Volume 62, Issue 9

In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals is presented. The proposed procedure guarantees a highly accurate evaluation of the overlap integrals with arbitrary values of quantum numbers, screening constants and internuclear distances. It is demonstrated that the computational accuracy of the proposed procedure is not only dependent on the efficiency of formulas, as has been discussed previously, but also on a number of other factors including the used program language package and solvent properties. The numerical results obtained, using the algorithm described in the present work, are in complete agreement with those obtained using the alternative evaluation procedure. We notice that the program works without any restrictions and in all ranges of integral parameters.

We study the level spacing distribution P(S) of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for P(S) is derived and its behaviour close to S = 0 is studied analytically, showing that there is linear level repulsion, unless there are additional constraints for the probability distribution of the matrix elements. The constraint of having only positive or only negative but otherwise arbitrary non-diagonal elements leads to quadratic level repulsion with logarithmic corrections. These findings detail and extend our previous results already published in a preceding paper. For symmetric real 2D matrices also other, non-Gaussian statistical distributions are considered. In this case we show for arbitrary statistical distribution of the diagonal and non-diagonal elements that the level repulsion exponent ρ is always ρ = 1, provided the distribution function of the matrix elements is regular at zero value. If the distribution function of the matrix elements is a singular (but still integrable) power law near zero value of S, the level spacing distribution P(S) is a fractional exponent power law at small S. The tail of P(S) depends on further details of the matrix element statistics. We explicitly work out four cases: the uniform (box) distribution, the Cauchy-Lorentz distribution, the exponential distribution and, as an example for a singular distribution, the power law distribution for P(S) near zero value times an exponential tail.

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shooting method applied to the solutions of nonlinear two-point BVPs. The comparison shows that the MDM is reliable, efficient and easy for solving the nonlinear twopoint BVPs.

Impedance spectroscopy is used for studying the electrical transport properties of bulk heterojunction solar cells. A replacement circuit is needed to translate the frequency response of the circuit to the individual interfaces and layers of the solar cell. As a material combination and device architecture, composites of P3HT and PCBM, sandwiched between a transparent ITO front electrode and an aluminum back electrode, as well as a polymer buffer layer were investigated. By varying the film thickness we identified an equivalent circuit capable to fit our experimental data. We found a dielectric constant for the P3HT and for the P3HT:PCBM bulk.

If λ1 >λ2 ≥λ3 ≥ · · · ≥λn are the eigenvalues of the molecular graph, then the Estrada index, a recently conceived molecular structure-descriptor is EE = n Σ i=1 e λi . The same alkanes, whose molecular graphs have extremal Wiener indices and λ1, are shown to be also extremal with regard to the Estrada index.

The thermal denaturation of β -hemocyanin from the gastropod Helix pomatia (β -HpH) at neutral pH was studied by means of differential scanning calorimetry (DSC). The denaturation was completely irreversible as judged by the absence of any endotherm on rescanning previously scanned samples. Two transitions, with apparent transition temperatures (Tm) of ca. 84 °C (main transition) and ca. 88 °C (minor transition), were detected by DSC in 20 mM MOPS buffer, containing 0.1 M NaCl, 5mM CaCl 2 and 5 mM MgCl 2 at pH 7.2 (buffer A), using a heating rate of 1.0 Kmin −1 . Both Tm values were dependent on the scanning rate, suggesting that the thermal denaturation of β -HpH is a kinetically controlled process. The T m and specific enthalpy values (ΔH cal ) for the thermal denaturation of β -HpH were found to be independent of the protein concentration, indicating that the dissociation of the protein into monomers does not take place before the rate-determining step of the process of thermal unfolding started. A successive annealing procedure was applied to obtain the experimental deconvolution of the irreversible thermal transitions. These transitions are tentatively attributed to the denaturation of, respectively, the wall (main transition) and the collar of the β -HpH molecule. The activation energies (E A ) of both transitions were found to be similar (about 500 kJ mol −1 ). In 130 mM glycine/NaOH buffer, pH 9.6 (buffer B), with β -HpH dissociated into subunits, the calorimetric profile had a more complex character. This could be ascribed to a different stability of the functional units (FUs) constituting the β -HpH subunit. FU d, which in the cylindrical didecameric β -HpH molecule is located in the wall, was markedly less stable than FU g, which belongs to the collar. The thermal denaturation of FUs d and g was described by the two-state irreversible model. On the basis of this model, the parameters of the Arrhenius equation were calculated.

The phase equilibria of CuBr-LiBr, CuBr-NaBr and CuBr-KBr were studied by difference scanning calorimetry (DSC) and X-ray powder diffraction. Extended solid solutions have been found in CuBr-LiBr, while mutual solid solubility of the components of CuBr-NaBr and CuBr-KBr seems to be negligible. It has been confirmed that K 2 CuBr 3 is stable at room temperature.

A simulated spent oxide fuel in a sintered pellet form, which contained the twelve elements U, Pu, Am, Np, Cm, Ce, Nd, Sm, Ba, Zr,Mo, and Pd, was reduced with Li metal in a molten LiCl bath at 923 K. More than 90% of U and Pu were reduced to metal to form a porous alloy without significant change in the Pu/U ratio. Small fractions of Pu were also combined with Pd to form stable alloys. In the gap of the porous U-Pu alloy, the aggregation of the rare-earth (RE) oxide was observed. Some amount of the RE elements and the actinoides leached from the pellet. The leaching ratio of Am to the initially loaded amount was only several percent, which was far from about 80% obtained in the previous ones on simple MOX including U, Pu, and Am. The difference suggests that a large part of Am existed in the RE oxide rather than in the U-Pu alloy. The detection of the RE elements and actinoides in the molten LiCl bath seemed to indicate that they dissolved into the molten LiCl bath containing the oxide ion, which is the by-product of the reduction, as solubility of RE elements was measured in the molten LiCl-Li 2 O previously.

Electrochemical synthesis of binary and ternary compounds in the system Ti-Si-B from chloridefluoride melts has been investigated by voltammetry and electrolysis. Electrochemical syntheses of titanium diboride, four titanium silicides (TiSi 2 , TiSi, Ti 5 Si 4 , Ti 5 Si 3 ), silicon tetraboride and a new ternary compound, Ti 5 Si 3 B 3 , have been found to be one-step processes. The stoichiometry of the deposited compounds has been found to correlate with the bulk concentration of Ti, Si and B ions in the melt.

The electrochemistry of titanium tetrachloride has been examined in trialkyl-substituted imidazolium tetrafluoroborate at 65 °C. Ti(IV) reduction was studied with chronopotentiometry and cyclic voltammetry in melts with different concentrations of TiCl 4 . The diffusion coefficient of Ti(IV) ranged between 1.1·10 −7 and 7·10 −8 cm 2 s −1 . The electroreduction of Ti(IV) was found to proceed via the sequence of one-electron steps, the relative stability of the low valence intermediates being dependent on the concentration of TiCl 4 in the electrolyte. The kinetics of an overlapping disproportionation reaction of Ti(II) was examined and its rate constant at low concentration (0.025 mol/l) of TiCl- was found to be k = 2 · 10 6 cm 3 mol −1 s −1 , Ti(0) being the final product of the stepwise reduction process at higher concentrations (0.03 - 0.14 mol/l).

Formation of oxyfluoroniobium compounds in the binary systems KF-Nb 2 O 5 and K 2 NbF 7 -Nb 2 O 5 and in the ternary system KF-K 2 NbF 7 -Nb 2 O 5 has been expected. Therefore the phase equilibrium and surface tension of the above systems have been determined. The three systems have only been investigated up to 20 mol% Nb 2 O 5 because of its limited solubility. The obtained results have confirmed the formation of oxyfluoroniobium compounds.

Fe-0.94%Mn alloys were boronized at 1210 K during 4 h by the powder pack method. Three distinct regions of cross-sections were found in such alloys. The boride layers were characterized by means of microscopy in terms of coating morphology and thickness. The hardness and thickness of the boride layers were measured, and it was observed that they depend strongly on the thermal processes performed before boronizing the alloys.

The compound bis(methyltriphenylphosphonium) tetrabromozincate(II), [C 19 H 18 P] 2 [ZnBr 4 ], Mr = 939.640, has a monoclinic unit cell, space group P2 1 . The lattice parameters are a = 9.7693(4) Å , b = 12.5508(4) Å , c = 16.5372(6) Å , α = 90.00°, β = 105.2670(11)°, γ = 90.00°, V = 1956.11(11) Å 3 , Z = 2, D x = 1.595 mgm −3 at T = 298 K. The structure consists of one distorted [ZnBr4] 2− tetrahedron and two [(CH 3 )(C 6 H 5 ) 3 P] + cations. Differential scanning calorimetry indicates a continuous second-order transition at (276±2) K that may be classified as a commensurate to incommensurate transformation. A first-order transition to a higher symmetry is associated with a four-fold rotation of the [ZnBr4] 2− ion and a change of entropy ΔS = 22.92 J/(K· mol) at T = (362±3) K. Dilatometric measurements showed a decrease of the lattice parameters in the temperature range 230 - 260 K, confirmed the transition at (276±2) K, and indicated the presence of a third transition at 282 K.