The behavior of charge carriers in polar materials is governed by electron-phonon interactions, which affect their mobilities via phonon scattering and may localize carriers into self-induced deformation fields, forming self-trapped polarons. We present a first-principles study of self-trapped polaron formation in paradigmatic polar semiconductors and insulators using the variational polaron equations framework and self-consistent gradient optimization. Our method incorporates long-range corrections to the electron-phonon interaction, essential for finite-size systems. We demonstrate how the variational approach enables the identification of multiple polaronic states and supports the analysis of polarons with arbitrarily large spatial extent via energy filtering. The potential-energy surfaces of the resulting polarons exhibit multiple local minima, reflecting distinct, symmetry-broken polaronic configurations in systems with degenerate band edges. Our findings align with previous theoretical studies and establish a robust foundation for future ab initio studies of polarons, especially those employing variational methods.

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• Electron-phonon coupling
• Polarons
• First-principles calculations
• Variational wave functional methods