The fitting basis is the same as described in q-AQUA 4-b and the ∆-ML 4-b to MB-pol; briefly, it consists of 200 "super PIPs" of Morse variables; these super PIPS are formed from sums of regular PIPs so as to ensure invariance with respect to permutation of monomers. The fitting RMS error for the whole data set is 6.3 cm -1 . Similar to the ∆V 2-b and ∆V 3-b , a switching function is applied to make ∆V 4-b decay to 0 smoothly when the maximum OO distance in a tetramer is within [6.0, 6.5] Å.