  Surfaces of metal oxides at working conditions are usually electrified due to
the acid-base chemistry. The charged interface compensated with counterions
forms the so-called electric double layer. The coupling of surface chemistry
and electric double layer is considered to be crucial but poorly understood
because of lacking the information at the atomistic scale. Here, we used the
latest development in density functional theory based finite-field molecular
dynamics simulation to investigate pH-dependence of the Helmholtz capacitance
at electrified rutile TiO$_2$ (110)-NaCl electrolyte interfaces. It is found
that, due to competing forces from surface adsorption and from electric double
layer, water molecules have a stronger structural fluctuation at high pH and
this leads to a much larger capacitance. It is also seen that, interfacial
proton transfers at low pH increase significantly the capacitance value. These
findings elucidate the microscopic origin for the same trend observed in
titration experiments.
