Ab initio Investigation of the Structure and Electronic Properties of Normal Spinel Fe2SiO4

Transition metal spinel oxides have recently been predicted to create efficient transparent conducting oxides for optoelectronic devices. These compounds can be easily tuned by doping or defect to adapt their electronic or magnetic properties. However, their cation distribution is very complex and band structures are still subject to controversy. We propose a complete density functional theory investigation of fayalite (Fe2SiO4) spinel, using Generalized Gradient Approximation (GGA) and Local Density Approximation (LDA) in order to explain the electronic and structural properties of this material. A detailed study of their crystal structure and electronic structure is given and compared with experimental data. The lattice parameters calculated are in agreement with the lattice obtained experimentally. The band structure of Fe2SiO4 spinel without Coulomb parameter U shows that the bands close to Fermi energy appear to be a band metal, with four iron d-bands crossing the Fermi level, in spite of the fact that from the experiment it is found to be an insulator.

Analytical solutions for three-dimensional Coulomb transition matrix at negative energy and integer values of interaction parameter

With the use of a stereographic projection of momentum space into a four-dimensional sphere of unit radius, the possibility of analytical solution of the three-dimensional two-body Lippmann–Schwinger equation with the Coulomb interaction at negative energy has been studied. Simple analytical expressions for the three-dimensional Coulomb transition matrix in the case of the repulsive Coulomb interaction and positive integer values of the Coulomb parameter have been obtained. The worked out method has also been applied to the generalized three-dimensional Coulomb transition matrix in the case of the attractive Coulomb interaction and negative integer values of the Coulomb parameter.

A theoretical study of the chemisty of Furan, Phrrole, Benzofuran, Indole, Dibenzofuran, and Carbazole

It is shown that it is possible, within the framework of the simple H�ckel molecular- orbital method, to account fully for all observations on electrophilic substitution in furan, pyrrole, benzofuran, indole, dibenzofuran, and carbazole, in terms of the π-electron distributions in these compounds. The values of coulomb parameters required to obtain this correlation are physically reasonable and in particular are in agreement with values found independently by a variable electronegativity self-consistent field calculation on pyrrole. The previously puzzling difference in orientation of substitution in benzofuran and indole is accounted for in the present study in terms of a difference in the auxiliary inductive effects of the two hetero-atoms. It seems possible to attribute this difference ultimately to differences in the CO and CN bond lengths and to differences in the effective nuclear charges for 2pπ atomic orbitals on the two hetero-atoms. Attention is drawn to an " isoprotonic principle " for estimating the value of the primary coulomb parameter of a hetero-atom. (It is probably a special case of a more general principle-that the primary coulomb parameter is predominantly determined by the charge on the core and scarcely depends upon the nature of the nucleus at the centre of the core.) A spurious H�ckel molecular-orbital model for the oxygen heterocycles is noted. It accounts for the chemistry of the heterocycles but represents a physically unsatisfactory view of the electronic properties of oxygen in these compounds.

The π-Electron distribution in Pyridine and the molecular-orbital parameters for nitrogen

The π-electron distribution in pyridine has been calculated by the self-consistent-field molecular-orbital method, including electron interaction explicitly. Empirical parameters analogous to the coulomb parameters in the simple molecular-orbital theory are not required in the calculations. The results have been compared with chemical properties of pyridine and have also been used to determine the most suitable values for the coulomb parameters in the simple molecular-orbital treatment of pyridine. It emerges that, in addition to a coulomb parameter to allow for the eleotronegativity of nitrogen being greater than that of carbon, an appreciable auxiliary coulomb parameter, representing an enhanced electronegativity of carbon atoms adjacent to the hetero-atom, must be introduced. This auxiliary parameter is necessary to allow for purely π-electron effects in the vicinity of a hetero-atom and is additional to any parameter which might be required owing to σ-electron polarization effects around the nitrogen atom.