Isolated Cluster Model Research Articles

Ab-initio investigations of icosahedral boron compounds with Al, Mg, C, O, Si atoms

The geometry and cohesive energy of isolated clusters — fragments of icosahedral boron compounds — with Al, Mg, C, O, Si substitution atoms have been calculated within the framework of DFT electron density theory using the Gamess software package. Electron density distribution between atoms has been investigated. The bulk modulus of the B12 cluster has been calculated on the basis of quantum chemical calculations and a thermodynamic series of cluster hardness has been constructed: HB22O2 > HB22C2 > HB24 > HB22Si2 > HB22Al2 > HB22Mg2. The calculated bulk modulus and hardness values based on the results of the first-principles study of the clusters are in good agreement with the experimental data for compounds with similar chemical compositions. The technique is applicable to the prediction of the choice of substitutional atoms in icosahedral boron groupings. Keywords: boron, boride, isolated cluster model, bulk modulus, hardness.

Cationic Zinc Species in ZSM-5 Zeolites: Structure and Stability from Embedded Cluster Modeling

Using embedded cluster models and the hybrid density functional–molecular mechanics scheme covEPE, we studied computationally various Zn species in ZSM-5 zeolites: Zn2+, [Zn(OH)]+, [Zn(H2O)]2+, and [ZnOZn]2+. The covEPE embedding approach accounts for the flexibility of the zeolite framework and long-range electrostatic interactions. Due to this flexibility of the embedded models, the mononuclear Zn-species in zeolite structures showed more (four) Zn-O contacts or shorter average Zn-O distances compared to the corresponding isolated cluster models. Comparing protonic and Zn-exchanged forms of the zeolites rings suggests that upon Zn-substitution O centers shift farthest, extending bonds in the five-ring and contracting distances in the six-ring. We also calculated energies of two types of formal reactions for exchanging protons in H-ZSM-5 by zinc ions: a reaction with zinc vapor which is exothermic by −73 to −112 kJ/mol and ion-exchange with an aqueous solution of a zinc salt which is exothermic by −33 to −124 kJ/mol; the latter value corresponds to [Zn(H2O)]2+ coordinated at a six-ring. Cluster embedding stabilizes the zinc exchanged form with respect to the protonic one in both types of reactions.

Reverse Hydrogen Spillover onto Zeolite-Supported Metal Clusters: An Embedded Cluster Density Functional Study of Models M6(M = Rh, Ir, or Au)

A density functional study using isolated cluster models of the zeolite framework (Vayssilov, G. N.; Rosch, N. Phys. Chem. Chem. Phys. 2005, 7, 4019) on supported metal clusters M6/zeo in a hydroxylated faujasite cage showed that for 12 metals M of the groups 8−11 the hydrogenated state, M6(3H)/zeo, is energetically preferred over the bare form M6/zeo(3H). The former state was obtained as result of reverse hydrogen spillover from zeolite OH groups onto the metal particle. In the present work, we reinvestigated this problem of identifying the favorable chemical state of zeolite-supported metal species for selected M6 model clusters (M = Rh, Ir, or Au) using an accurate quantum mechanics/molecular mechanics (QM/MM) approach where a QM partition is embedded in an extended zeolite lattice (MM). The embedding method covEPE, an improved variant of the elastic polarizable environment model EPE, adapted for polar-covalent materials, properly accounts for both the mechanical rigidity of the zeolite framework and t...

Vanadium-51 solid-state NMR electric field gradient tensors: A DFT-embedded ion and isolated cluster study of crystalline vanadium oxides

Density functional theory (DFT) calculations (6–311+G(2d,p)/B3LYP level of theory) of 51V electric field gradient (EFG) tensor elements are performed for embedded and isolated cluster models of orthovanadates. The structural models used to calculate the EFGs of 51V are (I) an isolated H 4VO 4 + cluster, (II) an isolated H n VO 4 n−3 cluster ( n=number of next-neighbor cations) (III) an isolated orthovanadate anion, VO 4 − x , and (IV) a VO 4 − x ion embedded in a finite point-charge array whose electrostatic potential, at the embedded ion, is equivalent to that of the infinite lattice. For models III and IV, a charge x is assigned estimating the covalence of the system. Models III and IV provide results in good agreement with the experiment. Calculations, employing the embedded and isolated VO 4 − x models, are used to discuss site assignments for AlVO 4. Correlations between quadrupole coupling parameters and deviations of the orthovanadate structure from ideal tetrahedral symmetry are shown.

Calculation and properties of trap structural functions for various spatially correlated systems

Thermoluminescence (TL) kinetics in spatially inhomogeneous systems can be studied by various Monte Carlo algorithms. Recently, a new analytical approach was suggested for the isolated cluster model. The theory is based on the concept of trap structural functions (TSFs). TSFs depend solely on topological properties of solids. Therefore, knowing TSFs for traps and recombination centres it is possible to calculate TL for various parameters, e.g. different heating schemes and different energy configurations. This paper presents some properties and methods of calculation of TSFs. Structural character of TSFs is verified numerically.

Calculation of soft atomic potentials caused by three-center bonds in silica glass

Properties of the SiOSi linkage stretched from 0.30 to 0.46 nm in vitreous silicon dioxide are studied with MNDO and PM3 quantum-chemical methods in an isolated cluster model. The soft atomic potential caused by the three-center bond is proved to arise in the stretched linkage. The calculated electronic structure of the three-center bond and vibrational properties of the linkage are discussed.

Magnetic susceptibility calculation of Cd1-xMnxS

The magnetic susceptibility of the semimagnetic semiconductor Cd1-xMnxS (x = 0.05, 0.10, 0.20, 0.35, 0.43) is measured by the Faraday method. Starting from the isolated cluster model in the nearest-neighbour approximation, and from the random distribution of Mn2+ ions, the temperature dependence of the magnetic susceptibility of Cd1-xMnxS is calculated. By comparing these results with the experimental data a significant deviation, increasing with the concentration, is noticed. Treating the probabilities of finding the Mn2+ ions as singlets, pairs or triplets as adjustable parameters (modified distribution), quantitative agreements are obtained for both concentrations. The results show an enhancement of the clustering when the concentration x increases. The probabilities for every type of cluster, in both distributions, are given. The same calculation is done using the ENNPA model and radial decay of the antiferromagnetic interaction J(Rv)= −10.5 Rv-7. In this model an agreement for both concentration is obtained. Results show the importance of the long-range contribution of the antiferomagnetic interaction.

Measurements and calculation of magnetic susceptibility of low-concentrated semimagnetic semiconductor GdxY2-O3

The low-concentrated gadolinium-yttrium mixed oxides GdxY2-xO3 (x = 0.02, 0.06, 0.10) were synthesized. Magnetic susceptibility was measured by the Faraday method in a temperature range 4 <T < 270 K and behaviour in accordance with the Curie-Weiss law was obtained. Starting from the exclusive 24d-site occupancy of Gd3+ ions for concentrations x ≤ 0.41 and from the short range of superexchange Gd(24d)-O-Gd(24d) interaction, the temperature dependence of the magnetic susceptiblity was calculated using the isolated cluster model in the nearest-neighbour approximation. If random distribution of magnetic ions is assumed, good agreement between calculated and experiments χ-1(T) data can be found only for the lowest concentration x = 0.02. Making use of both geometric and modified distributions, the enhancement of the clusterisation of the magnetic cations for increased concentrations x = 0.06 and 0.10 was found

Basis‐Modified hydrogen atoms as embedding atoms in ab initio chemisorption cluster model calculations on Si surfaces

AbstractA comparative and systematic ab initio study of different models simulating the Si (111) surface has been carried out for a variety of embedding hydrogen atoms including unmodified hydrogen atoms and modified hydrogen atoms described with a STO‐4G basis set and a Slater exponent optimized to have the cluster atoms as neutral as possible. The study has been extended to some chemisorption processes as Ag and Al on Si (111). The main conclusion of the present work is that neither the electronic structure of the isolated cluster models nor the nature of the chemisorption bond depend on the kind of embedding hydrogen atoms used to saturate the free valences of the cluster edge atoms. © John Wiley &amp; Sons, Inc.

Magnetic Susceptibility Calculation of Zn1‐xMnxS by the Nearest‐Neighbour Isolated Cluster Model

AbstractMagnetic susceptibility of semimagnetic semiconductor Zn1‐xMnxS (x = 0.05, 0.10) is measured by the Faraday method. Starting from the isolated cluster model in the nearest‐neighbour approximation, and from the random distribution of Mn2+ ions, the temperature dependence is calculated of the magnetic susceptibility of Zn1‐xMnxS. By comparing these results with experimental χ (T) data, good agreement is obtained only for lower concentration x = 0.05. Treating the probabilities of finding the Mn2+ ions as singles, pairs, or triplets as adjustable parameters (modified distribution), quantitative agreement is obtained for both concentrations. Probabilities for every type of cluster, in both distributions, are given. The results show an enhancement of the clusterisation when the concentration x increases.

Monte Carlo modelling of radical-ion recombination in multiparticle tracks

In the framework of the isolated cluster model for radical-ion recombination, the survival probability, recombination rate, escape probability and the ratio of the geminate recombination rate to the total recombination rate have been calculated using the Monte Carlo method. This ratio is important for interpreting the magnitude of magnetic field effects in recombination fluorescence. The results are compared with experiment.

A b i n i t i o self-consistent field and configuration interaction study of Cu5O and Ag5O as models for oxygen chemisorption on Cu(100) and Ag(100)

The lowest electronic states of Cu5O and Ag5O arising from interaction of atomic oxygen (3P) and the isolated cluster model on the 2E or 4A2 electronic states have been studied at the SCF, CASCI, MP2, and CIPSI levels using nonempirical pseudopotentials for the Ar (Kr) cores of Cu (Ag). The ground state of Cu5O and Ag5O is found to be 2E but only after inclusion of correlation effects. However, the energy difference between 2E and the 4A2 or 2A1 electronic states is rather small. The effects of electronic correlation have been analyzed in terms of nondynamical and dynamical contributions. It is shown that SCF values account for only about 25%–30% of the total binding energy, whereas inclusion of nondynamical correlation contributions allow to recover 50% of that value. Thus, dynamical correlation effects must be included in order to describe properly oxygen-cluster interaction occurring in these systems. Results are in good agreement with recent all electron CI studies carried out for Cu5O (2E).

Computer simulations of star cluster dynamics

The present article is intended as an introduction to numerical studies of small self-gravitating stellar systems. First we describe an integration method which is used to calculate the orbits of individual members subject to their mutual attractions. Direct integrations of close encounters and persistent binaries are rather time-consuming and also lead to greater errors. A simple regularization procedure is outlined, which can be used to study collision orbits as well as perturbed two-body motion with increased speed and accuracy. The main part is devoted to the results of four isolated cluster models containing 250 members and one system with 500 initially bound particles. The presence of a mass spectrum increases the evolution rate significantly. Heavy members tend to become more centrally concentrated, while an increasing proportion of light particles populate the extended halo region. The evolution is dominated by one heavy binary which becomes more strongly bound by close encounters with the lighter particles. About half the total energy is absorbed after only 6–18 mean crossing times and this development leads to an increased escape rate. A critical discussion is given of the main aspects of isolated cluster evolution and the results are compared with theoretical predictions. The qualitative agreement with theoretical considerations is on the whole satisfactory, but the numerical calculations show that the importance of multiple interactions involving binaries has been underestimated. The binary phenomenon is connected with the production of energetic escapers. These processes are discussed in some detail and a qualitative explanation is given of the energy sink behaviour. More realistic cluster models have been studied by introducing an external galactic field, as well as supernova events in which the heavy stars lose most of their mass instantaneously. The mass loss assumption is less important for the cluster stability because of competing effects. All cluster models with 250 members and an average initial mass of 0·87 m⊙ yield calculated half-lives below 3 × 10 8 years. The maximum value is reached for intermediate scale factors in the range 2–3 pc, when the combined effect of the internal dynamical evolution and the tidal field is minimized. The existence of the oldest galactic star clusters can therefore only be explained by assuming an increased initial particle number or the presence of an additional smooth mass component.

Low-Temperature Magnetization of Cu(NO3)2·2.5H2O

We have measured magnetization isotherms for single crystals of monoclinic Cu(NO3)2·2.5H2O between 1.2° and 4.2°K by a ballistic method. Fields up to 43 kOe were applied along the b axis, i.e., the long axis of the needlelike specimens. The character of the M vs H curves changes rapidly in this temperature interval. They are described in first approximation by a model of this salt in which Cu+ + ions are coupled by isotropic antiferromagnetic exchange, −JS1·S2, in isolated pairs. The best fit of the data with the isolated cluster model yields J = −5.23k and g = 2.23, in reasonable agreement with earlier susceptibility, specific heat, and proton resonance results. Several modifications of the model were considered in order to remove small systematic discrepancies. The addition of a very weak intercluster coupling in a molecular field approximation yields a quantitative fit of all the data. If H = H0+nM, we find n = −1.2 mole/cgs while J = −5.14k and g = 2.35, in even closer agreement with other observations. This weak antiferromagnetic coupling is large enough to explain the absence of hyperfine structure on paramagnetic resonances seen in the excited pair triplet state.