A fully atomistic model of a compact electric double layer at the rutile TiO2(1 1 0)-water interface is constructed by adding protons to bridging oxygens or removing them from H2O molecules adsorbed on terminal metal cation sites. The surface charge is compensated by F− or Na+ counter ions in outer as well as inner sphere coordination. For each of the protonation states the energy of the TiO2 conduction band minimum is determined relative to the standard hydrogen electrode by computing the free energy for the combined insertion of an electron in the solid and a proton in solution away from the double layer using density functional theory based molecular dynamics methods. Interpreted as electrode potentials, this gives an estimate of the capacitance which is compared to the capacitance obtained from the difference in the average electrostatic potentials in the solid and aqueous phase. When aligned at the point of zero charge these two methods lead to almost identical potential-charge profiles. We find that inner sphere complexes have a slightly larger capacitance (0.4 F m−2) compared to outer sphere complexes (0.3 F m−2).
JC is grateful for financial support from Emmanuel College Cambridge and the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom. We also acknowledge support from the UKCP consortium for access to HECToR, the UK's high-end computing resource funded by the Research Councils.