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We present a simple but accurate preselection method based on Schwarz integral estimates to determine the significant elements of the exact exchange matrix before its evaluation, thus providing an asymptotical linear-scaling behavior for non-metallic systems. Our screening procedure proves to be highly suitable for exchange matrix calculations on massively parallel computing architectures, such as graphical processing units, for which we present a first linear-scaling exchange matrix evaluation algorithm.
Kußmann et al. (Thu,) studied this question.