Self-consistent vertex corrected $GW$ with static and dynamic screening using tensor hypercontraction: assessment of molecular ionization potentials

TL;DR

This paper benchmarks tensor hypercontraction-accelerated self-consistent GW and vertex-corrected GW methods for molecular ionization potentials, demonstrating THC's efficiency and the systematic effects of vertex corrections.

Contribution

It introduces THC acceleration into fully self-consistent GW and vertex-corrected GW calculations, assessing their accuracy and computational efficiency on benchmark datasets.

Findings

THC decomposition introduces negligible errors in IP predictions.

Vertex corrections mainly cause systematic shifts rather than accuracy improvements.

THC provides a reliable and lower-cost approach for self-consistent GW calculations.

Abstract

In this work, we benchmark tensor hypercontraction (THC)-accelerated fully self-consistent $GW$ (sc$GW$) and vertex-corrected self-consistent $GW$ (sc$GW\Gamma$) methods for predicting molecular first ionization potentials (IPs). The vertex function, $\Gamma$, is inserted into the self-energy in a fully self-consistent manner, and representative sc$GW$ and sc$GW\Gamma$ variants are assessed across the $G_0W_0\Gamma29$ and $GW100$ data sets. We find that the THC decomposition introduces negligible errors into self-consistent $GW$ ionization potentials, indicating that the acceleration preserves the underlying fully self-consistent results. Across both benchmark sets, vertex-corrected sc$GW\Gamma$ methods primarily produce systematic shifts in the IPs relative to sc$GW$ rather than consistent accuracy improvements. These results identify THC as a reliable route to lower-cost sc$GW$ and sc$GW\Gamma$ calculations