text: molecular dynamics (MD) results. Diﬀerent approxima- 
  tions of the PM are employed for the case of NaCl elec- 
  trolyte solutions: a two component model (MSA2), that 
  only takes free ions into account, and two diﬀerent three 
  component models (MSA3 and BIMSA3), which include 
  a third species (the contact ion pair). As we proceed 
  to show, LPT allows us to select the best simple model 
  which accurately accounts for the thermodynamics and 
  the physical-chemistry of the system. 
  
  The ﬁrst stage consists in calculating the McMillan- 
  Mayer eﬀective ion-ion interaction potentials V eﬀ 
  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]. 
  1. 
  This setup corresponds to a concentration of 0.64 mol l− 
  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. 