A Unique Descriptor for Electron Polaron Migration: Larmor Radius

Polarons in metal oxides are in localized charge carriers that significantly influence material properties. The critical role of polarons in photocatalytic processes arises from their spatial distribution and dynamic properties. In this study, we propose a physically meaningful descriptor based on the potential of charged particles in a polarization field to quantify the relative stability of polaron configurations during migration. Taking a widely studied Rutile-phase TiO₂ as a typical model, we focused on electron addition, where Ti⁴⁺ centers are reduced to Ti³⁺ centers, leading to the formation of small polarons. Using the Rutile (110) surface, we employed a constrained density functional theory (CDFT) hybrid with a projection-operator diabatization (POD) method to investigate the migration barriers between different polaron configurations induced by oxygen vacancies. Our results demonstrate the accuracy and robustness of the proposed descriptor, establishing its potential for broader applications in understanding polaron behavior in transition metal oxides.