4
r  (Å)
2
4
6
8
4 6 8
0.5
1
1.5
4 6 8
0.5 mol.L
-1
g 12 (r)
1.5 mol.L
-1
g 12 (r)
1.5 mol.L
-1
g 11 (r)
1.5 mol.L
-1
g 22 (r)
FIG. 5: (Color online) RDF obtained from MC simulations
(diamond), BIMSA3 (solid line), and MSA-ﬁt (dot dashed)
at two concentrations.
The RDF obtained within BIMSA3 are compared with
the MC and MSA-ﬁt results in Fig.
5. Our BIMSA3
model accounts for the strong molecular peak of the CIP
and provides the correct distances of minimal approach;
whereas the naive MSA-ﬁt procedure ignores the former
and gives poor estimates for the latter. At larger sep-
arations, the BIMSA3 results do not reproduce the os-
cillations observed in the MC simulations, but the cor-
responding energy oscillations in the eﬀective potentials
are less thankBT . In addition, the perturbation term
of the BIMSA3 appears to be negligible compared to the
reference term for concentrations less than 1 mol l− 1. The
perturbation can then be omitted to obtain a fully ana-
lytical theory, determined by the hard sphere diameters
and the pair fraction given by LPT; with the free energy
and the RDF given in terms of the BIMSA and MSA so-
lutions, as described above. While the procedure we have
followed uses two diﬀerent approximations for the refer-
ence and perturbation terms (MSA vs BIMSA), these are
known to be accurate for the systems under consideration
and do not appear to be inconsistent with each other.
To conclude, we have combined MD simulations with
LPT to construct simple models of electrolyte solutions
which account for the molecular nature of the solvent.
The ﬁnal result is fully analytical and it yields the ther-
modynamic and structural properties of the solution, in
agreement with the original molecular description. The
methodology can in principle be adapted to any molecu-
lar description of the system (MD simulations involving
interaction potentials accounting for polarization eﬀects
or Car-Parrinello MD simulations for example) as long
as the ion-ion RDF are known. It can also be generalized
to study interfaces. The method appears to be a promis-
ing approach toward the description of the speciﬁc eﬀects
of ions, especially for complex systems whose modeling
requires an analytic solution.
The authors are particularly grateful to Werner Kunz
for fruitful discussions.
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