Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

An experiment on program development

As a contribution to programming methodology, the paper contains a detailed, step-by-step account of the considerations leading to a program for solving the 8-queens problem. The experience is related to the method of stepwise refinement and to general problem solving techniques.     

Scaling assumption for lattice animals in percolation theory

A scaling assumption for the numberg _ns of different cluster configurations with perimeters and sizen leads to the desired cluster numbers near the percolation threshold. The perimeter distribution function has a mean square width proportional ton for largen. The relation between the average perimeter and the cluster sizen for percolation has three different forms atp _c, belowp _c, and abovep _c and is closely related to the shape of the cluster size distribution.     

Oscillation spectra of seed NaCl crystals in aqueous solutions

Using the flicker-noise method (FNM), we investigated the oscillations of clusters in aqueous solutions of NaCl in the range of concentrations from 0.1 to 26.0 mass %. It has been established that in the solutions oscillators whose masses are similar to the masses of the models of aggregates of solvate clusters of ion pairs (SCIP) of salt with a different water content are present. In diluted solutions (<10%), the elementary SCIP has the form NaCl· 40H₂O. For the entire range of concentrations the SCIPs are given by structures based on the cubic system of the sodium chloride system. The base structure for them is a cube formed from 12 SCIPs of salt. The largest cluster revealed by the FNM method for all investigated concentrations of salt had a mass of ≈1.5 million D. The presence of NaCl in water leads to a collapse of its cluster structure, except for the smallest clusters (H₂O)_10…11, whose concentration increases with temperature or solution concentration. The distribution of SCIPs changes dramatically at a temperature above 300 K. The possible structures of SCIPs are given and the mechanism of their formation is discussed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 766–772, November–December, 2005.     

Tetrahedral chalcogenide clusters and open frameworks

By integrating porosity with electrical or optical properties, microporous chalcogenides may have unique applications. Here we review recent advances and discuss concepts in the synthesis and crystal structure of tetrahedral clusters and their frameworks. These chalcogenides can be viewed as trivalent metal chalcogenides doped with tetra-, di-, or monovalent metal cations. Low-valent cations help to increase the cluster size, while high-valent cations have the opposite effect.     

Conformally Invariant Quantization at Order Three

Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.     

Structures of large transition metal clusters

The present review surveys the results of X-ray diffraction studies of large stoichiometric transition metal clusters containing from 20 to 145 atoms in metal cores surrounded by ligand shells (72 compounds). Structures of such clusters have fragments of close packings (face-centered cubic (f.c.c.), hexagonal close (h.c.p.), and body-centered cubic (b.c.c.) packings) characteristic of crystalline bulk metals as well as mixed packings (f.c.c./h.c.p.), local close packings with pentagonal symmetry, and strongly distorted amorphous packings. The observed packing types, their distortions, and the relationship between the atomic structures of metal cores and the atomic radial distribution functions (RDF) are discussed. The structural principles established for the large clusters are applied to analysis of the experimental RDF for metal nanoparticles determined by X-ray diffraction and EXAFS spectroscopy.     

Time,Complex Systems,and Public Policy: A Theoretical Foundation for Adaptive Policy Making

Nonlinear Dynamics, Psychology, and Life Sciences - Can public policy development and implementation be improved by closely tracking and coordinating its timing with that of the regulated sector?...     

First-Known High-Nuclearity Copper–Nickel Carbonyl Cluster: [CuxNi35−x(CO)40]5− (with x=3 or 5) Containing an Unprecedented 35-Atom Three-Layer hcp Triangular Stacking Metal-Core Geometry

Reactions of [Ni₆(CO)₁₂]^2- (1) with CuBr₂ have given rise in small yields (10%) to the first example of a close-packed copper-nickel carbonyl cluster; its formulation as [Cu_xNi_35-x(CO)₄₀]^5- (with x=3 or 5) is based upon a low-temperature CCD X-ray crystallographic determination coupled with an elemental analysis and X-ray fluorescence measurements. This air-unstable black pentaanion (2) together with one co-crystallized bromide anion, six [NMe₄]⁺ counterions, and one solvated acetone molecule comprise the crystallographic independent part in a monoclinic unit cell of P2₁/n symmetry (with Z=4). The geometrically unprecedented 35-atom hcp M(A)₂M(B)₃Ni₃₀ polyhedron of pseudo-D_3h symmetry consists of a central 15-atom equilateral ₄M(B)₃Ni₁₂ triangle that is capped on both sides by two symmetry-related 10-atom equilateral ₃M(A)Ni₉ triangles. The 35-atom M(A)₂M(B)₃Ni₃₀ core is encapsulated by 40 COs, whose connectivities, due to an extra CO ligand on one of the three triangular sides, reduce the pseudo D_3h symmetry of the metal core to C_s. An elemental analysis via AA and X-ray fluorescence measurements resulted in Cu/Ni ratios of 3.2/31.8 and 3.7/31.3, respectively, that are consistent with the metal core being either Cu₅Ni₃₀ (i.e., M(A)=M(B)=Cu) or Cu₃Ni₃₂ (i.e., M(A)=Ni; M(B)=Cu). Several attempts to determine the actual stoichiometry of the metal core by use of electrospray FT/MS/ICR measurements were unsuccessful. The maximum metal-core diameter of 2 is ca. 0.41 nm parallel and 0.85 nm perpendicular to the principal 3-fold axis.     

Application of the Spherical Harmonic Model to the ν(CO) Vibrational Spectra of Some Fe(CO)4 and M(CO)5 (M=Cr, W) Transition Metal Cluster Carbonyl Species

When the Fe(CO)₄ and M(CO)₅ (M=Cr, W) groups are co-ordinated in C_3v and C_4v fashion, respectively, in transition metal carbonyl cluster species they contain two sets of non-symmetry related carbonyl groups. In the application of the spherical harmonic model (SHM) to the interpretation of the infrared spectra of these compounds it proves necessary first to treat these as for a normal, isolated, M(CO)₄ or M(CO)₅ group and then apply the SHM. This recognition gives insights into the general application of the SHM.