Elucidating the role of many-body forces in liquid water. I. Simulations of water clusters on the VRT(ASP-W) potential surfaces A method for the extraction of effective three-body potential parameters from high-level ab initio cluster calculations is presented and compared to effective pair potentials extracted at the same level. Dilute Li ϩ (aq) and Mg 2ϩ (aq) solutions are used as test cases and long molecular-dynamics simulations using these newly developed potentials were performed. Resulting thermodynamical, structural, and dynamical properties are compared to experiment as well as to the empirical effective pair potentials of Å qvist. Moreover, a new time-saving method for the correction of cluster energies computed with a relatively cheap ab initio method, to yield expensive, high-level ab initio energies, is presented. The effective pair approach is shown to give inconsistent results when compared to the effective three-body potentials. The performance of three different charge compensation methods ͑uniform charge plasm, Bogusz net charge correction, and counter ions͒ is compared for a large number of different system sizes. For most properties studied here, the system-size dependence is found to be small for system sizes with 256 water molecules or more. However, for the self-diffusion coefficients, a 1/L dependence is found, i.e., a very large system-size dependence. A very simple method for correcting for this deficiency is proposed. The results for most properties are found to compare reasonably well to experiment when using the effective three-body potentials.