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We present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties (e.g., atomic structure, binding energy, and the polaron level) reveals long-range electrostatic effects and the electron-phonon interaction as the two main contributors. We develop a correction scheme for DFT polaron calculations that significantly reduces thedoi:10.1088/1367-2630/aaaf44 fatcat:x23vg5i3w5hahjjoefuq5svr3m