Cluster models for the calcite (CaCO3) (001) surface were calculated by the ab initio Hartree-Fock method with the purpose of developing a model for studies of local surface reactions such as adsorption. The models were evaluated in terms of their density of states and charge distribution. The termination of a naked cluster model is important, and two methods of stabilizing the models were considered. An array of point charges, a method of stabilizing ionic models, was tested and found to work poorly. An alternative method was then tested in which cluster models of semi-ionic surfaces were stabilized by surrounding the cluster with water molecules. The water molecules around the cluster increased the stability of the model substantially and also made the model more realistic. An estimate for the energy of adsorption of water to the (001) surface of calcite is presented.