
%0 Journal Article
%A Michalewicz, Marek T. 
%A Nyberg, Per 
%T Equation-of-Motion <emph type="2">O</emph>(<emph type="2">N</emph>) Electronic Structure Studies of Very Large Systems (<emph type="2">N</emph> &#126; 10 <emph type="7">7</emph> )
%J Australian Journal of Physics
%D 1999/08/27
%V 52
%N 5
%P 919-927
%K 
%R https://doi.org/10.1071/PH99002
%U https://www.publish.csiro.au/paper/PH99002 
%X 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 &#215; 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. 
