StochasticGW-GPU: rapid quasi-particle energies for molecules beyond 10000 atoms

TL;DR

This work addresses the high cost of obtaining quasi-particle energies within the GW framework for very large systems. It extends stochastic GW with stochastic Resolution of Identity ($sROI$) and a gapped filtering strategy to GPU hardware, achieving near-linear scaling of the dominant steps and substantial speedups. The authors demonstrate QP energies for hydrogen-passivated silicon clusters up to $10001$ atoms (35144 electrons) with statistical error below $0.03$ eV, completing runs in minutes on large GPU deployments. The approach enables routine excited-state calculations for systems far beyond previous CPU-only capabilities, with significant implications for materials discovery and large-scale electronic structure studies.

Abstract

$\mathtt{StochasticGW}$ is a code for computing accurate Quasi-Particle (QP) energies of molecules and material systems in the GW approximation. $\mathtt{StochasticGW}$ utilizes the stochastic Resolution of the Identity (sROI) technique to enable a massively-parallel implementation with computational costs that scale semi-linearly with system size, allowing the method to access systems with tens of thousands of electrons. We introduce a new implementation, $\mathtt{StochasticGW-GPU}$, for which the main bottleneck steps have been ported to GPUs and which gives substantial performance improvements over previous versions of the code. We showcase the new code by computing band gaps of hydrogenated silicon clusters ($\textrm{S}\textrm{i}_{\textrm{x}}\textrm{H}_{\textrm{y}}$) containing up to 10001 atoms and 35144 electrons, and we obtain individual QP energies with a statistical precision of better than $\pm0.03$ eV with times-to-solution on the order of minutes.

Figures (5)

• Figure 1: Block diagram of the main steps of the StochasticGW algorithm. Each MPI rank performs the same operations on a different set of data (see text for details). Steps enclosed in shaded boxes have been ported to GPUs.
• Figure 2: $\textrm{S}\textrm{i}_{\textrm{8381}}\textrm{H}_{\textrm{1620}}$ cluster. Silicon and hydrogen atoms shown as brown and white spheres, respectively.
• Figure 3: (Top) plot of the log of the absolute magnitudes of Chebyshev coefficients used to construct the gapped filter for the $\textrm{S}\textrm{i}_{\textrm{8381}}\textrm{H}_{\textrm{1620}}$ cluster. (Bottom) Reconstructed filter, where the inset shows an expansion of the region of the band gap. The purple vertical lines in the inset indicate the positions of $E_{HOMO}^{KS}$ and $E_{LUMO}^{KS}$.
• Figure 4: QP orbital energies and band gaps for each cluster.
• Figure 5: Wall times spent in each portion of the code for calculations on the HOMO state of $\textrm{S}\textrm{i}_{\textrm{8381}}\textrm{H}_{\textrm{1620}}$, with different numbers of Monte Carlo samples.