A modification of the central force model (CFM) that describes the dissociation of water molecules into OH- and H+ ions is proposed for molecular dynamics simulations of energetic particle bombardment of water ice. The model keeps all the properties of the CFM but permits charge exchange between oxygen and hydrogen atoms when the water molecule starts to dissociate after collision with an energetic projectile. The reaction products, therefore, have the correct integer charges, -1 and +1 for hydroxyl and a proton. The threshold for the ionic dissociation is corrected to be at the right value, 17.2 eV, in a vacuum. Using the proposed model, total cross-sections for ionic dissociation as functions of the projectile energy are estimated for Ar and C projectiles colliding with water molecules in a vacuum and water ice. Carbon projectiles are demonstrated to produce more dissociated ions at energies lower than 300 eV. Argon projectiles are more effective in breaking the molecules at higher energies.