Atomic and electronic structure of Na10K10Cs n clusters

Density functional theory is used to study the atomic and electronic structures of Na₁₀K₁₀Cs _n clusters with up to sixty atoms. The simplifying approximation has been made of replacing the external potential of the ionic background by its spherical average about the cluster centre in the iterative process of solving the Kohn-Sham equations for each geometry tested. The search for the equilibrium geometry is performed by employing the technique of simulated annealing. We have always found segregation of Cs atoms to the surface as well as a rather neat separation of different species in different (radial) regions of the cluster. This layering effect appears to be consistent with a tendency to maximize electronegativity differences. When the cluster is big enough, Cs atoms begin to appear also inside the cluster. Those geometrical effects do not perturb the electronic magic numbers well known for pure alkali metal clusters.     

Enrichment and segregation in alkali heteroclusters

A spherical average pseudopotential method (SAPS) is used to investigate some properties of compound alkali clusters. The effect that the substitution of a Sodium atom by a Lithium atom in a Na _n cluster has on the stabilities and geometries is studied forn≤21. We have found that substitution is always energetically possible. On the other hand equiatomic Na _n Cs _n clusters are considered in the size rangen≤16. We find a strong segregation effect of the Cesium atoms towards the cluster surface. This agrees with what happens in liquid Na _x Cs_1?x alloys.     

Distribution of interatomic distances in large metallic clusters

Spherically averaged pseudopotential (SAPS) calculations have been done for Mg _n clusters, withn up to 250 within the framework of density functional theory. The electronic structure is computed resorting to the Thomas-Fermi-Dirac-Weizsäcker (TFDW) approximation for the kinetic energy. The equilibrium geometries have been obtained by minimizing the total cluster energy with respect to the atomic positions using the steepest-descent method. The ground state geometries obtained in this way are formed by spherical atomic shells, the number of them increasing with cluster size, up to a number of four for the biggest sizes considered here. An analysis of the distribution of the interatomic distances shows that the more internal is the shell, the more contracted are the interatomic distances. This effect diminishes progressively with increasing cluster size. For the purpose of comparison, similar calculations have been done with Cs _n clusters in the same size range, allowing us to reproduce previous results obtained using a more elaborated density functional technique (Kohn-Sham method). The inhomogeneous contraction of interatomic distances then appears as a general fact for simple metallic clusters and not only for alkaline ones.     

Density functional theory of the collective electronic excitations in NanKn clusters

The collective electronic response of Na_nK_n clusters has been studied for some model structures. In their low-temperature lowest-energy structure, those clusters have all the K atoms on the surface. The collective oscillation frequencies for clusters with the K atoms segregated to the surface are red-shifted with respect to the corresponding frequencies for isomers with a very similar underlying skeleton but with the Na atoms segregated to the surface. The collective frequency varies smoothly with respect to the degree of relative segregation. These results may be useful in the analysis of the collective response of large alloy clusters and microcrystals. © 1995 John Wiley & Sons, Inc.     

General properties of the electronic structure of alkali metal clusters and Ia-IIa mixed clusters

The results of the systematic ab-initio CI investigation of neutral and charged Li _n , Na _n , BeLi _k and MgNa _k clusters are summarized and analyzed. The general characteristic features of the electronic structure are pointed out:a) The participation of the atomic orbitals, which are empty in Ia and IIa metal atoms, allows for a higher valency of these atoms in clusters.b) Jahn-Teller and pseudo-Jahn-Teller effects strongly influence the electronic and geometric structure of clusters.c) Deformations of cluster geometry can lead to biradicaloid structures with higher spin multiplicity in their ground states.d) The peculiarities of the electronic structures of clusters can be deduced from the presence of many “surface” atoms. The theoretical results agree with experimental data presently available and they are useful for interpretation of the experimental findings.     

Ab initio molecular orbital theory study of GaAs clusters: The geometry

We have studied the structure and geometry of neutral and charged atomic clusters consisting of Ga and As atoms via ab initio Hartree–Fock (HF) and second‐order Møller–Plesset methods. The Ga_mAs_n cluster with m≠n composition prefers a nontetrahedral geometry in the charge neutral (q=0) state. These clusters tend to be stable in tetrahedral geometry when appropriately charged. The Ga_mAs_n cluster with m=n composition (1:1 ratio of Ga to As atoms) tends to be stable in a tetrahedral geometry in the charge neutral (q=0) state. With increasing size of the cluster, the geometry of Ga_nAs_n cluster approaches the zinc‐belende‐type crystalline structure. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 563–573, 2000     

A theoretical study of alkali metal atomic clusters: From Lin to Csn (n = 2–8)

A theoretical study of the electronic structure of the first members of the alkali metal atomic clusters series Li_n to Cs_n (n = 2–8) has been done. The geometries of some isomers of the neutral, positive, and negative charged clusters have been determined. Some important properties have also been calculated: atomic binding energies, vertical and adiabatic ionization potentials, vertical and adiabatic electron affinities, static dipole polarizabilities, and energy gaps. Whenever possible they have been compared with experimental values yielding a reasonable agreement which supports some new values as reliable predictions. The data have been discussed in light of the periodic table of elements trends. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Optical response of cesium coated C60

Photoabsorption spectra are reported for Cs _n ⁺ and C₆₀Cs_n ⁺ + clusters for n=40, 60, 120 and 310. The spectra were obtained by heating the mass selected clusters in a beam by means of photoabsorption until they evaporated metal atoms. The resulting mass loss was observed in a time-of-flight mass spectometer. The plasmon-like resonance in pure Cs clusters shifts to lower energies with decreasing cluster size. The collective electronic excitations in clusters containing C₆₀ are split in energy as would be expected for fullerene molecules coated with layers of metal.     

Stability of hollow spheroidal silicon clusters Sin and SinHn

The structures of Si_n and Si_nH_n fullerenes with 20 ≶n ≶60 are calculated in the MINDO/3 approximation using the Monte Carlo technique for geometry optimization. The calculations show that spheroidal silicon clusters consisting of more than 36 atoms are stable and the bond energy increases with their size. This increase is not noticed for compact clusters calculated as an alternative. For n ≥40-50, the latter have lower bond energies compared to fullerenes. The geometry optimization of the tetrahedral cluster Si₄₅ results in a structure close to spheroidal, which gains in bond energy. The addition of hydrogen atoms to small deformed fullerenes and their geometry optimization make it possible to obtain stable spheroidal structures Si_nH_n whose bond energy is greater than that of alternative compact silicon hydride clusters. When the size of spheroidal clusters Si_nH_n increases, i. e., when n > 36, the hydrogen elimination barriers decrease abruptly; the Si_nH_n diamond structure of the cluster is more advantageous when n ≥50.     

Structural Evolution and Superatoms in Molybdenum Atom Stabilized Boron Clusters: MoB<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n </Emphasis>= 10–24)

Doping transition metal atom is known as an effective approach to stabilize an atomic cluster and modify its structure and electronic properties. We herein report the effect of molybdenum doping on the structural evolution of medium-sized boron clusters. The lowest-energy structures of MoB_n (n?=?10, 12, 14, 16, 18, 20, 22, 24) clusters are globally searched using genetic algorithm combined with density functional theory calculations. We found that Mo doping has significantly affected the grow behaviors of B_n clusters, leading to a structural evolution from bowl-like to tubular and finally endohedral cage. The size-dependent binding energy, HOMO–LUMO gap, vertical ionization potential and vertical electron affinity show that MoB₁₂, MoB₂₂ and MoB₂₄ clusters have relatively higher stability and enhanced chemical inertness. More interestingly, the endohedral MoB₂₂ cage is identified as an elegant superatom, which satisfies 18-electron closed shell configuration well.     

Ionic vibrational breathing mode of metallic clusters

The energy of the vibrational mode with spherical symmetry, in which the ionic cores oscillate in the radial direction around the equilibrium geometry (ionic breathing mode) is calculated for trivalent (Al_N, 2≤N≤50) and monovalent (Na_N, 2≤N≤73; Cs_N, 2≤N≤74) metallic clusters. The ground-state total energy is calculated using density functional theory, with a spherically averaged pseudopotential to describe the ion–electron interaction and optimizing the geometry by the simulated annealing technique. The energy of the ionic mode is calculated by diagonalization of the dynamical matrix including the electronic relaxation in the linear response approximation. The compressibility and bulk modulus of the metallic cluster are obtained from the energies of the monopole oscillations. These energies present a linear behavior on the inverse of the cluster radius, which is analyzed using a semiclassical liquid drop mass formula for the total energy of the clusters and a scaling model. The values of the vibrational frequencies present electronic shell closing effects for the three metals.©1997 John Wiley & Sons, Inc.     

Über Alkalimetall-Suboxide. VII. Das metallreichste Cäsiumoxid—Cs7O

On Alkali Metal Suboxides. VII. The Caesium Oxide with the Highest Metal Content, CS₇O Preparation, crystal growth and X-ray investigations with modified Guinier technique and single crystal diffractometer between 0° and ?170°C are reported for the compound Cs₇O. A simple nitrogen evaporator is described. — The structure of Cs₇O corresponds to the formula [Cs₁₁O₃]Cs₁₀. Single crystal investigations at ?20 and ?l70°C lead to nearly identical atomic distances within the “ionic cluster” Cs₁₁O₃, whereas distances between these clusters and within the oxygen free parts of the structure vary as in metallic caesium.     

Computer simulations of photoionization

The Energy Distribution of Ionizing Transitions (EDIT) for (Cs₂O) _n clusters has been calculated using the technique of molecular dynamics. Isomerization, thermal atomic motion and the electronic density of states all contribute to the shape of these curves.     

The evolution of electronic structure in AlnCom

The ionization potentials of Al_nCo_m clusters (n>m) have been bracketed using laser photoionization mass spectrometry. We find the electronic shell structure manifested in the ionization potentials of Al_n for n≥7 is observed also for Al_nCo and Al_nCo₂, and is consistent with cobalt contributing one electron to the conduction band of the cluster. However, with increasing number of cobalt atoms, this simple picture breaks down; all vestiges of aluminum cluster electronic shell structure are absent for m≥4.     

Abundance of Na cluster ions ejected from a liquid metal ion source

Sodium cluster ions Na⁺ _n withn ranging up to 25 have been observed from a liquid sodium ion source by using a magnetic mass analyzer. Ion intensity as a function of cluster size showed distinct steps and local maxima atn=3, 5, 11, 13 and 19 (magic numbers), and a pronounced odd-even alternation. The features in the ion abundance curve are attributed to the relative stability of cluster ions. The observed magic numbers are only partially explained by the electronic shell model, indicating need to include a consideration of atomic structure in a cluster.     

Atom desorption energies for sodium clusters

The desorption energies of supported sodium clusters have been determined as a function of cluster size. Na _n clusters were formed by surface diffusion of sodium atoms adsorbed from a thermal atomic beam on a LiF(100) single crystal. Measurements have been performed by temperature programmed thermal desorption. The signals reflect fractional order desorption kinetics. The average cluster size could be controlled by varying the total number of sodium atoms on the surface. It was determined from scattering experiments. We find that the binding energies vary between 0.55 and 0.8 eV and only approach a constant value for clusters with diameters as large as 1,000 Å.     

Argon Adsorption on Cationic Gold Clusters Aun+ (n ≤ 20)

The interaction of Au_n⁺ (n ≤ 20) clusters with Ar is investigated by combining mass spectrometric experiments and density functional theory calculations. We show that the inert Ar atom forms relatively strong bonds with Au_n⁺. The strength of the bond strongly varies with the cluster size and is governed by a fine interplay between geometry and electronic structure. The chemical bond between Au_n⁺ and Ar involves electron transfer from Ar to Au, and a stronger interaction is found when the Au adsorption site has a higher positive partial charge, which depends on the cluster geometry. Au₁₅⁺ is a peculiar cluster size, which stands out for its much stronger interaction with Ar than its neighbors, signaled by a higher abundance in mass spectra and a larger Ar adsorption energy. This is shown to be a consequence of a low-coordinated Au adsorption site in Au₁₅⁺, which possesses a large positive partial charge.     

Ionization energies of cesium and cesium oxide clusters

The vertical ionization potentials of 7 cesium and 86 oxidized cesium clusters were determined using the technique of photoionization mass spectrometry. The spectra were obtained using a tunablecw dye laser for clusters in a mass range 1 to 2024 amu. The vertical ionization potentials (IP) are presented as a function of size and composition. The ionization energies of cesium clusters, Cs_n, decrease with cluster size. Unusually low IP were observed for the enneamer, Cs₉, and for the cesium monoxide Cs₁₁ O. With increasing oxidation of the cesium metal clusters the IP decreases (suboxides) reaches a minimum at Cs(Cs₂O)_n and then increases (superoxides).     

Theoretical study of aromaticity in inorganic tetramer clusters

Ground state geometry and electronic structure of M ₄ ^2- cluster (M = B, Al, Ga) have been investigated to evaluate their aromatic properties. The calculations are performed by employing the Density Functional Theory (DFT) method. It is found that all these three clusters adopt square planar configuration. Results reveal that square planar M ₄ ^2- dianion exhibits characteristics of multifold aromaticity with two delocalised π-electrons. In spite of the unstable nature of these dianionic clusters in the gas phase, their interaction with the sodium atoms forms very stable dipyramidal M₄Na₂ complexes while maintaining their square planar structure and aromaticity.