Mu, mu_id, mu_ex, fix widom and fix gcmc

Dear Lammps community,

First I run the in.gcmc.h2o example under the directory of examples\mc using lammps-23Jun2022, and the final data file named has been got. The mu value in in.gcmc.h2o is -8.1 kcal/mol.

Then I modified the flexible SPC/E in in.widom.spce into rigid SPC/E water models to keep consistent with those in.gcmc.h2o, to run Widom insertion to calculate the mu_ex. The modified in script is named in.widom.rigidspce. The data file read in is

I also use the equation mu_id = K * T * ln(ρ * ∧^3) to calculate the mu_id.
From my understanding, the sum of the calculated mu_id and the simulated mu_ex should be ~8.1 kcal/mol. But the results have a large discrepancy.

The widom.log.lammps is attached, in which f_mywidom[1] is averaged as 80.5 kcal/mol. The calculated mu_id is -4.8 kcal/mol. The sum is 75.7 kcal/mol.

Related files including and in.widom.rigidspce are also attached. Any comments are welcome. Thank you very much. (17.4 KB)
in.widom.rigidspce (918 Bytes)
widom.log.lammps (1.4 MB)

Recently I was using fix widom to calculate excess chemical potential, but the output of excess chemical potential is always zero during operation, the file is below, what is the reason for this?
With best wishes!