To help set the target for MSE in heat capacity i.e. finding the maximal allowable error in C P,res with acceptable V res error, we set bounds of accuracy for the heat capacity as estimated using rigid four-site water models. From classical mechanics, the rigid water model has 6 DOF and the real water molecule has 9 DOF. In a rigid water model C P ig is always lower than the experimental C P ig because of the difference in the degrees of freedom (DOF). One could analytically correct the effect of missing degrees of freedom in C P ig,sim . However, the effect of the missing degrees of freedom on the intermolecular interactions cannot be analytically estimated. If we arbitrarily fix the MSE for C P res,sim to a very low value, the errors in residual molar volume will cease to decrease after a certain value. Thus, we must iteratively find the optimal value of MSE in C P res,sim resulting from the effect of missing degrees of freedom on the intermolecular interactions, which results in maximum reduction of RMSE in residual molar volume. We used different values of the MSE for C P res,sim between 1-200 (J/mol/K) 2 for our parameterization problem which gave us maximum reduction in properties based on pressure derivatives, especially density. We observed that if we allowed a minimum MSE of 100 (J/mol/K) 2 i. e. RMSE of 10 J/mol/K in C P res,sim , we were able to reduce the MSE in residual molar volume surface by up to two orders of magnitudes compared to existing water models.