Quantum-Chemical Modeling of the Effect of a Continuous Random Network on Stabilization of Charged and Neutral Defects in a-S

Quantum-chemical modeling of the stabilization of neutral and charged defects in amorphous sulfur (a-S) has been carried out. The atoms constituting the three nearest coordination spheres of a defect were modeled using the cluster approximation at the HF/6-31G* level. The interaction of the defect region with distant fragments of a continuous random network was calculated using the polarizable continuum model (PCM), in which the medium surrounding the cluster was considered as a continuum with the experimental permittivity for a-S. The energy of formation of charged defects E _def based on threefold coordinated sulfur atoms (C ₃ ⁺ , ₃ ^? )is close to the homolytic bond cleavage energy E _b. For neutral defects, E _def < E _b. Such defects can be the sites with a negative correlation energy, which are responsible for specific properties of chalcogenide glassy semiconductors.     

Thermal expansion of methanol + cyclohexane near the critical solution point

We report precise measurement of volume changes as function of temperature in the one phase region of methanol + cyclohexane near the critical solution point. We find a value for the critical exponent α of 0.11 ± 0.07 in the region 11 Mk < T – T_c < 6.4 K. This value agrees with the Ising value of $\text{1}\text{8}$. For temperatures closer to Tc we observe a stronger divergence. In addition we observe unusual behavior over a small region of temperature centered at T – T_c = 15 mK.     

Discrete models of growth and dynamical percolation in chemistry

Space-time lattice (cellular automaton) models of pattern formation and growth are described. Suitable local rules for automation evolution represent the spreading of wave fronts of activity in an excitable medium. A random distribution of seeds produces expanding rings that fuse and are annihilated. The seeding density, p_A, is used as a scaling parameter to give unique, reduced dynamics in an arbitrary dimension d. For d = 2, in this (continuum) picture, the rings fuse globally (percolate) at a critical instant, t?_c = 0.45. For the unscaled time evolution, dynamical percolation is examined in the p_A × t plane. A swath of these percolating states is found. On the “explosion” boundary of this swath the percolation cluster just forms; on the “implosion” boundary it breaks up. Using a small-sample method the fractal dimension of the critical (boundary) cluster is estimated to be 1.9 (±0.01). Also percolation for continuously emitting seeds, which produce “discs” of activity, is related to ring evolution.     

Crystal chemistry of fluorite-like clathrates AB 3F10

Crystal chemical analysis of the structures of clathrates AB ₃F₁₀ derived from the structural type KY₃F₁₀ was carried out. As the structure-forming fragment, a truncated octahedron is considered obtained by connecting 24 F^? anions of the outer faces of {YF₈} antiprisms that form the cluster {Y₆F₃₂}. Four modes of connection of these truncated octahedra giving B ₃F₁₀ frameworks were established, two modes involving common edges and two modes involving common hexagonal faces. Edge connection corresponds to known structural types in which the {B ₆F₃₂} clusters are arranged as cubic close packing of spheres (structural type KY₃F₁₀) or as hexagonal close packing of spheres (structural type β-KYb₃F₁₀). Face connection gives rise to motifs similar to those formed by carbon atoms in diamond and lonsdaleite structures. The former motif corresponds to the recently established structure of (H₃O)Yb₃F₁₀ · H₂O. For the latter motif, a model of the hypothetical hexagonal phase ThEr₂F₁₀ was proposed (space group P6₃/mmc, a = 1.1058 nm, b = 1.8007 nm, Z = 8), which was characterzed, in terms of the bond valence method, the global instability index GII = 0.065.     

Use of a size-consistent energy functional in many electron theory for closed shells

If the ground state wave-function ψ_gr is written as ψ_gr = Φ_o+X, withX as the correlation part satisfying (φ_o¦x) = 0, andx expressed as an expansion in terms of pair, pair-pair etc. cluster functions, then the expectation value of the energyE = (ψ_gr¦H¦ψ_gr)/(ψ_gr¦ψ_gr) has the property that the normalization term in the denominator completely cancels the unlinked part of the numerator, as noted by Sinanoglu. We use Cizek's coupled-pair ansatz ψ_gr = exp(T ₂)Φ₀ for transcribing Sinanoglu's expansion in a many-body language to study the behaviour of the size-consistent (linked) energy functional thus generated. For calculating the matrix-elements of the cluster components ofT, we use two recipes: (1) a variational determination of the cluster components using Euler's principle for the energy functional akin in spirit to the Varied Portion Approach (VPA) of Sinanoglu and (ii) a nonvariational determination of the cluster components using the conventional coupled-cluster theory. Results are presented for model test systems and are compared with variational CI and nonvariational coupled-cluster values. It has been observed that the values obtained from the size-consistent energy functional from the cluster components obtained from methods (i) and (ii) are quite close and both compare well with the nonvariational coupled-cluster results. Some useful simplifications afforded by the VPA are also indicated. A brief perspective of the method vis-a-vis other related theories is also given.     

Possible large magnetic moments in 4d transition metal clusters

The electronic structure and magnetism of 13 atom clusters of ruthenium, rhodium and palladium having face centered cubic(fcc) geometry has been studied using a Gaussian orbital basis and the local spin density approximation. Calculations were done for the lattice spacings relevant to the bulk crystal lattice. Using the fixed moment states as input potentials, as many as 3 self-consistent states were obtained for these clusters. The 3 converged states of Rh₁₃ cluster is found to have magnetic moments of 0.69 _μB , 1.00 _μB and 1.46 _μB . Out of these states, 0.69 _μB moment state is found to be the ground state. But the total energy difference between the 0.69 _μB and 1.00 _μB state is very small. The 1.46 _μB moment state coincides with the state reported previously by other authors which was obtained using the discrete variational method. The experimentally observed moment was around 0.47 _μB . Our calculated moment is closer to the experimentally observed moment than the previously reported moment, but is still a bit larger. Ru₁₃ cluster is also found to have large moments, and 3 self-consistent states are also obtained for this cluster. The 3 magnetic moments of the Ru₁₃ cluster are 0.46 _μB , 0.62 _μB and 1.08 _μB . Out of these states, 0.62 _μB moment state is found to be the ground state. For the Pd₁₃ cluster, in addition to the nonmagnetic state previously reported, a state with magnetic moment of 0.46 _μB is also found to exist indicating possible magnetism in cluster phase.     

Experimental determination of deposition induced cluster deformation

We describe an experimental method to measure the cluster deformation of metal clusters deposited on a substrate. It is based upon the sensitivity of the cluster plasmon resonance on the geometric shape of the clusters; it uses optical spectroscopy with polarized light in oblique incidence. The proposed method was applied to silver clusters (mean diameter 2R = 2nm) produced in a supersonic beam and deposited on a quartz glass substrate. Cluster deposition and optical measurements were performed in situ in vacuum. At an estimated particle velocity of 1.5 · 10³ ms ^-1, we evaluated an axial ratio of c/a = 0.86 for the deposition induced deformation. This result is compared to data from molecular dynamical simulations. By varying the substrate coverage, the critical cluster coverage for the onset of electromagnetic cluster-cluster coupling and coalescence was determined to amount to 0.1 cluster-monolayers.     

Theory for spin relaxation in small magnetic metal clusters

We discuss the magnetic properties of small neutral transition-metal clusters like Fe _n and Co _n deduced from Stern-Gerlach deflection experiments. We claim that the asymmetric Stern-Gerlach deflection profiles are due to a transfer from electronical angular momentum to the cluster rotation, allowing for a depopulation of the high energy magnetic levels. For finite temperatures we consider two limiting cases. First, the cluster magnetization is assumed to be tied to the random orientation of the cluster easy axes due to the lattice anisotropy. This causes a surprisingly small magnetization for small external magnetic fields. For larger fields and also for increasing temperatures the magnetization is released from the cluster geometry and allowed to align itself parallel to the field. In the second case the clusters are treated as an ensemble of superparamagnetic particles. Here, the effect of the anisotropy is less visible. The cluster lattice anisotropy per atom is expected to decrease for increasing cluster size. Preliminary results support this.     

Structure and analysis of atomic vibrations in clusters of Cu n (n ≤ 20)

The binding energy, equilibrium geometry, and vibration frequencies of free clusters Cu _n (2 ≤ n ≤ 20) are calculated using the potentials of interatomic interactions found using the tight-binding approximation. The nonmonotonic dependence of the clusters’ minimum vibration frequency on their sizes and the extreme values for the number of atoms in a cluster n = 4, 6, 13, and 19 is demonstrated. It is noted that this result agrees with the theoretical and experimental data on stable structures of small and medium metallic clusters.     

Theoretical study of isomerism of compounds of CO and CO2 molecules with aluminum clusters Al13, Al12Ti,and Al12Ni

Structural characteristics, vibrational frequencies, and energies of isomers of compounds of CO and CO₂ molecules with the centered aluminum cluster Al₁₃ and its doped analogues Al₁₂M (M = Ti and Ni) have been calculated by the density functional theory method. For the Al₁₂MCO compounds, the most favor-able are two “fragment” isomers in which the C and O atoms are separated and built into the cluster cage, completing it to a 14-vertex polyhedron. In one of them, the C and O atoms are in the capping positions over adjacent trigonal MAl₂ faces; in the second isomer, there is the five-coordinate C* atom located in the center of a tetragonal MAl3 face and bound to the central Al atom through the long fifth bond. The “coordinated” isomers, in which the CO molecule is coordinated as a ligand to a cluster vertex, edge, or face, are unstable to removal of CO for Al₁₃CO, close in energy to the fragment isomers for Al₁₂NiCO, and considerably higher on the energy scale than the fragment isomers but remain stable to CO removal for Al₁₂TiCO. For the Al₁₂MCO₂ compounds, the most favorable is the fragment isomer in which both oxygen atoms are in the capping positions over adjacent faces and the C* atom is five-coordinate. The alternative oxo carbonyl isomer Al₁₂MO(CO) is close to the lowest-lying one in the case of M = Ni and is ～56 kcal/mol higher on the energy scale in the case of M= Ti. The less stable Al₁₂M(CO₂) isomer is the complex in which the CO₂ ligand is coordinated to an M-Al edge. According to calculations, addition of CO to Al₁₂MO and addition of CO₂ to Al₁₂M to form, respectively, Al₁₂MO(CO) and Al₁₂M(CO₂) can occur without noticeable barrier. The Al₁₂M(CO₂) and Al₁₂MO(CO) isomers are separated by a barrier, moderate for M = Ti (～16 kcal/mol) and small for M = Ni (～6 kcal/mol).     

Irreversible adsorption of latex particles on fibrinogen covered mica

Physicochemical properties of bovine plasma fibrinogen (Fb) in electrolyte solutions were characterized. These comprised the diffusion coefficient (hydrodynamic radius), determined by the DLS method, electrophoretic mobility and the isoelectric point. The hydrodynamic radius of Fb was 12 nm for pH<5. The number of uncompensated (electrokinetic) charges on the protein N _c was calculated from the electrophoretic mobility data. It was found that for pH<5.8 the electrokinetic charge was positive, independently of the ionic strength and negative for pH>5.8. For pH=3.5 the value of N _c , was 26 for 10^?3 M. Similar electrokinetic measurements were performed for the mica substrate using the streaming potential cell. It was shown that for pH=3.5 and 10^?3 M, the zeta potential of mica remained negative (?50 mV). This promoted an irreversible, electrostatically driven adsorption of Fb, which was confirmed in experiments carried out under diffusion-controlled transport. The surface concentration of Fb on mica was determined directly by AFM counting. By adjusting the time of adsorption, Fb monolayers of desired coverage were produced. Independently, the presence of Fb on mica was determined quantitatively by the colloid enhancement method, in which negatively charged latex particles were used, having the diameter of 800 nm. It was found that for Fb coverage below 0.05 the method was more sensitive than other indirect methods. The experimental data obtained in latex deposition experiments were adequately interpreted in terms of the random site model used previously for polyelectrolytes. It was shown that adsorption sites consisted of a cluster of two Fb molecules. It was concluded that the colloid enhancement method can be successfully used for detecting the presence of proteins at solid substrates and to determine the uniformity of monolayers in the nanoscale.     

Production of large sodium clusters (Nax,.x⩽65) by seeded beam expansions

Seeded beam expansions of high-temperature sodium vapour in helium, neon, argon, krypton and nitrogen carrier gases are examined. Photoionization coupled with mass spectroscopic detection is used to determine beam constituents. Contrary to non-seeded supersonic expansions, in which the abundance of sodium clusters observed decreases exponentially with increasing cluster size, large abundances of higher clusters (Na_x, x ?65) are observed. Maxima centered at m/z = 161, m/z = 437 and m/z = 874 occur under certain conditions.     

Hydrodynamic interaction between macromolecules in sedimentation

The sedimentation constant of hard spheres decreases with concentration, due to the effect of backflow and distortion of the hydrodynamic field. For macromolecules at the θ-temperature, this effect of concentration is much smaller than that of equivalent spheres. Pyun and Fixman suggest that intertwinement of macromolecules gives rise to increase of the sedimentation velocity. However, their detailed model of intertwined molecules is unrealistic. An alternative model is proposed by considering a pair of intertwined homologous molecules with N_i and N_j segments respectively, as a single molecule with (N_i + N_j) segments. This model leads to a simple expression for the concentration coefficient in the sedimentation velocity, containing an adaptable parameter, χ_ij, characterising the probability of intertwining. The probability of intertwining is put equal to the probability of intermolecular approach to within a distance of R_int and χ_ij is defined by χ_ij = 2R_int/(R₁ + R_j), with R_i and R_j the friction equivalent molecular radii. From experiments on a number of sharp polystyrene fractions in cyclohexane at T = θ, a value χ_ji = 2.2 is deduced, decreasing with increase of molecular weight. Qualitative agreement is found between experimental results and predictions from the model. Quantitative agreement is not expected in view of uncertainties in the model. In ternary systems, containing molecules of different velocity, probably additional effects operate besides backflow, field distortion and intertwinement.     

Electronic structures and stabilities of sodium clusters: jellium-sphere dimer calculation

Bonding properties of sodium-cluster dimers, (X ₄)₂ and (X ₈)₂, whereX _n is a jellium sphere corresponding to a cluster ofn atoms, were investigated by the linear-combination-of-jellium-orbitals method with local-spin-density-functional approximation. The stability ofn=8 clusters, observed in the experiment, is discussed in relation to the binding properties of dimers. We have found that (1) the (X ₄)₂ bonding has a covalent character, which makes theX ₈ formation favorable, and (2)X ₈ has an inert property because the force between jellium spheres in (X ₈)₂ is due to a weak dispersion force.     

Time-of-flight mass and photoelectron spectroscopy study of LaC n -

Mass spectra of LaC _n ^- were taken by using a laser-vaporization source (LVS) and pulsed arc cluster ion source (PACIS) applied to La-carbon composite rods (1:130 atomic ratio). The mass spectrum using the LVS with annealing procedure has shown several magic numbers for LaC _n ^- (n = 44, 50, 60, and 70), whereas only small LaC _n ^- (up to n = 14) have been observed in the mass spectrum using the PACIS. Photoelectron spectra of some of these have been measured using a magnetic-bottle type time-of-flight electron spectrometer. These results indicate the exsistence of a few conformational isomers for small La-containing carbon cluster negative ions LaC _n ^- (n = 5–8).     

Insulator—conductor transition in tetracyanoplatinate complexes

The changes in electronic structure of the tetracyanoplatinate complex accompanying the transition [Pt(CN)^2?₄]_n(insulator) + oxidant → [Pt(CN)^{2 ?q+}₄]_n(conductor) have been investigated with a cluster model approach. Calculations for trimer (n = 3) cluster models of the insulator and conductor have been performed with the self-consistent-field Xα Dirac scattered-wave method. Based on the cluster electronic structure, we infer that the valence band edge in the insulator is not d_zz like, but consists of metal (dδ + dπ) and ligand character. Partial oxidation of this band results in a shortening of the inter-stack distance, leading in turn to a partially occupied d_zz-like valence band. Thus electron transport occurs along the Pt backbone.     

Multiple morphological micelles formed from the self-assembly of poly(styrene)-b-poly(4-vinylpyridine) containing cobalt dodecyl benzene sulfonate

A series of supramolecular block copolymers were prepared using poly(styrene)-b-poly(4-vinylpyridine)(PS-b-P4VP) which coordinated with cobalt dodecyl benzene sulfonate (Co(DBS)₂) in tetrahydrofuran (THF). Fourier transformation infrared spectroscopy (FTIR), UV-vis absorption spectroscopy (UV) and differential scanning calorimetry (DSC) showed that Co(DBS)₂ coordinated to the lone electron pairs of the pyridine nitrogens in the P4VP block and leaded to complexes. The supramolecular block copolymers could self-assemble into nanosized micelles with different shapes and dimensions in THF, depending on the number of Co(DBS)₂ groups per 4-vinylpyridine (repeat unit was denoted by n) and the ratio between PS block length and P4VP block length. Transmission electron microscopy (TEM) results showed that when the number of repeat units of P4VP was more than that of PS, micelles with different interesting shapes such as spheres, rods, vesicles, large compound vesicles (LCVs) and the large compound micelles (LCMs) were observed if increasing the content of the Co(DBS)₂ in PS-b-P4VP copolymer/THF solution; When the number of repeat units of P4VP was less than that of PS, the micelle morphologies changed from spheres to rods, bi-layer, and LCMs if the Co(DBS)₂ content was increased progressively.     

Photoelectron spectroscopy of transition metal-sulfur cluster anions

Metal (M)-sulfur cluster anions (M = Ag, Fe and Mn) have been studied using photoelectron spectroscopy (PES) with a magnetic-bottle type time-of-flight electron spectrometer. The M_nS _m ^? cluster anions were formed in a laser vaporization cluster source. For Ag-S, the largest coordination number of Ag atoms (n _max) is generally expressed as n _max =2m ? 1 in each series of the number of S atoms (m). For Fe?S and Mn?S, it was found that the stable cluster ions are the ones with compositions of n=m and n=m±1. Their electron affinities were measured from the onset of the PES spectrum. For Ag?S, the EAs of Ag₁S_m are small and around 1 eV, whereas those of Ag_nS_m (_n ≥ 2) become large above 2 eV. The features in the mass distribution and PES suggest that Ag₂S unit is preferentially formed with increasing the number of Ag atoms. For Fe?S and Mn?S, the PES spectra of Fe_nS _m ^? /Mn_nS _m ^? show a unique similarity at n ≥ m, indicating that the Fe/Mn atom addition to Fe_nS _n ^? /Mn_nS _n ^? has little effect on the electronic property of Fe_nS_n/Mn_nS_n. The PES spectra imply that the Fe_nS_n cluster is the structural framework of these clusters, as similarly as the determined structure of the Fe_nS_n cluster in nitrogenase enzyme.     

Quantum chemical DFT calculations of the local structure of the hydrated electron and dielectron

The adiabatic bound state of an excess electron is calculated for a water cluster (H₂O) ₈ ^? in the gas phase using the DFT-B3LYP method with the extended 6-311++G(3df,3pd) basis set. For the liquid phase the calculation is performed in the polarizable continuum model (PCM) with regard to the solvent effect (water, ? = 78.38) in the supermolecule-continuum approximation. The value calculated by DFT-B3LYP for the vertical binding energy (VBE) of an excess electron in the anionic cluster (VBE(H₂O) ₈ ^? = 0.59 eV) agrees well with the experimental value of 0.44 eV obtained from photoelectron spectra in the gas phase. The VBE value of the excess electron calculated by PCM-B3LYP for the (H₂O) ₈ ^? cluster in the liquid phase (VBE = 1.70 eV) corresponds well to the absorption band maximum λ_max = 715 nm (VBE = 1.73 eV) in the optical spectrum of the hydrated electron hydr e _hydr ^? . Estimating the adiabatic binding energy (ABE)e _hydr ^t- in the (H₂O) ₈ ^? cluster (ABE = 1.63 eV), we obtain good agreement with the experimental free energy of electron hydration ΔG ₂₉₈ ⁰ (e _hydr ^? ) = 1.61 eV. The local model (H₂O) ₈ ^2? of the hydrated dielectron is considered in the supermolecule-continuum approximation. It is shown that the hydrated electron and dielectron have the same characteristic local structure: -O-H{↑}H-O- and -O-H{↑↓}H-O-respectively.