Note on the physical basis of spatially resolved thermodynamic functions

The spatial resolution of extensive thermodynamic functions is discussed. A physical definition of the spatial resolution based on a spatial analogy of partial molar quantities is advocated, which is shown to be consistent with how hydration energies are typically spatially resolved in the molecular simulation literature. It is then shown that, provided the solvent is not at a phase transition, the spatially resolved entropy function calculated by first-order grid inhomogeneous solvation theory [Nguyen CN, Young TK, Gilson MK. Grid inhomogeneous solvation theory: hydration structure and thermodynamics of the miniature receptor cucurbit [7] uril. J Chem Phys. 2012;137(4):044101] satisfies the definition rigorously, whereas that calculated by grid cell theory [Gerogiokas G, Calabro G, Henchman RH, et al. Prediction of small molecule hydration thermodynamics with grid cell theory. J Chem Theory Comput. 2014;10(1):35-48] most likely does not. Moreover, for an ideal gas in an external field, the former theory is shown consistent whereas the latter is not. Finally, consistent with the proposed definition and with the case of an ideal gas in an external field, we derive an approximate expression for the solvent contribution to the free energy of solvation in the limit of infinite dilution from the spatial variation of the density around the solute.

Automated summary

The spatial resolution of extensive thermodynamic functions is discussed in this study. A physical definition of the spatial resolution based on a spatial analogy of partial molar quantities is proposed and shown to be consistent with the spatial resolution of hydration energies in molecular simulations. The study also compares different computational methods and finds that the entropy function calculated using first-order grid inhomogeneous solvation theory satisfies the proposed definition, while grid cell theory likely does not. The study concludes by deriving an approximate expression for the solvent contribution to the free energy of solvation in the limit of infinite dilution based on the spatial variation of density.