No abstract

A new computational scheme is presented for the performance of LCAO−MO calculations in the SCF−Xα model. The scheme is intended to be applicable for large systems and to be more accurate than the scattered−wave SCF−Xα method. The Xα potential is fitted by least−squares to a linear combination of Gaussians, and the approximated SCF−Xα equation is solved by the conventional Rayleigh−Ritz variational method. The muffin−tin approximation is avoided, and matrix elements are calculated analytically in contrast to the discrete variational scheme. Some illustrative results are given for the ionization energies and equilibrium geometries of small molecules. It is found that over−all performance of the method is satisfactory for both ionization energies and equilibrium geometries.

Curved-wave−multiple-scattering cluster calculations with the FEFF6 code were used to interpret experimental AlK-edge near-edge X-ray absorption fine structure (NEXAFS) spectra of various minerals and Y zeolites for energies ∼15 eV above threshold. Octahedral, tetrahedral, and square planar geometries of Al can be easily distinguished from each other utilizing characteristic features in the NEXAFS data. NEXAFS line shapes are used for determining the geometrical conformations of Al atoms in Y zeolites with one or more conformational geometries. In the H−Y zeolite, separate contributions to the NEXAFS from tetrahedrally and octahedrally coordinated Al atoms are identified. The differences in the octahedrally coordinated Al spectra in the H−Y zeolite compared with spectra for standard octahedrally coordinated Al compounds can be attributed to the presence of very small nonregular clusters of octahedrally coordinated Al dispersed over the zeolite. However, the presence of some pentacoordinated Al cannot be excluded.

The Al K-and L II/III -edge XANES of aluminium oxide are interpreted using empirical molecular orbital theory (EHMO) and ab initio self-consistent field real space multiple scattering calculations (FEFF8). Most features in the XANES at the K-and L II/III -edges are interpreted as shape resonances; although some fine structure, visible at both edges, arises from multiple scattering over the medium range (∼15 Å). The change in local symmetry between octahedral and tetrahedral Al explains the observed differences in the electronic structure. First, Al p-d hybridization is allowed only in tetrahedral symmetry, resulting in a lower absorption edge in tetrahedral Al than in the octahedral. Second, only in octahedral Al do the oxygen orbitals near the valence band maximum (the HOMOs) have the right symmetry to mix with the Al p orbitals just above the band gap (the LUMOs). This gives a more screened core hole in the octahedral case. Calculations on distorted octahedral Al sites reveal both p-d and s-d hybridizations; however, the latter is less prominent. The diffuse d orbitals, which hybridize with the p or s orbitals in tetrahedral or distorted octahedral symmetry, are primarily responsible for the fine structure in the near-edge region (0-15 eV) that is determined by medium-range scattering (up to ∼15 Å). The observed difference in the magnitude of this fine structure at the K-and L II/III -edges is caused by the different degrees of d orbital hybridization with the s and p orbitals.