Kohn-Sham density functional theory (DFT) can be used to simulate small polarons in the adiabatic, strong-coupling limit. Accordingly, it is understood as the ab initio successor of Pekar’s Polaron . In this talk, we review two methods to predict small-polaron energies using the supercell approach. That is, 1) the conventional “charge in a supercell” approach and 2) the approach introduced by Sadigh et al. . For each approach the calculated polaron properties are tested in two ways: Their dependence on the underlying exchange-correlation functional and convergence with the supercell size. As a result, we propose a correction for approach 2), which allows obtaining numerically converged results in moderately sized supercells using (computationally cheap) semi-local XC functionals . Eventually, we present a systematic investigation of the polaron potential energy surface unfolding challenging issues for sampling methods like molecular dynamics.
 S.I. Pekar, Zh. Eksp. Teor. Fiz 16, 335 (1946)
 B. Sadigh et al., Phys. Rev. B 92, 075202 (2015)
 S. Kokott et al., New J. Phys. 20, 033023 (2018)