The binding of zinc (Zn) ions to proteins is important for many cellular events. The theoretical and computational description of this binding (as well as that of other transition metals) is a challenging task. In this paper the binding of the Zn ion to four cysteine residues in the structural site of horse liver alcohol dehydrogenase (HLADH) is studied using a synthetic peptide mimic of this site. The study includes experimental measurements of binding constants, classical free energy calculations from molecular dynamics (MD) simulations and quantum mechanical (QM) electron structure calculations. The classical MD results account for interactions at the molecular level and reproduce the absolute binding energy and the hydration free energy of the Zn ion with an accuracy of about 10%. This is insufficient to obtain correct free energy differences. QM correction terms were calculated from density functional theory (DFT) on small clusters of atoms to include electronic polarisation of the closest waters and covalent contributions to the Zn-S coordination bond. This results in reasonably good agreement with the experimentally measured binding constants and Zn ion hydration free energies in agreement with published experimental values. The study also includes the replacement of one cysteine residue to an alanine. Simulations as well as experiments showed only a small effect of this upon the binding free energy. A detailed analysis indicate that the sulfur is replaced by three water molecules, thereby changing the coordination number of Zn from four (as in the original peptide) to six (as in water).