GW Plus Cumulant Approach for Predicting Core-Level Shakeup Satellites in Large Molecules

Recently, the GW approach has emerged as a valuable tool for computing deep core-level binding energies as measured in X-ray photoemission spectroscopy. However, GW fails to accurately predict shakeup satellite features, which arise from charge-neutral excitations accompanying the ionization. In this work, we extend the GW plus cumulant (GW + C) approach to molecular 1s excitations, deriving conditions under which GW + C can be reliably applied to shakeup processes. We present an efficient implementation with O(N⁴) scaling with respect to the system size N, within an all-electron framework based on numeric atom-centered orbitals. We demonstrate that decoupling the core and valence spaces is crucial when using localized basis functions. Additionally, we meticulously validate the basis set convergence of the satellite spectrum for 65 spectral functions and identify the importance of diffuse augmenting functions. To assess the accuracy, we apply our GW + C scheme to π-conjugated molecules containing up to 40 atoms, predicting dominant satellite features within 0.5 eV of experimental values. For the acene series, from benzene to pentacene, we demonstrate how GW + C provides critical insights into the interpretation of experimentally observed satellite features.