You can use Gaussian 09 or other versions of Gaussian program to calculate Gibbs free energy of any reaction. You have first to model the surface and obtain its Gibbs free energy. After that you model the absorption of the proton on the surface. Finally, the change in Gibbs free energy is the difference in Gibbs energy between final and initial states. I can recommand the following publications that calculate Gibbs free energy for similar systems:
ABDULSATTAR, M. A., RESNE, A. L., ABDULLAH, S., MOHAMMED, R. J., ALARED, N. K., & NASER, E. H. (2018). CHLORINE GAS SENSING OF SnO2 NANOCLUSTERS AS A FUNCTION OF TEMPERATURE: A DFT STUDY. Surface Review and Letters, doi:10.1142/S0218625X1850172X
Abdulsattar, M. A., & Almaroof, H. M. (2017). Adsorption of H2 and O2 gases on ZnO wurtzoid nanocrystals: A DFT study. Surface Review and Letters, 24 doi:10.1142/S0218625X18500087
In general, no software can directly give the Gibbs free energy (G), thus, the Gibbs free energy of materials can be calculated using the following equation:
G(P, T)=F+PV
where P is the pressure and F=F(V, T) is the Helmholtz free energy, which is a function of temperature and volume.