Hydrogen-intercalated transition metal oxides such as ${\mathrm{V}}_2{\mathrm{O}}_5, \mathrm{Mo}{\mathrm{O}}_3$, and $\mathrm{W}{\mathrm{O}}_3$ are important functional materials in energy storage and information processing. At low hydrogen concentrations, intercalation introduces protons and polarons, with polaron hopping often acting as the primary mechanism for electronic conduction. However, polarons and protons can interact associatively, and affect the mobility of polarons. Using first-principles calculations at the SCAN+$U$ level, we quantify the polaron-proton association energies and polaron migration barriers that govern polaron mobility in the presence of protons. We find that polaron association with protons significantly increases migration barriers, particularly across the van der Waals gap in layered ${\mathrm{V}}_2{\mathrm{O}}_5$ and $\mathrm{Mo}{\mathrm{O}}_3$ oxides. Moreover, beyond electrostatic association, protons affect polaron migration through hydrogen bonding, which distorts the metal–oxygen–metal (M–O–M) bonds and reduces the orbital overlap between metal sites. This results in a counterintuitive outcome: the polaron migration barrier is higher when the migration path goes through the hydroxide ion (M–OH–M), as compared to the path that leads away from the proton (M–O–M). Consequently, this mechanism renders protons to act as “unidirectional valves,” establishing a preferential direction for polaron migration. These findings highlight a nontrivial role of protons in polaron migration in transition metal oxides and offer insights for designing energy-efficient electrochemical devices.

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• Carrier dynamics
• Electronic structure
• Polarons
• Transition metal oxides
• Density functional theory