Computing Surface Acidity Constants of Proton Hopping Groups from Density Functional Theory-Based Molecular Dynamics:...

Proton transfer at metal oxide/water interfaces plays an important role in electrochemistry, geochemistry, and environmental science. The key thermodynamic quantity to characterize this process is the surface acidity constant. An ab initio method that combines density functional theory-based molecular dynamics (DFTMD) and free energy perturbation theory has been established for computing surface acidity constants. However, it involves a reversible proton insertion procedure in which frequent proton hopping, e.g., for strong bases and some oxide surfaces (e.g., SnO₂), can cause instability issues in electronic structure calculation. In the original implementation, harmonic restraining potentials are imposed on all O-H bonds (denoted by the V_rH scheme) to prevent proton hopping and thus may not be applicable for systems involving spontaneous proton hopping. In this work, we introduce an improved restraining scheme with a repulsive potential V_rep to compute the surface acidities of systems in which proton hopping is spontaneous and fast. In this V_rep scheme, a Buckingham-type repulsive potential V_rep is applied between the deprotonation site and all other protons in DFTMD simulations. We first verify the V_rep scheme by calculating the pK_a values of H₂O and aqueous HS^- solution (i.e., strong conjugate bases) and then apply it to the SnO₂(110)/H₂O interface. It is found that the V_rep scheme leads to a prediction of the point of zero charge (PZC) of 4.6, which agrees well with experiment. The intrinsic individual pK_a values of the terminal five-coordinated Sn site (Sn_5cOH₂) and bridge oxygen site (Sn₂O_brH⁺) are 4.4 and 4.7, respectively, both being almost the same as the PZC. The similarity of the two pK_a values indicates that dissociation of terminal water has almost zero free energy at this proton hopping interface (i.e., partial water dissociation), as expected from the acid-base equilibrium on SnO₂.