Density functional theory (DFT) study of water autoionization in solvated clusters

We have implemented a cluster-continuum method using density functional theory to model water clusters and various charged species derived from water. The two aims of this study are to determine the minimal basis required for proper modeling of water autoionization and to determine the minimum number of explicit water molecules required to properly model the energetics of solvation. The thermodynamics of water autoionization converge following a modified power law to deliver chemically accurate values of the Gibbs energy change for autoionization with tractably small clusters. Convergence is slower and not exponential as assumed in previous work. We identify the n = 21 set of clusters as the first effectively bulk water like clusters that can capture the energetic influence of both the first and second solvation shells. In this cluster, a water molecule is encapsulated in the center of a closed shell of other water molecules that hydrogen bond to form five-membered rings. The total energy change for clusters with n ≥ 21 calculated using both the RPBE-D3 and ωB97X-D exchange-correlation functionals with the 6-311+G** basis set is shown to deliver good approximations to the free energy change at 298 K. This is true even though neither functional models the individual enthalpy or entropy contributions particularly well.