where the W and U double-circles are white, indicating (in the context of the current study) that they are involved in the definition of the z-coordinate (i.e. the COM of DS -relative to the water GDI). All U and W coordinates that are orthogonal to the z CV are integrated within the diagrams. Mixture diagrams in which there is no connected path between any pair of white double-circles will have no z-dependence and therefore vanish when taking free energy differences. The quantities F W ⊕C and F W are independent of z since they refer to systems in which the solute is decoupled from the solvent, and are therefore constant with respect to all DS -z-positions relative to the water GDI. All thermodynamic quantities presented here are reported as differences relative to bulk-dissolved solutes, so Eq. 8 becomes: F