Electron-phonon interaction and band structure renormalization using Gaussian orbital basis sets

Electron-phonon interactions lead to a renormalization of the electronic band structure. Its first-principles evaluation is computationally expensive and relies on specific approximations. The authors present here an $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ approach that combines non-adiabatic Allen-Heine-Cardona theory with supercell calculations in a Gaussian basis. This allows the inclusion of contributions beyond the rigid-ion approximation and thereby increases the accuracy, while maintaining moderate computational costs.