Electron-Phonon Coupling in Many-Body Perturbation Theory: Developments within the Quasiparticle Self-Consistent GW approximation and LMTO Formalism

The calculation of electron-phonon (e-ph) coupling from first principles is a topic of great interest in materials science, offering a robust, non-empirical framework to understand and predict a wide range of physical phenomena. While significant progress has been made using the Kohn-Sham framework of density functional theory (KS-DFT), it is increasingly evident that standard approximations in KS-DFT often fall short of providing accurate results. These shortcomings are frequently linked to the non-local nature of the exchange-correlation potential, prompting the development of advanced methodologies within DFT and many-body perturbation theory. Despite these efforts, a highly reliable and efficient first-principles approach to accurately capture e-ph interactions remains elusive. To address this challenge, we introduce a novel field-theoretical methodology that integrates the foundational work of Baym and Hedin with the Quasiparticle Self-Consistent GW (QSGW) approximation, implemented within the Questaal electronic structure suite. Our approach, based on a response function framework, ensures that Pulay-like incomplete-basis-set corrections are not required to account for changes in basis functions, paving the way for a high-fidelity description of e-ph coupling.