Simple nonpolarizable molecular mechanics potentials were developed for Li+ Na+, and K+ with the adaptive force matching (AFM) method using the second order Moller-Plesset perturbation theory (MP2) with the frozen core approximation as reference. The effects of different choices of core orbitals and basis sets in the MP2 calculations were investigated for Na+ and Li+ For Na+, correlating the 2s2p electrons in MP2 changes its hydration free energy by 18 kJ/mol, which is surprisingly large, constituting to about 5% of the intrinsic hydration free energy of the ion. Whereas correlating the 2s2p electrons with the aug-cc-pCVTZ basis set leads to the best agreement with experiments, with the aug-cc-pVTZ basis set, a better hydration free energy will be obtained if the 2s2p are kept as frozen core orbitals. Even with nonpolarizable energy expressions, the AFM derived ion potentials predict the experimental hydration free energies of the various salts within 2% of experimental values, suggesting the robustness of the fitting procedure. However, the 2% agreement can only be achieved if the core correlation is modeled appropriately in the MP2 reference calculations.