Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets

TL;DR

This paper introduces a low-scaling $GW$ computational method with high accuracy, enabling the study of larger systems like phosphorene nanosheets and providing reliable electron energy predictions.

Contribution

The authors develop an improved low-scaling $GW$ algorithm that achieves benchmark accuracy and applies it to large phosphorene nanosheets, demonstrating size-dependent electronic properties.

Findings

Achieves a mean absolute deviation of 6 meV on the $GW100$ benchmark set.

Accurately predicts excitations within 0.1 eV of conventional schemes.

Reveals size-dependent fundamental gaps in phosphorene nanosheets.

Abstract

$GW$ 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 $O(N^4)$ 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, semi-core 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 $\times$ 1.3 nm, 88 atoms) to 2.4 eV (6.9 nm $\times$ 4.8 nm, 990 atoms) at the $\text{ev}GW_0$@PBE level.