Many-Body Second Order Green's Function Theory for Ab Initio Molecular Quantum Electrodynamics
arXiv:2606.26076v1 Announce Type: new Abstract: In this work, we develop two many-body quantum electrodynamic methods to calculate the ground-state energies of strongly coupled light-matter molecular systems. Specifically, we extend the second-order many-body Green's function theory (GF2) for electronic systems to incorporate electron-boson couplings. We employ two ansätze to treat the bosonic part of the system, namely the coherent-state (CS) and Lang-Firsov (LF) transformed vacuum state. These are combined with the GF2 method to construct two new approaches, which we refer to as CS-GF2 and LF-GF2. We benchmark CS- and LF-GF2 by studying various molecular systems inside an optical cavity. We investigate $\mathrm{H}_2$ and $\mathrm{LiH}$ potential energy surfaces, keto-eneol tautomerization energy barrier, van-der Waals interactions between two $\mathrm{H_2}$ molecules and the torsional potential energy surface of the ethylene molecule, $\mathrm{C_2H_4}$. Both methods provide highly accurate energies, with only modest additional improvement observed in LF-GF2.