Water free proton transport in imidazole functionalised silicon dioxide material: Calculation of free energy barrier dependent on the mCEC proton coordinate

Free energy barriers are calculated using the modified centre of excess charge (mCEC) coordinate and the umbrella sampling formalism. Proton transport is described on propylimidazole functionalised silicon dioxide surfaces by a quantum mechanical-molecular mechanical coupling (QM/MM) coupling approach, coupling the density functional-based tight binding method (DFTB) to a classical force field. The proton transport between imidazole groups on the dry surface is shown to be favourable. Besides the comparison of competing transport mechanisms, we discuss the influence of the proton coordinate and the choice of the reaction coordinate.