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

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