ij (r), by
inverting the radial distribution functions (RDF) gij(r)
obtained by MD. The simulations were carried out on
a box of 2000 water molecules and 48 NaCl pairs us-
ing the same interaction potentials as in reference [16].
This setup corresponds to a concentration of 0. 64 mol l− 1.
NPT ensemble sampling at standard pressure and tem-
perature was enforced, with a time step of 1 fs and a
pressure bath coupling constant of 1 ps. An equilibration
run of 0.25 ns was followed by a production run of 0.6 ns
for ﬁve diﬀerent initial conﬁgurations. The averages of
the resulting RDF were then used for the potential inver-
sion via the HNC closure [15]. These eﬀective potentials
are assumed to be concentration independent and will be
used for simulations at all concentrations.
Subtracting the long-range Coulombic potential
V LR
ij (r) (which depends on the dielectric constant of the
solvent) from V eﬀ
ij (r), we obtain the short-range contri-
bution V SR
ij (r) to the eﬀective potentials. These are given
in Fig.
1 (species 1 and 2 refer to Na + and Cl − free ions,
respectively). All the short-range potentials exhibit os-
cillations corresponding to the solvent layering between
the ions, but this eﬀect is particularly important for the
cation-anion interaction: a considerable potential barrier
(≳ 2kBT ) separates the ﬁrst two attractive wells. To
serve as a reference, Monte Carlo (MC) simulations were
performed with these eﬀective potentials; a comparison
between MD and MC RDF is also provided in Fig.
1. The
excellent agreement between both sets of RDF validates
the HNC inversion procedure [17], and allows us to com-