where V W (R W ) given by Eq. 1 represents the total waterwater potential energy for instantaneous configuration, R W , and the black inner-circle indicates that we are integrating over all water coordinates. For the configurational integral of a mixture of two species, for example water and C 12 E 6 , Z W ⊕C (where ⊕ denotes the direct sum of W and C degrees of freedom), there is full intra-species coupling, and so each species has its own black double circle, and all inter-species pairs are coupled through Eq. 2, which is represented with a double line connecting the two double circles, as follows: