Even the spread of squared errors in V res and density, represented in tables and figures in SI section 2, is lowest for GOPAL by two to five orders of magnitude compared to previous models. However, there is not a significant improvement in the errors over better previous models including OPC, TIP-ST and TIP-FB in S res , C Pres and H res , which come from the first and second derivatives of Gibbs energy with respect to temperature. The latter observation points to the fact that the previous models have done a very good job of fitting water models to properties that are derived from the derivatives of Gibbs energy with respect to temperatures, such as entropy and heat capacity. The likely reason is that these previous water model parameterizations were performed only for a single pressure (i. e. atmospheric pressure), and thus the optimization approaches never included the changes of different properties for water that behave as a function of pressure and temperature simultaneously.