Capturing electronic correlations in electron-phonon interactions in molecular systems with the GW approximation

Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is however unclear how general this enhancement is, and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW and equation-of-motion coupled-cluster calculations. We find that GW can increase the magnitude of the electron-phonon coupling across this set of molecules by an average factor of 1.1-1.8 compared to DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as an accurate way of computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.