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

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.Electronic structure of disordered systems, TBH, Equation-of-Motion metho