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.