Perturbation theory for excited states. IV

Two of the perturbation methods developed in Paper I (CIPT and SCPT) are extended for use with uncoupled Hartree-Fock perturbation theory. Corrections to the uncoupled results are discussed and it is found that it is possible to correct using functions which when applied to ground state calculations are equivalent to the geometric approximation. It is also shown that CIPT and SCPT can be applied to ground state calculations and that when coupled perturbed orbitals are used CIPT and SCPT are equivalent to the usual coupled perturbation theory.     

Exact solutions for spherically confined hydrogen‐like atoms

We present exact analytical solutions for the much‐studied problem of a hydrogen‐like atom confined in a spherical box of radius R. These solutions, which are obtained for all states and all R, are expressed directly in terms of the Kummer M‐functions whose analytical and numerical properties are well known, and may be calculated using standard computing packages. The solutions are illustrated by precise calculations that yield accurate energies E for any given radius R, or for R when E is known. In the special case where E = 0, it is shown that the solution may be expressed in terms of Bessel functions. Finally, the physical assumptions made in applying this model to describe atomic confinement are discussed critically. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Transport of solutes through calix[4]pyrrole-containing cellulose acetate films

Films of cellulose acetate containing different concentrations of meso-octamethyl-porphyrinogen (calix[4]pyrrole) were prepared and characterized using UV-vis and FTIR spectroscopy, DSC and SEM. Incorporation of calix[4]pyrrole into cellulose acetate leads to a decrease in the degree of hydrophilicity of the polymeric matrix. However, a slight increase in the percentage of water uptake of the polymer is found with an increase of the initial amount of calix[4]pyrrole in the composite composition. This effect can be related to the plasticizing effect that the calix[4]pyrrole provokes in the cellulose acetate. A comparative study of transport parameters of oxygen and some non-associated electrolytes (sodium, copper(II) and nickel chlorides) was carried out. The diffusion coefficients of molecular oxygen through cellulose acetate films decrease with an increase of the concentration of calix[4]pyrrole in the composite films. The transport (diffusion and permeation) of the above mentioned electrolytes through a set of composite films shows a decrease of permeability and diffusion coefficients with an increase of calix[4]pyrrole concentration. Such behaviour is typical of systems where interactions between the polymer and diffusing species occur. However, from the analysis of the distribution coefficient, it was found that those interactions are only dependent on the calix[4]pyrrole content for 2:1 electrolytes.     

Why the constituent interchange model does not predict the dimensional counting rule to any finite order in QCD

We demonstrate that the constitutent interchange diagram for nucleon nucleon elastic scattering contains a pinch singularity. This means that it predicts that \(\frac{{d\sigma }}{{dt}} \sim s^{ - 9} f\left( \theta \right)\) for high energy elastic scattering, at least to any finite order in QCD. We also show how the dimensional counting rule may perhaps be recovered by summing a suitable infinite series of graphs.     

Studies under Continuous Irradiation of Photochromic Spiro[fluorenopyran‐thioxanthenes]

New indeno‐fused spiro[benzopyran‐thioxanthenes] were synthesized (see 3a – d in Scheme 3) and their photochromic properties evaluated under continuous irradiation (Table 1). When submitted to irradiation for several minutes with a Xe lamp, the system behaved as one constituted by two open colored forms with different thermal bleaching rates and different susceptibilities to degradation. An increase in irradiation time led to significant degradation and to the apparent predominance of the open colored form with the faster bleaching rate.     

Bounds for Hartree-Fock perturbation theory

Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.