Figure 2 . (a, b) The radial distribution functions and (c, d) the radial orientation distribution functions of MeCN predicted by the MDFT in comparison with relevant MD simulation.57 Na+: left panel; Cl-: right panel.
As the radial distribution function is highly orientation-dependent, the structural criterion involving both local density and orientation angle are utilized to determine the solvation diameters of ions in MeCN. The essential idea is that at certain orientations the local densities within the first solvation shell are very low and make no contribution to the solvation number. To justify this postulation, we compute the molecular number within the solvent shell at each orientation angle:
. (13)
where is the molecular number at the specific orientation within the solvent shell determined by the first density valley position , as discussed in the eq.(2).
The reduced number, , for Cl- are plotted inFigure 3 (a) . Interestingly, most of MeCN molecules within the first shell surrounding Cl- distribute with the orientation ranging from 0.5 to 1, and the maximum reduced number is found at = 0.75. This trend confirms the above analysis. To distinguish the non-contributing molecules, we introduce a critical value of , below which the corresponding reduced number is small and thus makes no contribution to the solvation diameter. This critical value should be sort of universal, and valid for many other simple ions as well. To determine this critical value, we take the measured solvation diameter of Cl-from experiment (i.e., 7.52 Å58 ) as a benchmark, and then determine critical structural orientation as = 0.68. The applicability of this criterion is tested for evaluating the solvation diameter of other simple anions in MeCN.Figure 3 (b) shows the solvation diameters of Cl-, Br- and I- in MeCN predicted by the MDFT. As can be seen, the predictions of Br- and I- are in a good agreement with the experimental measurements. Therefore, we speculate that this structural criterion is applicable for predicting the solvation diameters of anions in confined MeCN solvent.