The chemical potential as a function of the density is subsequently calculated by using (µ water (P ),V,T) simulations so that the density is used as an intermediate quantity easy to compute in order to obtain the µ water (P ) relationship. In our work, another approach is proposed : we performed (N,P,T) MD simulations to retrieve the density that is used to fix the simulation box in RASPA to run subsequent (N,V,T) simulations where the NCMC move is used to compute µ water (P ) with our adapted version of the Widom insertion technique. The comparison between different methods to calculate µ water (P ) is reported on Figure . For the sake of comparison, we run the same (N, V, T ) simulation but use instead Widom insertion moves to estimate the µ water (P ) relationship. It is clear that this last approach is not suited for the computation of the chemical potential in such dense fluid because the probability of intrusion is very low due to an overestimation of the chemical potential at high pressure induced by interpenetration of sample molecule with other water molecules. On the contrary, by using the NCMC move, the system is relaxed during insertion of the sample molecule and the chemical potential calculated with the modified Widom technique 55 is in agreement with those calculated by Desbiens and co-workers. In addition, we verify that both methods yields the same slope of chemical potential of pure water as a function of pressure (e.g., same molar volume v water (P )), as shown in Figure .