High-throughput superconducting $T_{\mathrm{c}}$ predictions through density of states rescaling

First principles computational methods can predict the superconducting critical temperature $T_{\mathrm{c}}$ of conventional superconductors through the electron-phonon spectral function. Full convergence of this quantity requires Brillouin zone integration on very dense grids, presenting a bottleneck to high-throughput screening for high $T_{\mathrm{c}}$ systems. In this work, we show that an electron-phonon spectral function calculated at low cost on a coarse grid yields accurate $T_{\mathrm{c}}$ predictions, provided the function is rescaled to correct for the inaccurate value of the density of states at the Fermi energy on coarser grids. Compared to standard approaches, the method converges rapidly and improves the accuracy of predictions for systems with sharp features in the density of states. This approach can be directly integrated into existing materials screening workflows, enabling the rapid identification of promising candidates that might otherwise be overlooked.