Central force potentials designed to model water are investigated by means of integral equation theories and computer simulations. We consider an associating neutral model which yields molecules with the geometry of the water molecule and that incorporates an effective pair potential aimed at describing the hydrogen bond interaction. In addition we study a charged version of the Hamiltonian, which provides a realistic description of the properties of liquid water. These models are analyzed in the full association limit, which is obtained by imposing a number of bonds per particle compatible with the water geometry, i.e., 2 and 1 for OH and HH correlations, The structure of the neutral model presents remarkable resemblances with that obtained using realistic models of water. In addition, the atomic Ornstein-Zernike theory along with the hypernetted-chain closure provides an accurate description of the structure of this anisotropic molecular system. The consideration of the full association limit introduces important improvements in the theoretical description of the charged central force model. The performance of this approach in the prediction of thermodynamic, structural, and dielectric properties of liquid water is investigated and the results compared with simulation and experimental data.