Quantum chemistry based potentials for classical molecular dynamic (MD) simulations have been derived for K+ cation in water. Water was represented using the SPC/E, TIP4P, RPOL potentials. The K+-water potentials were parameterized to reproduce the quantum chemistry binding energy of a K+/water complex. The gas-phase binding energies and enthalpies, the excess enthalpy and free energy of K+ hydration, K+ hydration structure and K+ mobility were determined from molecular mechanics and MD simulations, and compared with experimental data. All potentials were able to accurately predict K+ hydration structure and K+ self-diffusion coefficient at infinite dilution limit.