We use piecewise-linear functionals to study the polaron energy landscape and hopping rates in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, which we adopt as an example of an anisotropic material hosting multiple polaronic states. We illustrate various functionals for polaron localization, including a hybrid functional and two types of semilocal functionals, and discuss how to ensure the piecewise-linearity condition. Then, we determine the formation energies of stable polarons, and show that single-site and multisite polaronic states can be found in close energetic competition. We calculate the hyperfine and superhyperfine parameters associated with each polaron, and discuss the comparison with experiment. Next, we perform nudged-elastic-band calculations to determine energy landscapes and hole transfer rates of all first-nearest-neighbor polaron hoppings. We show that when the piecewise-linearity condition is ensured polaron properties are robust upon variation of the functional adopted, including formation energies, energy barriers, and charge transfer rates. This supports the use of semilocal functionals for calculating polaron transport properties.

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• Hopping transport
• Polarons
• Density functional theory