Just my .02 on this discussion.
Direct particle insertion only provides good results if:
- your solvent contains enough spontaneous cavities of sizes that can accommodate the molecules of the solute,
- the interactions are not very directional, i.e., the presence of the solute does not induce important reorganization of the solvent molecules.
In all other cases the method gives poor statistics and requires a big computational effort. I understand your solute is water… if your solvent does not “feel” the strong dipolar interactions (H-bonds) then test-particle insertion may not be the way to evaluate the chemical potential.
You should try more suitable free energy methods that proceed through stepwise insertion of the solute molecule and progressive activation of the solute-solvent interactions, allowing the solvent to reorganize and “equilibrate" around the solute. A few are already implemented in LAMMPS packages.