Relationship between external pressure, fugacity and chemical potential

[Ambroise]

Dear RASPA community,

I am simulating water adsorption in a rigid hydrophobic Zeolite. I am puzzling to grasp the relationship that links the external pressure "ExternalPressure" and the fugacity coefficent "FugacityCoefficient" in RASPA input script with the chemical potential calculated by RASPA to perform a GCMC simulation.

Instead of using the peng-Robinson state equation to calculate the fugacity, I input indeed myself the fugacity properly calculated before running a simulation for my water model. However, by using the widom insertion method to calculate the chemical potential of a box with only water (for tests), there is a mismatch with the expect chemical potential corresponding to the input fugacity coefficient.

For information, I used the relationship from statistical physics to compute the fugacity coefficient phi for input in RASPA:

phi = fugacity/P_ext = exp((mu_real(P_ext,T)-mu_perfect_gas(P_ext,T))/RT)

Is this relation used in RASPA or am I wrong?

Any help would be greatly appreciated!  :)