(a) Velocity autocorrelation function (7.8) calculated by the all-atom MD model of K+ ion (blue solid line), by the coarse-grained model (1.2)–(1.5) (green dotted line) and by the fictitious particle model (7.1)–(7.4) for N=3 (red dashed line), where the parameters of (7.1)–(7.4) are α1,1=5.64×102 ps−2, α1,2=73.8 ps−1, α1,3=3.42×103 ps−2, α1,4=80.9 Å ps−3/2, α2,1=1.26× 102 ps−2, α2,2=21.3 ps−1, α2,3=7.27×102 ps−2, α2,4= 3.43×10−1 Å ps−3/2, α3,1=72.1 ps−2, α3,2=2.02×102 ps−1, α3,3=3.26×10−1 ps−2 and α3,4=1.22× 102 Å ps−3/2. The parameters of the coarse-grained model (1.2)–(1.5) are given in table 3. (b) The same computations for Na+ ion, where the parameters of the fictitious particle model (7.1)–(7.4) are α1,1=3.05×103 ps−2, α1,2=3.08×102 ps−1, α1,3=8.99× 103 ps−2, α1,4=98.7 Å ps−3/2, α2,1= 96.5 ps−2, α2,2=2.48×102 ps−1, α2,3=4.62×102 ps−2, α2,4=15.8 Å ps−3/2, α3,1=23.5 ps−2, α3,2=25.5 ps−1, α3,3=3.82×102 ps−2 and α3,4=1.18×103 Å ps−3/2.