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Photo-emission spectroscopy directly probes individual electronic states, ranging from single excitations to high-energy satellites, which simultaneously represent multiple quasiparticles (QPs) and encode information about electronic correlation. First-principles description of the spectra requires an efficient and accurate treatment of all many-body effects. This is especially challenging for inner valence excitations where the single QP picture breaks down. Here, we provide the full valence spectra of small closed-shell molecules, exploring the independent and interacting quasiparticle regimes, computed with the fully-correlated adaptive sampling configuration interaction (ASCI) method. We critically compare these results to calculations with the many-body perturbation theory, based on the $GW$ and vertex corrected $GWΓ$ approaches. The latter explicitly accounts for two-QP quantum interactions, which have been often neglected. We demonstrate that for molecular systems, the vertex correction universally improves the theoretical spectra, and it is crucial for accurate prediction of QPs as well as capturing the rich satellite structures of high-energy excitations. $GWΓ$ offers a unified description across all relevant energy scales. Our results suggest that the multi-QP regime corresponds to dynamical correlations, which can be described via perturbation theory.