First-Principles Free-Energy Barriers for Photoelectrochemical Surface Reactions: Proton Abstraction at TiO_{2}(110).

We explicitly calculate the free-energy barrier for the initial proton abstraction in the water splitting reaction at rutile TiO_{2}(110) through ab initio molecular dynamics. Combining solid-state embedding, an energy based reaction coordinate and state-of-the-art free-energy reconstruction techniques renders the calculation tractable at the hybrid density-functional theory level. The obtained free-energy barrier of approximately 0.2 eV, depending slightly on the orientation of the first acceptor water molecule, suggests a hindered reaction on the pristine rutile surface.