Gibbs free energy of hydration of a proton and standard hydrogen electrode potential were evaluated using high-level quantum chemical calculations. The solvent effect was included using the cluster continuum model, which treated short-range effects by quantum chemical calculations of proton-water complexes, and the long-range effects by a conductor-like polarizable continuum model. The harmonic solvation model (HSM) was employed to estimate enthalpy and entropy contributions due to nuclear motions of the clusters by including the cavity-cluster interactions. Compared to the commonly used ideal gas model, HSM treatment significantly improved the contribution of entropy, showing a systematic convergence toward the experimental data. (C) 2016 Elsevier B.V. All rights reserved.