Meanwhile, water is also one of the most studied systems in theoretical chemistry. Numerous water force fields have been proposed and we can only give a very brief and incomplete overview to the most relevant ones here. The most widely used water models are rigid and with point charges and Lennard-Jones interaction centers 67 placed on either atoms or fixed virtual sites (e.g., BF, 68 TIP4P, 64 TIP5P, SPC, and SPCE 71 etc). Flexible models with similar functional forms were also developed to allow the internal vibrations of the molecule, aiming to study the corresponding nuclear quantum effects (NQE) in water. Beyond the fixed point charge approximation, polarizable force fields such as AMOEBA and MPID were built, aiming for a better description to the electrostatics by introducing both high order multipoles and explicitly polarizable sites. It is noted that most of these models are fitted empirically or semi-empirically to bulk water experimental data, thus they may not reproduce the PES accurately at atomic level. Such infidelity can largely limit the transferability and predictive power of the model.