The activation of anti-tumour drug cis-diamminedichloroplatinum(II) (cisplatin) is explored using hybrid Hartree-Fock-density functional theory (the B3LYP functional). Two models are employed - a small model in which only the moieties taking part in the stepwise activation process (cis-Pt[NH₃]₂[Cl]₂ + H₂O → cis-Pt[Cl][NH₃]₂[H₂O]⁺ + Cl^- and cis-Pt[Cl][NH₃]₂ [H₂O]⁺ + H₂O → cis-Pt[NH₃]₂[H₂O]²⁺ + Cl^-) are included, and a larger model initially including six water molecules. It is concluded that the overall energetics are strongly dependent on both basis set level used and on the explicit solvatization of the leaving chloride ligands. The main effect is found for the relative energy of the intermediate, the singly aquated species, where the smaller model predicts this to be endothermic by around 6 kcal/mol irrespective of inclusion of vibrational effects or solvation model. With the larger model, the first activation step is thermoneutral with an activation barrier of 22.9 kcal/mol, whereas the second aquation reaction is endothermic by 12.5 kcal/mol and has a barrier in the order of 26 kcal/mol. The computed energy surface is in close agreement with available experimental data, and supports the prediction that the species in aqueous solution (i.e. before reaching cellular DNA) is in fact the mono-aquated form rather than the fully hydrated species.