  Many popular methods for the calculation of chemical potentials rely on the
insertion of test particles into the target system. In the case of liquids and
liquid mixtures, this procedure increases in difficulty upon increasing density
or concentration, and the use of sophisticated enhanced sampling techniques
becomes inevitable. In this work we propose an alternative strategy, spatially
resolved thermodynamic integration, or SPARTIAN for short. Here, molecules are
described with atomistic resolution in a simulation subregion, and as ideal gas
particles in a larger reservoir. All molecules are free to diffuse between
subdomains adapting their resolution on the fly. To enforce a uniform density
profile across the simulation box, a single-molecule external potential is
computed, applied, and identified with the difference in chemical potential
between the two resolutions. Since the reservoir is represented as an ideal gas
bath, this difference exactly amounts to the excess chemical potential of the
target system. The present approach surpasses the high density/concentration
limitation of particle insertion methods because the ideal gas molecules
entering the target system region spontaneously adapt to the local environment.
The ideal gas representation contributes negligibly to the computational cost
of the simulation, thus allowing one to make use of large reservoirs at minimal
expenses. The method has been validated by computing excess chemical potentials
for pure Lennard-Jones liquids and mixtures, SPC and SPC/E liquid water, and
aqueous solutions of sodium chloride. The reported results well reproduce
literature data for these systems.
