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Extremely fast parallel implementation of the equation-of-motion method forelectronic structure computations is presented. The method can be applied tonon-periodic, disordered nanocrystalline samples, transition metal oxides andother systems. It scales linearly,O(N), runs with a speed of up to43 GFLOPS on a NEC SX-4 vector-parallel supercomputer with 32 processors andcomputes electronic densities of states (DOS) for multi-million atom samplesin mere minutes. The largest test computation performed was for the electronicDOS for a TiO2 sample consisting of 7,623,000 atoms.Mathematically, this is equivalent to obtaining the spectrum of ann × n Hermitian operator(Hamiltonian) where n = 38;115; 000. We brieflydiscuss the practical implications of being able to perform electronicstructure computations of this great speed and scale.

Equation-of-Motion O(N) Electronic Structure Studies of Very Large Systems (N ~ 10 7 )