Effect of surface modes on the six-dimensional molecule-surface scattering dynamics of H2-Cu(100) and D2-Cu(111) systems

We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H(2)(v,j)/D(2)(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the "stochastic" treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D?2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H(2)(v,j)-Cu(100) system, and dissociative chemisorption-physisorption for both H(2)(v,j)-Cu(100) and D(2)(v,j)-Cu(111) systems. Calculated sticking probabilities by either 4D?2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D?2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H(2) molecule substantially, and (b) the sticking probabilities due to the collision of H(2) on Cu(100) and D(2) on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D).     

Meso-diacylated calix[4]pyrrole: structural diversities and enhanced binding towards dihydrogenphosphate ion

Meso-diacylated calix[4]pyrrole was obtained via acid catalysed condensation of meso-acylated dipyrromethane with acetone. Selective presence of flexible substituents at the calix[4]pyrrole periphery led to interesting structural motifs in the solid state along with enhanced binding towards anions, especially dihydrogenphosphate ion via anchoring.     

Twisting (conformational changes)-based selective 2D chalcogeno podand fluorescent probes for Cr(III) and Fe(II)

The fluorenoazomethine containing chalcogeno podand fluorescent probes having N, O/S/Se coordinating donor unit show donor specific 'turn-on' recognition property towards metals (Cr(III), Fe(II) and Cu(II)), where the fluorescence signals are controlled by the conformational change of the ligand framework on binding with the metal ion.     

The effect of phonon modes on the H2(v, j)/D2(v, j)-Cu(1nn) scattering processes

We include the effect of the phonon modes originating from the three layers of Cu(1nn) surface atoms on the dynamics of incoming molecular [H(2)(v, j)/D(2)(v, j)] degrees of freedom (DOFs) through a mean-field approach, where the surface temperature is incorporated into the effective potential by considering Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes calculated within harmonic approximation. Such time and temperature dependent effective Hamiltonian is further subdivided assuming a weak coupling between the two sets of molecular DOFs, namely, (x, y, z, Z) and (X, Y), respectively, in particular, to reduce the computational cost and the corresponding coupled quantum dynamical equations of motion have been formulated in terms of Time Dependent Discrete Variable Representation (TDDVR) approach. We demonstrate the workability of TDDVR method to investigate the scattering of H(2)(v, j) on Cu(1nn) surface by calculating the reaction probabilities and scattering cross-sections. Calculated results show that the phonon modes affect (a) the state-to-state transition probabilities of the scattered H(2) molecule substantially but chemisorption and physisorption processes negligibly and (b) the reaction probability of the incoming D(2) molecule noticeably.     

On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis

We consider the inverse problem of identifying a general source term, which is a function of both time variable and the spatial variable, in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary. We transform this inverse problem into a problem of solving a compact linear operator equation. For the regularization of the operator equation with noisy data, we employ the standard Tikhonov regularization, and its finite dimensional realization is done using a discretization procedure involving the space $L^2(0,\tau;L^2(Ω))$. For illustrating the specification of an a priori source condition, we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation.     

Studies in nickel(IV) chemistry. Electron transfer kinetics of the reaction between tris(dimethylglyoximato)nickelate(IV) and hexacyanoferrate(II) in aqueous medium

The kinetics of electron transfer from hexacyanoferrate(II) to tris(dimethylglyoximato)-nickelate(IV), Ni(dmg)₃^2?, to produce Fe(CN)₆^3? and Ni(dmgH)₂, follows a pseudo-first-order disappearance in the Ni(IV). The pseudo-first-order rate constants k_obs are linearly dependent on [Fe(CN)₆^4?]₀ in a fiftyfold range of 2 × 10^?4?1 × 10^?2M, and the average values of k_obs/[Fe(CN)₆^4?]₀ range from 194M^?1·s^?1 at pH = 5.20 to 0.2M^?1·s^?1 at pH = 9.07 in aqueous medium at 35°C and μ = 0.57M. Results are interpreted in terms of a probable mechanism involving rate-determining outer sphere one-electron transfer steps from the reductant and one-protonated reductant species to the unprotonated and one-protonated Ni(IV) species present in solution. The more electrophilic one-protonated reductant species apparently reacts several orders of magnitude faster than the unprotonated one.     

Oscillatory free convection flow of a second order fluid from a vertical plate

This paper investigates the problem of free convection flow of a second order liquid in the boundary layer from a semi-infinite vertical plate in which the mean surface temperature varies as a function of the distance from the leading edge of the plate. Study of the oscillatory flow is restricted to small amplitudesε only. Several graphs have been drawn and tables have been presented to depict the effect of elasticity of the liquid and Prandtl number on the velocity and temperature distributions and Nusselt number.     

Tetrameric zirconium(IV) compounds derived from oxozirconium(IV) chloride and heterocyclic aldimines and ketimines

Summary Interaction of ZrOCl₂:8H₂O, [Zr₄(OH)₈(H₂O)₁₆]Cl₈ 12H₂O, with the heterocyclic, aldimines (PyAlA) and heterocyclic ketimines (AcPyA) in Me₂CO in the presence of HC(OEt)₃ yields white amorphous compounds of the type [Zr₄(OH)₁₂(H₂O)₈(PyAlA)₂]Cl₄ and [Zr₄(OH)₁₂(H₂O)₁₀(AcPyA)]Cl₄. Presumably these compounds have a tetrameric dodecahedral structure, derived from the parent. The analytical data, i.r., electrical conductance and t.g. measurements all favour the tetrameric formulation. The t.g. studies also indicate the intermediacy of complex species, which lose water and the Schiff base ligands, with increase in temperature.     

C3-bonded hetero-β-diketonates of palladium(II)

Reactions of PdL₂ complexes, where LH = benzoylacetone, dibenzoyl methane, or dipivaloyl methane, with pyridine and neat β-diketones (L ¹H trifluoroacetylacetone, hexafluoroacetylacetone, thenoyltrifluoroacetone and pivaloyltrifluoroacetone) in toluene resulted in the formation of central carbon (C³) bonded hetero-β-diketonate complexes of the formula [Pd(L)(C³-L′)py]. These were characterized by microanalyses, IR and ¹H NMR spectral data.