Solid-state batteries, in which solid electrolytes (SEs) replace their liquid alternatives, promise high energy density and safety. However, understanding the relation between SE composition and properties, stemming from intricate interactions among constituent sublattices that involve non-local electronic and nuclear dynamics, remains a critical and unsolved challenge. Here, we evaluate electronic structure methods and demonstrate that a density-functional approach incorporating non-local and many-body effects in exchange-correlation interactions provides predictive results for the local structure and diffusion properties of SEs. Focusing on argyrodite SEs (Li