A method for molecular ionization potentials

A new method for one-electron propagator calculations of molecular inization potentials is proposed, using a large matrix technique The results of some trial calculations on molecular nitrogen are given.     

An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

Comparing the Atomic Structures of Binary MO2-SiO2 (M = Ti, Zr or Hf) Xerogels

The incorporation of transition-metal oxides into silica can give materials with useful optical, electronic or catalytic properties. For example, ZrO₂-SiO₂ and HfO₂-SiO₂ materials are of interest due to their high dielectric constants. Here we present a comparison of extended X-ray absorption fine structure and small-angle X-ray scattering results for acid-catalysed binary (MO₂) _x (SiO₂)_{1 – x} (M = Ti, Zr or Hf) xerogels, with x up to 0.4 and heat treatments up to 750°C. Detailed observations for TiO₂-SiO₂ and ZrO₂-SiO₂ xerogels provide a basis for interpretation of new results for HfO₂-SiO₂ xerogels. At low concentrations metal atoms are homogeneously incorporated into the silica network. Ti adopts coordinations of 4 or 6, and Zr and Hf both adopt higher coordination of 6 or 7 (the larger coordinations being due to ambient moisture). At higher concentrations, phase separation of metal oxide occurs. Such regions become clearly separated from the silica network for TiO₂, but remain very finely mixed with silica network for ZrO₂ and HfO₂.     

Second-order Green's function calculations of the ionization potential of a (H2)7 chain embedded in a homogeneous electric field

Summary The vertical ionization potential and the related pole strength of a model alternant chain of 14 hydrogen atoms subject to a homogeneous electric field, parallel to the chain and of increasing intensity are calculated, in the framework of a 6–31G** basis set, at the second-order level of the many-body Green's function theory. Trends observed with orbital relaxation, pair removal and pair relaxation effects are interpreted in terms of deformations of the electron density.     

Transition Metal Atom Sites in Ternary ZrO2-TiO2-SiO2 Xerogels

There has been much work on the binary TiO₂-SiO₂ and ZrO₂-SiO₂ materials prepared by sol-gel because of the beneficial properties resulting from incorporation of Ti and Zr. In contrast the ternary TiO₂-ZrO₂-SiO₂ xerogels have been relatively little studied. We report the results of a study of those xerogels having Zr:Ti:Si ratios of 5:15:80, 10:10:80 and 15:5:80 heated to 750°C and to 1000°C. The study includes X-ray diffraction, small angle X-ray scattering, X-ray absorption spectroscopy at Ti and Zr K-edges, and ¹⁷O MAS-NMR. The study has benefited from close comparison with similar previous studies of the binary systems. The metal atoms in the ternary systems are shown to be predominantly homogeneously mixed in the silica network, as observed for the respective binary systems. The clear exception is for the sample with a minority of Zr, which after heat treatment at 750°C shows the presence of phase separation attributed to the formation of an amorphous precursor of ZrTiO₄; at 1000°C this phase crystallises. In samples with higher Zr content the crystallisation of a ZrO₂ tetragonal phase was observed. The data obtained illustrate well the strength of a research methodology in which a common batch of samples is studied using a coherent suite of modern structural probes.