First-Principles Approach to Electron-Vibration Interaction in Molecules from an Atomic Orbital Basis: The...

The electron-phonon/vibration interaction is crucial for electronic structures of solids and molecules, such as governing superconductivity and modifying band structures. While the Allen-Heine-Cardona (AHC) theory is widely used for evaluating phonon-induced band renormalization in periodic systems, it has not been rigorously assessed for molecular systems. Previous AHC-based studies of molecular systems are predominantly based on plane-wave basis sets under periodic boundary conditions. In this work, we implement the AHC theory with different levels of approximation for molecular systems by employing a full-potential all-electron framework with an atomic orbital basis and explicitly including Pulay corrections in the electron-vibration matrix elements. Our results indicate that both adiabatic and non-adiabatic formulations of the AHC theory can become unreliable for molecular systems, suggesting that an accurate description of the vibronic renormalization requires the explicit evaluation of electron-vibration self-energy. We further introduce the G₀W₀ approximation to the electronic self-energy to incorporate the many-body electronic effects. The agreement between computed vibronic spectral functions and experimental photoemission spectroscopy supports the proposed methodology. This work applies and implements first-principles electron-vibration renormalization in molecules while offering insights into understanding the role of many-body effects in phonon-induced band renormalization for periodic systems.