Scientists have developed two new theoretical methods, named CS-GF2 and LF-GF2, to calculate the ground-state energies of molecular systems strongly coupled to light. These methods extend the second-order Green's function theory (GF2), typically used for electronic systems, to incorporate electron-boson (photon) couplings. This capability is crucial for understanding and designing materials in the context of molecular quantum electrodynamics (molecular QED).

The new approaches are based on two distinct treatments for the bosonic part of the system: a coherent-state (CS) and a Lang-Firsov (LF) transformed vacuum state. By combining these approximations with the GF2 theory, the CS-GF2 and LF-GF2 methods are derived. The accuracy of these tools is fundamental for predicting the behavior of molecules in environments where the interaction with electromagnetic fields is significant, such as within optical cavities.

To validate CS-GF2 and LF-GF2, the researchers applied them to various molecular systems inside an optical cavity. They investigated the potential energy surfaces of molecules like H₂ and LiH, the energy barrier for keto-enol tautomerization, van der Waals interactions between two H₂ molecules, and the torsional potential energy surface of ethylene (C₂H₄). Both methods provided highly accurate energies, with only modest additional improvement observed in the LF-GF2 method. These results demonstrate the robustness and reliability of the new tools for molecular QED research.