ELF MAPS FOR THE AL2SIO5 POLYMORPHS

            The Electron Localization Function , η(r), is a powerful tool for examining the bonded interactions between atoms in molecules and crystalline materials through graphical representations.  For the vast majority of bonded systems of chemical interest, it has been demonstrated that the dominant term in η(r) is ρ(r) _s^5/3 / Σ_i|∇ψ(r)_{i, s}|², which appears in the denominator of the η(r) definition, where ρ(r)_s = Σ_i|ψ(r)_{i, s}|² is the one-electron orbital probability density and Σ_i|∇ψ(r)_i,s|² is the kinetic energy density at r.  This study examines the η(r) isosurfaces for the Al₂SiO₅ polymorphs kyanite, sillimanite, and andalusite to see how different coordination and geometry of the cations and anions affect the η(r) isosurfaces.  The Al₂SiO₅ polymorphs were chosen due to the variety of aluminum coordination states (4-, 5- and 6-fold), and the 18 crystallographically nonequivalent oxygens that have coordination numbers ranging from two (Al-O-Si), three (Al₃-O, Al₂-O-Si) and four (Al₄-O).  Examination of the η(r)   isosurfaces indicates that their shapes are dependent on the coordination and geometry of the oxygen atoms but are insensitive to coordination of the surrounding cations.  Thirteen of the nonequivalent O atoms are bonded to two Al atoms and one Si atom and are associated with two different η(r) isosurface shapes.  The shape of the η(r) isosurface is dependent on the distance that the O atom lies from a plane defined by the three surrounding cations: at a distance greater than 0.2Å the η(r) can be defined as horseshoe shaped and at a distance less then 0.2Å it can be described as concave hemispherical.  This feature is also seen in the η(r) isosurfaces for the O atoms bonded to three Al atoms where the isosurfaces can be defined as trigonally toroidal and uniaxially trigonally toroidal.  The η(r) isosurface for the two- and four-fold coordinated O atoms are comparable to those described for the Si-O-Si bond with concave hemispherical, mushroom, and banana defined shapes.  In addition, the study shows that the η(r) maps are homeomorpically related to the deformation electron density maps.