responds to the contact ion pair (CIP) is thus completely
ignored by the MSA2 calculation. If the MSA diameters
are directly ﬁtted to reproduce the MC osmotic pres-
sure, much smaller values are obtained. These MSA-ﬁt
hydrated diameters, which are compared to the MSA2
diameters in the bottom part of Fig.
2, are averages of
the CIP and the solvent-separated ion pair.
To overcome this diﬃculty, we have explicitly intro-
duced the CIP in our model (species 3). Straightforward
calculations, based on a characteristic-function formal-
ism, allow us to deﬁne an equivalent model in which
the free ions and the CIP are explicitly taken into ac-
count [19, 20]. We apply this formalism by deﬁning a
pair as an anion and a cation at a distance less than
4˚
A, which corresponds to the position of the eﬀective
potential maximum. The interaction between free, like
charges in this new system remains unchanged, and the
cation-anion interactions are easily approximated by ex-