Massively parallel calculations of the electronic structure of non-periodic micro-crystallites of transition metal oxides

Abstract We report massively parallel computations of the electronic density of states of a non-periodic micro-crystalline of rutile TiO2 with a sample of 491 520 atoms. Mathematically, the problem is equivalent to solving an n × n eigenvalue problem, where n ∼ 2 500 000. We used MasPar MP-1 and MasPar MP-2 autonomous SIMD computers with up to 16 384 processing elements (PEs) with the entire computing time ∼ 1.5 h (on 4K MasPar MP-2). We used the equation of motion method and the non-trivial tight binding model in our calculations and conclude that these methods when implemented on the massively parallel SIMD computer architectures, are very well suited for studying the electronic structure of complex non-periodic systems with both point and extended defects.

[1]  K. Vos.  Reflectance and electroreflectance of TiO2 single crystals. II. Assignment to electronic energy levels , 1977 .

[2]  G. J. Morgan,et al.  The electronic structure and conductivity of large models of amorphous silicon , 1992 .

[3]  A. Fujishima,et al.  Electrochemical Photolysis of Water at a Semiconductor Electrode , 1972, Nature.

[4]  Morgan,et al.  Model of hydrogenated amorphous silicon and its electronic structure. , 1993, Physical review. B, Condensed matter.

[5]  V. Henrich.  The nature of transition-metal-oxide surfaces , 1983 .

[6]  M. Schmeits,et al.  Electronic structure of ideal TiO2(110), TiO2(001), and TiO2(100) surfaces , 1984 .

[7]  D. Bonnell,et al.  A scanning tunneling microscopy and spectroscopy study of the TiO2−x(110) surface , 1992 .

[8]  D. Bonnell,et al.  Structure of the Reduced TiO2(110) Surface Determined by Scanning Tunneling Microscopy , 1990, Science.

[9]  David Beeman,et al.  Vibrational properties of elemental amorphous semiconductors , 1977 .

[10]  B. L. Maschhoff,et al.  Interaction of water, oxygen, and hydrogen with TiO2(110) surfaces having different defect densities , 1992 .

[11]  Zhaoming Zhang,et al.  Electronic interactions in the vanadium/TiO2(110) and vanadia/TiO2(110) model catalyst systems , 1992 .

[12]  Munnix,et al.  Electronic structure of point defects on oxide surfaces. , 1986, Physical review. B, Condensed matter.

[13]  G. J. Morgan,et al.  The double-sign anomaly of the Hall coefficient in amorphous silicon : verification by computer simulations , 1992 .

[14]  D. Weaire,et al.  A comparison of the recursion method and the equation-of-motion method for the calculation of densities of states , 1985 .

[15]  J. W. Halley,et al.  Photoelectrochemical spectroscopy studies of titanium dioxide surfaces: theory and experiment , 1991 .

[16]  V. Henrich.  The surfaces of metal oxides , 1985 .

[17]  B. Hickey,et al.  Application of the equation-of-motion method to the calculation of optical properties , 1991 .

[18]  R. Alben,et al.  Exact results for a three-dimensional alloy with site diagonal disorder: comparison with the coherent potential approximation , 1975 .

[19]  Munnix,et al.  Origin of defect states on the surface of TiO2. , 1985, Physical review. B, Condensed matter.

[20]  David J. Smith,et al.  Interaction of small and extended defects in nonstoichiometric oxides , 1984, Nature.

[21]  D. Weaire,et al.  A new numerical method for the calculation of the conductivity of a disordered system , 1977 .

[22]  J. W. Halley,et al.  Electronic properties of disordered anodic TiO2 (001) surfaces: Application of the equation‐of‐motion method , 1992 .

[23]  T. Madey,et al.  Adsorption and electron stimulated desorption of NH3/TiO2(110) , 1992 .

[24]  Michalewicz,et al.  Electronic structure of multiple vacancies in rutile TiO2 by the equation-of-motion method. , 1990, Physical Review B (Condensed Matter).

[25]  V. Henrich,et al.  Interaction of H2S with high defect density TiO2(110) surfaces , 1989 .

[26]  B. Hickey,et al.  The density of states and spectral function in amorphous Si obtained using the equation of motion method in k-space , 1986 .

[27]  F. A. Grant.  Properties of Rutile (Titanium Dioxide) , 1959 .

[28]  Richard L. Kurtz,et al.  UPS synchrotron radiation studies of NH3 adsorption on TiO2(110) , 1992 .

[29]  J. W. Halley,et al.  Equation of motion method for the electronic structure of disordered transition metal oxides , 1992 .

[30]  D. Weaire,et al.  The Anderson localization problem. I. A new numerical approach , 1977 .