Swift GW beyond 10,000 electrons using sparse stochastic compression

Abstract

We introduce the concept of fractured stochastic orbitals (FSOs), short vectors that sample a small number of space points and enable an efficient stochastic sampling of any general function. As a first demonstration, FSOs are applied in conjunction with simple direct-projection to accelerate our recent stochastic GW technique; the new developments enable accurate prediction of G0W0 quasiparticle energies and gaps for systems with up to Ne > 10, 000 electrons, with small statistical errors of ±0.05 eV and using less than 2000 core CPU hours. Overall, stochastic GW scales now linearly (and often sub-

Surface‐supported cluster catalysis: Ensembles of metastable states run the show

“…This method uses fundamentally the same techniques needed for local‐potential DFT, which handle efficiently cells with up to 10,000 electrons, and scale mildly, as O(N e 2 ) where N e is the number of electrons in the system. Note that in practice even a few hundred samples are sufficient to describe the long‐range exact exchange so the combined deterministic‐stochastic method is only about two to five times more expensive than traditional deterministic local‐potential DFT …”

Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies

“…This method was applied to the G 0 W 0 approximation as described in earlier publications. 56,60,61 In contrast to the previous work, the starting point is no longer constrained to DFT with local functionals. The stochastic formulation of Σ GW Γ X c is a new development.…”

“…This is consistent with previous observations. 56,[59][60][61]76 In practice, stochastic computation of the induced charge density requires only a few random states η (typically between 4 and 20), i.e., the number of states that are propagated by Eq. 42 is much smaller than the number of occupied states.…”

“…Another set of stochastic orbitals is used only for sparse stochastic compression and time-ordering of the induced potentials. 61 We use Eqs. 34 and 37, in which W P (t) and W x (t) are computed deterministically.…”

“…To lower the computational cost, GW Γ X is implemented using real-time stochastic numerical techniques. 8,[56][57][58][59][60][61] Up to now, stochastic calculations of QP energies were limited to G 0 W 0 with DFT based on the local density approximation (LDA) to exchange and correlation (xc). Here, we first extend the methodology to HF and hybrid xc functionals.…”