Theory of forward glory scattering for chemical reactions: New derivation of a uniform semiclassical formula for the scattering amplitude

The theory of forward glory scattering is investigated for a state-to-state chemical reaction whose scattering amplitude can be written as a Legendre partial wave series. Legendre series occur in the exact quantum theory of reactive scattering when the initial and final helicity quantum numbers are zero, as well as in many approximate theories of chemical reactions. The starting point for the semiclassical theory is a two-dimensional integral representation for the scattering amplitude. A uniform semiclassical approximation is derived that is valid for angles both on, and off, the axial caustic associated with the glory. The derivation is the first application to a concrete problem in molecular physics of a method outlined by J. N. L. Connor and H. R. Mayne in 1979 for the uniform semiclassical evaluation of multidimensional integrals. The approach exploits the theory of singularities of differential mappings. The key step in the derivation is an exact one-to-one change of variables in the neighbourhood of the stationary phase points that locally reduce the two-dimensional phase of the integrand to a non-polynomial canonical form. The derivation complements a different semiclassical glory analysis reported in a companion paper.     

Electrostatic potential in cylindrical dielectric media using the image charge method

We derive a simple analytical expression for the electric potential produced by a point charge in a cylindrical pore with relative permittivity different from that of the surrounding medium. The interface between the pore and the surrounding media may contain electric charge or be electrically neutral. The expression reduces to the known solutions when the surrounding dielectric medium is identical to the pore or an electric conductor. We discuss the convergence of the series expansion and numerically evaluate the electrostatic potential inside the cylindrical pore. The calculated potential shows the effect of the dielectric permittivity difference of the media. The results demonstrate that the expression can be implemented in a numerical dynamic simulation of charged systems in cylindrical geometry. We also give an expression for the case when the source charge is in the medium outside the cylinder.     

Potential energy surfaces in algebraic molecular models using coherent states

The potential energy surfaces provided by the coherent states formalism for the case of interacting one-dimensional oscillators is investigated. The case of two interacting oscillators modelled with Morse potentials are considered in detail. First the traditional treatment is presented in order to identify the need to establish a new transformation between the parameters and the classical variables that allow the full Hamiltonian to be recovered. To this end the connection between the su(2) algebraic model and the usual treatment in configuration space was taken into account. It is shown that the coherent state approach when applied to recover the potential energy surface (PES) from a polyad preserving Hamiltonian is viable only in systems with a local mode behaviour. For molecules with a normal mode behaviour the approach is still valid, but the polyad must be broken in order to recover the PES. Our approach is evaluated through the calculation of the force constants for H₂O and CO₂, representative examples of local and normal behaviours.     

Surface aided replica exchange algorithm applied to the prewetting transition

A novel algorithm, termed surface aided replica exchange (SARE), was introduced in which the fluid–surface interaction was varied in order to generate different replicas in a particular ensemble. Exchange between replicas was allowed with a probability of acceptance obtained by imposing detailed balance. The method was implemented in a modified isothermal-isobaric ensemble that permitted precise characterization of the prewetting line of a simple adsorbed fluid. The prewetting line for each surface was characterized by computing the adsorption of the fluid as a function of pressure, and the wetting temperature estimated for each surface.     

Improved techniques for the calculation of ab initio ion-neutral interaction potentials: application to coinage metal ions interacting with rare gas atoms

Ab initio values for the potential energy functions for ion–neutral interactions can be tested by comparison with gaseous ion transport coefficients, but only if special care is taken to compute the interaction potentials accurately over wide ranges of internuclear separation. This is illustrated here by a reanalysis of the ab initio values for the coinage metal ions interacting with rare gas atoms, precise calculations of the transport cross sections over extremely wide ranges of energy, and similarly precise calculations of the zero-field ion mobilities as functions of gas temperature and the field-dependent ion mobilities at various fixed temperatures. The calculations indicate that the mobilities for Ag⁺(¹S) moving in Ne or Ar can distinguish between the existing, very similar ab initio potentials. They also show that substantial differences exist among the mobilities of the coinage metal anions and the ground and excited states of the cations. The techniques implemented are recommended for future ab initio calculations.     

Ab initio investigation of the electronic and vibrational properties for the (CaLi)+ ionic molecule

A wide adiabatic study has been performed for numerous electronic states of CaLi⁺ molecular ion. The adiabatic potential energy curves and their spectroscopic constants (R_e, D_e, ω_e and T_e) have been calculated using an ab initio approach including a nonempirical pseudo-potential for the Ca and Li cores with the core polarisation potentials operator through full configuration interaction (FCI). Thereafter, the energies of vibrational levels and their spacing for all these states have been reported. In addition, the electric dipole moment curves have been investigated for the (1-19) Σ, (1-12) Π and (1-8) Δ electric states. Moreover it lets us check the extreme transition dipole moments (TDM). These behaviours of TDM are more accustomed to estimate the radiative lifetimes for all vibrational levels in 2¹Σ⁺ and 3¹Σ⁺ states. Also, the bound-bound and the bound-free contribution have been calculated precisely and by employing a Franck–Condon (FC) approximation.     

Application of experimental design for optimization of erbium determination by high-resolution continuum source electrothermal atomic absorption spectrometry using lanthanum as a chemical modifier

ABSTRACT

In this paper, lanthanum was used as a chemical modifier for the direct determination of erbium by high-resolution continuum source electrothermal atomic absorption spectrometry. A two-step experimental design was used for optimization, first a full factorial design was conducted for identification of significant factors, and then a central composite design was carried out for final optimization of the significant factors. The optimum parameters were obtained as follows: atomization temperature of 2500°C, pyrolysis temperature of 1600°C, and pyrolysis time of 10?s in the presence of lanthanum as a chemical modifier. Under optimum conditions, the characteristic mass, limit of detection, and limit of quantification were 29?pg, 0.71, and 2.4?µg?L^?1, respectively. The precision of the method, estimated as the relative standard deviation for 10 replicate measurements of 50?µg?L^?1 of erbium, was 1.8%. The optimized method was applied to determine erbium content in sediments and rock samples. The determined values of erbium in sediment certified reference materials were in satisfactory agreement with the certified values according to the t-test for a 95% confidence level.     

Size-dependent electron chemical potential: Effect on particle charging

Electrostatic charging of particles of identical composition, but different sizes, is a poorly understood phenomenon that may be of importance in dust storms, generation of lightning, numerous technological applications involving solid particulates, and in the agglomeration of lunar dust and inter-stellar dust clouds. We show that under optical excitation, the relative magnitude of surface to volume de-excitation gives size-dependent electron and hole concentrations. The consequent differences in chemical potentials can lead to charge transfer between particles of different size. The direction of charge transfer, from large to small or vice versa, depends critically on the properties of the materials.     

The extension of the ILDM concept to reaction–diffusion manifolds

In the present work, the method of simplifying chemical kinetics based on Intrinsic Low-Dimensional Manifolds (ILDMs) is modified to deal with the coupling of reaction and diffusion processes. Several problems of the ILDM method are overcome by a relaxation to an invariant system manifold (Reaction–Diffusion Manifold – REDIM). This relaxation process is governed by a multidimensional parabolic partial differential equation system, where, as an initial solution, an extended ILDM is used. Furthermore, a method for the solution and tabulation of the manifold is proposed in terms of generalized coordinates, with a subsequent procedure for the integration of the reduced system on the found manifold. This modification of the ILDM significantly improves the performance of the concept and allows us to extend its area of applicability. Illustrative comparative calculations of detailed and reduced models of flat laminar flames verify the approach.