Search Results (8)

Experimentally accessible stable polyhedral clusters of gallium differ from clusters of its lighter homologue boron by having sterically demanding external groups such as tBu₃Si, (Me₃Si)₃Si, (Me₃Si)₃C, (Me₃Si)₂N, and fluorenyl. This restricts closo deltahedral [Ga_nR_n]^z gallane chemistry to octahedral derivatives such as Ga₆R₆²⁻ (R = SiBuPh₂, SiBu^t₃) and Ga₆R₆ (R = SiMe(SiMe₃)₂) in which the bulky external silyl groups are spread out because of the relatively high local curvature of the degree 4 vertices of the central Ga₆ octahedron. The structures of larger gallium clusters are based on alternatives to closo deltahedra having exclusively high local curvature degree 4 vertices such as the 8-vertex square antiprismatic Ga₈R₈ (R = fluorenyl) or, more commonly, larger polyhedra or fused polyhedra with some bare gallium vertices. Some of the larger gallium clusters can be considered to be spherically aromatic systems with closed shells according to the jellium model. Examples include [Ga₁₃(SitBu₃)₆]⁻ with 8 cluster electrons corresponding to a filled 1S²1P⁶ shell as well as [Ga@Ga₁₈{C(SiMe₃)₃}₆]⁻ with 52 cluster electrons, Ga₂₂{E(SiMe₃)₃]₈, (E = C, Si) and Ga@Ga₁₁{GaN(SiMe₃)₂}₁₁ with 58 skeletal electrons, and [Ga₂₆{Si(SiMe₃)₃}₈]²⁻ with 72 cluster electrons. The 10-vertex species Ga₁₀{Si(SiMe₃)₃}₆, [Ga₁₀(SitBu₃)₆]⁻, and Ga₁₀(SitBu₃)₆ have structures consisting of a fusion of two polyhedra sharing bare gallium vertices with skeletal electron counts, suggesting a multicenter core bond in each of the two polyhedral cavities. Full article

Transition-metal-doped clusters have long been attracting great attention due to their unique geometries and interesting physical and/or chemical properties. In this paper, the geometries of the lowest- and lower-energy CoK_n (n = 2–12) clusters have been screened out using particle swarm optimization and first principles relaxation. The results show that except for CoK₂ the other CoK_n (n = 3–12) clusters are all three-dimensional structures, and CoK₇ is the transition structure from which the lowest energy structures are cobalt atom-centered cage-like structures. The stability, the electronic structures, and the magnetic properties of CoK_n clusters (n = 2–12) clusters are further investigated using the first principles method. The results show that the medium-sized clusters whose geometries are cage-like structures are more stable than smaller-sized clusters. The electronic configuration of CoK_n clusters could be described as 1S1P1D according to the spherical jellium model. The main components of petal-shaped D molecular orbitals are Co-d and K-s states or Co-d and Co-s states, and the main components of sphere-like S molecular orbitals or spindle-like P molecular orbitals are K-s states or Co-s states. Co atoms give the main contribution to the total magnetic moments, and K atoms can either enhance or attenuate the total magnetic moments. CoK_n (n = 5–8) clusters have relatively large magnetic moments, which has a relation to the strong Co-K bond and the large amount of charge transfer. CoK₄ could be a magnetic superatom with a large magnetic moment of 5 μ_B. Full article

A superatom is a cluster composed of a specific number of atoms. We recently found that the superatom-like X@Ga₁₂ (X = Li~Kr) clusters has the periodic energy levels of the specific orbitals 2S and 2P by means of the DV-Xα molecular orbital calculation method. This periodicity in energy levels has not been seen in 1D or 1F orbitals. We supposed that the periodicity of the energy levels of the 2S and 2P superatomic-like orbitals come from the same symmetry between atomic orbitals as the central atom X and the surrounding specific orbitals, according to the Jellium model. Both the s and p atomic orbitals of the central atom X in the superatom-like X@Ga₁₂ have a large shielding effect, suggesting that the s and p atomic orbitals interact strongly with both 2S and 2P superatomic-like orbitals. The energy level periodicity has the potential to periodically change the number of electrons located in the 1D and 1F orbitals, which is related to magnetic properties and is expected to be useful for novel magnetic devices by periodically controlling the magnetism of superatoms. Full article

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals. Full article

Electron rescattering has been well studied and simulated for cases with ponderomotive energies of the quasi-free electrons, derived from laser–gas and laser–surface interactions, lower than 50 eV. However, with advents in longer wavelengths and laser field enhancement metallic surfaces, previous simulations no longer suffice to describe more recent strong field and high yield experiments. We present a brief introduction to and some of the theoretical and empirical background of electron rescattering emissions from a metal. We set upon using the Jellium potential with a shielded atomic surface potential to model the metal. We then explore how the electron energy spectra are obtained in the quantum simulation, which is performed using a custom computationally intensive time-dependent Schrödinger equation solver via the Crank–Nicolson method. Finally, we discuss the results of the simulation and examine the effects of the incident laser’s wavelength, peak electric field strength, and field penetration on electron spectra and yields. Future simulations will investigate a more accurate density functional theory metallic model with a system of several non-interacting electrons. Eventually, we will move to a full time-dependent density functional theory approach. Full article

Based on the unbiased CALYPSO (Crystal structure Analysis by Particle Swarm Optimization) structure searching method in combination with density functional theory (DFT), the geometrical structures and electronic properties are investigated theoretically for Ga₆ and Ga₅X (X = B, C, N, O, F, Al, Si, P, S, Cl) clusters. The PBE0 exchange-correlation functional and the 6-311G(d) basis set is carried out to determine global minima on potential energy surfaces. The relative stabilities of the clusters are examined by the binding energies and substitution reaction. Following the predictions of the Jellium model, the Ga₅B cluster with the 18 valence electrons is the most stable structure. At last, with the obtained lowest energy structures, some physical properties such as electrons transfer, molecular orbitals, and total and partial densities of states are discussed, respectively. Full article

Reducing the size from the bulk material to nanoparticles produces a scaling behavior in physical properties in the later ones, due to the large surface-to-volume fraction. By further size reduction, entering into the subnanometric cluster region, physical properties are largely affected by strong quantum confinement. These quantum size effects (HOMO-LUMO gap), the small size and the specific geometry award subnanometric clusters with totally new and fascinating properties, including cluster photoluminescence, enhanced catalytic activity, etc. In this review, we report an introduction to the physical properties of clusters based on the jellium model; the controlled synthesis by microemulsion methods and the catalytic properties in different areas as heterogeneous catalysis, photocatalysis or electrocatalysis among others. Full article

We present a method for calculating the energy levels and wave functions of any atom or ion with a single valence electron encapsulated in a Fullerene cage using a jelluim-shell model. The valence electron-core interaction is represented by a one-body pseudo-potential obtained through density functional theory with strikingly accurate parameters for Mg⁺ and which reduces to a purely Coulombic interaction in the case of H. We find that most energy states are affected little by encapsulation. However, when either the electron in the non-encapsulated species has a high probability of being near the jellium cage, or when the cage induces a maximum electron probability density within it, the energy levels shift considerably. Mg⁺ shows behavior similar to that of H, but since its wave functions are broader, the changes in its energy levels from encapsulation are slightly more pronounced. Agreement with other computational work as well as experiment is excellent and the method presented here is generalizable to any encapsulated species where a one-body electronic pseudo-potential for the free atom (or ion) is available. Results are also presented for off-center hydrogen, where a ground state energy minimum of -14.01 eV is found at a nuclear displacement of around 0.1 Å. Full article