Defects have a profound effect on the electronic and transport behavior of materials. They play an important role in many photoelectric devices. Here, we investigate by means of constrained density functional theory (C-DFT) the spatial distribution and transport properties of bipolarons that are induced by surface oxygen vacancies (${\mathrm{O}}_{\mathrm{v}}$) on reduced rutile $\mathrm{Ti}{\mathrm{O}}_2$ (110) surfaces. We find that bipolarons preferentially localize in a subsurface geometry, followed by a mixed surface-subsurface localization, while a surface state is the energetically least preferred location for bipolarons. We show that this unique behavior is caused by an interplay of the splitting of titanium $d$ orbitals, the orbital symmetry, and the electrostatic potential. Also, the polaron transport properties are examined, both parallel and perpendicular to the surface. The introduction of water molecules on the surface can effectively lead to the transfer of subsurface polarons to a position on the surface. The preferred transfer direction of polarons changes from the [001] direction to the [110] direction when the water coverage exceeds one-half monolayer. This characteristic behavior is strongly related to the synergetic effect of the electronic coupling strength and the transition barrier at different water coverages. Our findings reveal the energetic order of bipolaron localizations, their transport properties, and the effect of water on a reduced rutile $\mathrm{Ti}{\mathrm{O}}_2$ (110) surface, hence leading to a better understanding of the role of polarons in photoelectric applications.

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• First-principles calculations
• Polarons
• Transport phenomena
• Surfaces