Electron-phonon interactions in transport properties of WO$_{3}$*

High doping concentrations can be achieved in tungsten trioxide (WO$_{3})$, which has an ABO$_{3}$ perovskite structure with an empty A site. Using first-principles calculations, we investigate the role of LO phonon scattering in electron transport. We use density functional theory to calculate electronic structure and vibrational spectra. Various approaches to electron-phonon coupling are investigated, and the role of spin-orbit splitting in the scattering mechanisms is examined. We compare WO$_{3}$ to other perovskites and find that the mobility of WO$_{3}$ is enhanced due to the absence of an A-site atom and the presence of spin-orbit coupling.