Low-Scaling GW with Benchmark Accuracy and Application to Phosphorene Nanosheets

Funding Information: The Gauss Centre for Supercomputing is acknowledged for providing computational resources on SuperMUC-NG at the Leibniz Supercomputing Centre under the Project IDs pn69mi and pn72pa. We also thank the CSC - IT Center for Science for providing computational resources. J.W. acknowledges funding from DFG SFB 1277 (Project A03). P.S. acknowledges funding by the NCCR MARVEL, funded by the Swiss National Science Foundation. D.G. acknowledges financial support by the Academy of Finland (Grant No. 316168). Publisher Copyright: © 2021 The Authors. Published by American Chemical Society. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.GW is an accurate method for computing electron addition and removal energies of molecules and solids. In a conventional GW implementation, however, its computational cost is O(N4) in the system size N, which prohibits its application to many systems of interest. We present a low-scaling GW algorithm with notably improved accuracy compared to our previous algorithm [J. Phys. Chem. Lett. 2018, 9, 306-312]. This is demonstrated for frontier orbitals using the GW100 benchmark set, for which our algorithm yields a mean absolute deviation of only 6 meV with respect to canonical implementations. We show that also excitations of deep valence, semicore, and unbound states match conventional schemes within 0.1 eV. The high accuracy is achieved by using minimax grids with 30 grid points and the resolution of the identity with the truncated Coulomb metric. We apply the low-scaling GW algorithm with improved accuracy to phosphorene nanosheets of increasing size. We find that their fundamental gap is strongly size-dependent varying from 4.0 eV (1.8 nm × 1.3 nm, 88 atoms) to 2.4 eV (6.9 nm × 4.8 nm, 990 atoms) at the evGW0@PBE level.Peer reviewe