Density functional perturbation theory and electron-phonon coupling in FHI-aims

Density-functional perturbation theory (DFPT) extends density functional theory (DFT) to compute the response properties of the electronic density. Depending on the type of external perturbation applied, DFPT can provide insights into a wide range of material properties. These include force constant matrices, phonons, polarizabilities, dielectric properties, electron-phonon coupling, non-adiabatic matrix elements, NMR shifts, and J-couplings. The electronic structure software FHI-aims features a unique local-orbital atom-based real-space implementation of linear response, built on a coupled perturbed self-consistent field (CPSCF) approach within DFPT. This framework enables the prediction of thermal and electrical response properties in materials. Previously, the linear response implementation contained significant code duplication, complicating maintenance and development. In this project, the code was refactored to improve structure and reduce redundancy. Around ten CPSCF implementations were consolidated into a unified DFPT module, reducing code size by over 60% while enhancing functionality. Common low-level routines were merged to streamline future development, and new modules were introduced for calculating specific response properties. The refactored DFPT code is now more modular, scalable, and user-friendly for both researchers and developers. It supports calculations for polarizability, dielectric constants, IR spectra, electron-phonon coupling, electronic friction. The previous implementation did not allow metallic systems to be studied, but our developments now make this possible. We additionally discuss recent developments to the electron-phonon coupling driver in FHI-aims, which allows phonon modes and linewidths to be evaluated amongst other properties.