adiabatically shaped constriction, or equivalently its minimum width, leads to formation of self-selecting magic wire configurations, i.e., a discrete configurational sequence of enhanced stability, originating from quantization of the electronic spectrum, namely, formation of transverse subbands due to the reduced lateral dimensions of the wire. These subbands are the analogs of shells in finite-size, zero-dimensional fermionic systems, such as metal clusters, atomic nuclei, and 3 He clusters, where magic numbers are known to occur. These variations in the energy result in oscillations in the force required to elongate the wire and are directly correlated with the stepwise variations of the conductance of the nanowire in units of 2e 2 /h. The oscillatory patterns in the energetics and forces, and the correlated stepwise variation in the conductance are shown, numerically and through a semiclassical analysis, to be dominated by the quantized spectrum of the transverse states at the narrowmost part of the constriction in the wire.

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Section: Introductionmentioning

confidence: 60%

Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires

1998

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“…Of particular interest for motivating the present work (due to spatial-symmetry-breaking aspects) has been the meanfield description of deformed nuclei and metal clusters (exhibiting ellipsoidal shapes). At a first level, deformation effects in these systems can be investigated via semi-empirical mean-field models, like the particle-rotor model 19 of Bohr and Mottelson (nuclei), the anisotropicharmonic-oscillator model of Nilsson (nuclei 20 and metal clusters 21 ), and the shell-correction method of Strutinsky (nuclei 22 and metal clusters 23,24 ). At the microscopic level, the mean field is often described 25,26 via the selfconsistent single-determinantal Hartree-Fock (HF) theory.…”

Section: B Background On the Mean-field Breaking Of Symmetries In Otmentioning

confidence: 99%

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

2003

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We present a group theoretical study of the symmetrybroken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N -electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hückel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N -electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via post-Hartree-Fock projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetrybreaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.

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“…The propensity of materials systems of reduced size to undergo selfselection of size and shape, as well as their ability to spontaneously adopt optimal configurations by self-organization, are among the unique properties of nanoscale materials systems. Examples include magic number sequences that reflect enhanced stabilities of particular sizes [e.g., number of cluster atoms (20)(21)(22) or radii of nanowires (23)(24)(25)] originating from electronic shell effects (a concept familiar from nuclear structure studies) and͞or from particular geometrical atomic packing arrangements; shape deformations effects (21,22), akin to Jahn-Teller distortions (familiar in molecular and nuclear systems) that lift spectral degeneracies with consequent stabilization gained through such spontaneous symmetry-lowering (or breaking); and self-assembly processes underlying formation of nanostructures and nanoparticle arrays (10,(26)(27)(28)(29)(30).…”

Section: Small Is Different: Physical and Chemical Phenomena In Nanosmentioning

confidence: 99%

“…These self-selection processes are portrayed in systematic size-dependent patterns characterizing the properties of nanoscale structures, including cluster abundances, single-particle and collective excitations (i.e., ionization potentials, electron affinities, optical absorption spectra, and plasmon excitations), odd-even variations of the properties of metal clusters (particularly, simple sp-bonded metals) (20-22), magnetic properties (31)(32)(33), charging characteristics, fragmentation barriers and fission dynamics of charged clusters (6,21,(34)(35)(36)(37), chemical adsorption and reactivities of free (gas-phase) and surface-supported clusters (38)(39)(40)(41)(42)(43)(44)(45)(46), and correlated force oscillations and conductance quantization steps in nanowires (13,14,23,25,(47)(48)(49).…”

Section: Small Is Different: Physical and Chemical Phenomena In Nanosmentioning

confidence: 99%

Materials by numbers: Computations as tools of discovery

Landman

2005

Proc. Natl. Acad. Sci. U.S.A.

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Current issues pertaining to theoretical simulations of materials, with a focus on systems of nanometer-scale dimensions, are discussed. The use of atomistic simulations as high-resolution numerical experiments, enabling and guiding formulation and testing of analytic theoretical descriptions, is demonstrated through studies of the generation and breakup of nanojets, which have led to the derivation of a stochastic hydrodynamic description. Subsequently, I illustrate the use of computations and simulations as tools of discovery, with examples that include the self-organized formation of nanowires, the surprising nanocatalytic activity of small aggregates of gold that, in the bulk form, is notorious for being chemically inert, and the emergence of rotating electron molecules in two-dimensional quantum dots. I conclude with a brief discussion of some key challenges in nanomaterials simulations.nanocatalysis ͉ nanoscience ͉ nanowires ͉ quantum dots ͉ simulations of materials

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Shell-Correction Methods for Clusters

Cited by 18 publications

References 100 publications

Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires

Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

Materials by numbers: Computations as tools of discovery

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