  Electronic states in a crystal can localize due to strong electron-phonon
(e-ph) interactions, forming so-called small polarons. Methods to predict the
formation and energetics of small polarons are either computationally costly or
not geared toward quantitative predictions. Here we show a formalism based on
canonical transformations to compute the polaron formation energy and
wavefunction using ab initio e-ph interactions. Comparison of the calculated
polaron and band edge energies allows us to determine whether charge carriers
in a material favor a localized small polaron over a delocalized Bloch state.
Due to its low computational cost, our approach enables efficient studies of
the formation and energetics of small polarons, as we demonstrate by
investigating electron and hole polaron formation in alkali halides and metal
oxides and peroxides. We outline refinements of our scheme and extensions to
compute transport in the polaron hopping regime.
