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

Extremely fast parallel implementation of the equation-of-motion method for electronic structure computations is presented. The method can be applied to non-periodic, disordered nanocrystalline samples, transition metal oxides and other systems. It scales linearly, O(N), runs with a speed of up to 43 GFLOPS on a NEC SX-4 vector-parallel supercomputer with 32 processors and computes electronic densities of states (DOS) for multi-million atom samples in mere minutes. The largest test computation performed was for the electronic DOS for a TiO2 sample consisting of 7,623,000 atoms. Mathematically, this is equivalent to obtaining the spectrum of an n × n Hermitian operator (Hamiltonian) where n = 38;115; 000. We briefly discuss the practical implications of being able to perform electronic structure computations of this great speed and scale.