Computing Surface Acidity Constants of Proton Hopping Groups from Density Functional Theory-Based Molecular Dynamics: Application to the SnO2(110)/H2O Interface.

Abstract

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 VrH 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 Vrep to compute the surface acidities of systems in which proton hopping is spontaneous and fast. In this Vrep scheme, a Buckingham-type repulsive potential Vrep is applied between the deprotonation site and all other protons in DFTMD simulations. We first verify the Vrep scheme by calculating the pKa 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 Vrep scheme leads to a prediction of the point of zero charge (PZC) of 4.6, which agrees well with experiment. The intrinsic individual pKa values of the terminal five-coordinated Sn site (Sn5cOH2) and bridge oxygen site (Sn2ObrH+) are 4.4 and 4.7, respectively, both being almost the same as the PZC. The similarity of the two pKa 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.