Fig. 3.

(A) The nonuniform density $\rho \left(r\right)$ and (B) the Gaussian smoothed charge density ${\rho }^{q\sigma }\left(r\right)$ of water around a harshly repulsive solute with an effective hard sphere diameter of $R_{\text{HS}}\approx 12$ Å for the full SPC/E, GT, and LMF theory mimic systems. Note that the Gaussian smoothing results in nonzero ${\rho }^{q\sigma }\left(r\right)$ inside the solute core. (C) The probability distribution, $P\left({\theta }_{\text{OH}}\right)$, of the angle made by water O–H bonds and the water–solute distance vector for the same systems. The shaded region serves to highlight the deviation of the GT system from the full results. (D) Solvation free energies scaled by the solute surface area, $\tilde{G}=\stackrel{⌣}{G}/4\pi R_{\text{HS}}^2$, obtained in the full, GT, and LMF systems. (Inset) The behavior of the free energies at large $R_{\text{HS}}$. LMF corrections are on the order of 10 $k_{\text{B}}T$ at $R_{\text{HS}}=12$ Å.