Selection of chemical potential or excess chemical potential in fix gcmc

In Lammps Manual (v13Apr 2017), the fix gcmc command, the Syntax section, it said that:

“mu = chemical potential of the ideal gas reservoir (energy units)”

Then, in the Description section , it said this :

“ The chemical potential is a user-specified input parameter defined as:

μ=μ_id + μ_ex ”

(1)The Question is : does “chemical potential of the ideal gas reservoir” mean: the chemical potential of the “ideal gas” reservoir, or the “ideal” gas reservoir ? Which value I’m supposed to choose: μ,μ_id, or μ_ex ?

(2)

Through Widom’s Test Particle Insertion method, I got a value of = -23.33 KJ/mol of water, which is comparable to the excess chemical potential of -22.8 KJ/mol in Agarwal et al.(2014)[1] ’s work.
Corti (1998) [2] also stated that:
“Widom [1, 2] showed that the excess chemical potential μex of a system of N interacting particles is given by

μex = - kT ln< exp(- φ/kT)>N

So the Question is : from Widom’s Test Particle Insertion method, I got the excess chemical potential, could this excess chemical potential be used in ficx gcmc represent the mu value ?

[1] Agarwal, A.; Wang, H.; Schütte, C.; Site, L. D. Chemical potential of liquids and mixtures via adaptive resolution simulation. The Journal of chemical physics 2014, 141 (3), 034102.

[2] Corti, D. S. Alternative derivation of Widom’s test particle insertion method using the small system grand canonical ensemble. Molecular Physics 1998, 93 (3), 417-420.

In Lammps Manual (v13Apr 2017), the fix gcmc command, the Syntax section, it said that:
“mu = chemical potential of the ideal gas reservoir (energy units)”

A. That is a slight misnomer. The "gas reservoir" does not have to be ideal. It does not even have to be a gas. It is simply an imaginary reservoir of atoms/molecules with the specified chemical potential.

Then, in the Description section , it said this :
“ The chemical potential is a user-specified input parameter defined as:
μ=μ_id + μ_ex ”

(1)The Question is : does “chemical potential of the ideal gas reservoir” mean: the chemical potential of the “ideal gas” reservoir, or the “ideal” gas reservoir ? Which value I’m supposed to choose: μ,μ_id, or μ_ex ?

A. μ, that's why we call it mu.

(2)
Through Widom’s Test Particle Insertion method, I got a value of <mu>= -23.33 KJ/mol of water, which is comparable to the excess chemical potential of -22.8 KJ/mol in Agarwal et al.(2014)[1] ’s work.
Corti (1998) [2] also stated that:
“Widom [1, 2] showed that the excess chemical potential μex of a system of N interacting particles is given by
μex = - kT ln< exp(- φ/kT)>N”
So the Question is : from Widom’s Test Particle Insertion method, I got the excess chemical potential, could this excess chemical potential be used in ficx gcmc represent the mu value ?

A. Yes, it could, if you faithfully work out the correct value of mu_id according to the formulae on the doc page, with correct units, etc. A more practical approach, or at least a way to check your numbers, is to run fix gcmc with a few different values of mu in a suitable range, so as to generate equilibrated low pressure gas phases. For sufficiently low pressures, both the density and pressure will vary exponentially with mu.

[1] Agarwal, A.; Wang, H.; Schütte, C.; Site, L. D. Chemical potential of liquids and mixtures via adaptive resolution simulation. The Journal of chemical physics 2014, 141 (3), 034102.
[2] Corti, D. S. Alternative derivation of Widom's test particle insertion method using the small system grand canonical ensemble. Molecular Physics 1998, 93 (3), 417-420.