Reliably calculate pKa is not easy, mostly because accurate evaluation of solvation free energy of ions is difficult (not only implicit solvation model is needed, but also sometimes consideration of explicit solvent molecules is important). There are numerous papers discussing how to calculate pKa reasonably, see e.g.
J. Chem. Theory Comput., 15, 6025 (2019)
J. Phys. Chem. A, 123, 7430 (2019)
Regarding Shanon entropy, see recent reviews
Acta Phys. -Chim. Sin., 32, 98 (2016) DOI: 10.3866/PKU.WHXB201510302
WIREs Comput Mol Sci., e1461 (2019) DOI: 10.1002/wcms.1461