<p>This dataset includes the input files, modified EPW code and python code to reproduce the results and recreate the figures from the paper of Nina Girotto Erhardt and Samuel Poncé: "Higher-order nonadiabaticity governs the temperature dependence of the phonon spectrum". Density functional perturbation theory computes phonons within the adiabatic framework. While many studies addressed the failure of the adiabatic approximation, the first-order nonadiabatic phonon spectrum contains certain crucial deficiencies. The first-order approximation is inadequate to describe the temperature dependence of the spectrum, underestimates phonon linewidth in the zone-center, overestimates its nonadibatic correction, and exhibits prominent nonadiabatic splitting. We show how accounting for the electron broadening by going beyond the first-order approximation mitigates these deficiencies  and improves experimental agreement.</p>