In contrast, most widely used water models are closely related to the oldest common molecular mechanics models. We discuss some of the most common simple water models here to show how the current work builds on past developments and compare both the parameterization approach and experimental optimization targets of these models. TIP, TIP3P and TIP4P models were parameterized to reproduce structural and energetic results for water dimer and density of liquid water at a single temperature of 298 K, using Monte Carlo simulations with short simulations commensurate with the simulation resources that were available at the time. SPC-E includes corrections due to self-polarization and cannot give good results for protein-based force field which does not account for the polarization effects. Because of this, the self-solvation-free energy for SPC-E is approximately 4.8 kJ/mol greater than the other water models. This can cause errors in the interpretation of solvation-free energy (excess chemical potential) of small molecules which are parameterized with respect to TIP3P water model. A number of efforts have followed to try to improve early rigid water models without breaking too far from their simple framework. Glättli et al. proposed the need for a better parameterized rigid, non-polarizable water model, and used a trial and error approach to change HOH, LJ sites, charge, bond length to the improve structural, dielectric thermodynamic and transport properties, resulting in the SPC/S water model. A more holistic parametric search method was proposed by Horn et al., which the authors used to design TIP4P-EW model. TIP4P-Ew was parameterized by fitting the parameters to experimental density and heat of vaporization for a range of temperatures at single pressure (i. e. atmospheric pressure), with Ewald summation of electrostatics (hence the "EW"). Horn et al. searched parameter space by minimizing the square of the residual between simulated and experimental density at multiple temperatures and at 1 atm pressure. However, their algorithm perturbed only σ O , O and q O for a fixed same vapor phase geometry. Horn et al. adopted the assumptions made in the TIP4P model for geometrical parameters that the liquid phase molecular geometry of the water molecule should not be very different from that of the experimentally observed gas phase geometry. However, the effect of this assumption was never examined. Similarly, all the TIPnP water models use the experimental gas phase OH bond length (r OH ), and HOH bond angle ( HOH), and only parameterize oxygen's LJ parameters σ O , O and charge q O for 3 site models. In four-site rigid water models, the distance between the virtual site which carries negative charge of the oxygen atom, (r OH ), in the plane of the water molecule, along the angle bisector of HOH is also optimized.