Long-range exact exchange is a must for having correct charging energies in DFT and for resonance studies. However, exact exchange for large systems (especially long range exact exchange) scales cubically with system size which prevented its practical application with grid-based or plane-wave methods to systems with more than very few hundreds of occupied orbitals. We overcome the scaling hurdle by rewriting the exact exchange operator as an overlap (convolution-free) with a set of few hundred random vectors. As the system gets larger, then due to a decrease of the tuned long-range parameter, the statistical errors diminishes so that for large silicon clusters the total statistical errors (not just per-electron) decrease and the HOMO/LUMO energies converge to about 0.05/0.01eV, respectively, with computational cost that is only about three times or less that of LDA. We demonstrate the method on silicon clusters with up to 3000 electrons and show that the results agree well (and may even supersede) that of G0W calculations, also done stochastically.

Long-range exact exchange DFT for giant systems using stochastic exchange

251st National Meeting (2016)

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