Stepwise coupling of groups in a molecule

In this section, we examine the molecular basis of a group-additivity approach. As we shall see, the problem is essentially the same as treated in the previous section i.e., it originates from a split of the solute-solvent intermolecular potential function into two or more parts. 

Consider a solute of the form X— Y, where X and Y are two groups, say CH3 and CH3 in ethane, or CH3 and OH in methanol. We assume that the solute-solvent interaction may be split into two parts as follows  

As in the preceding section, where we had split the interaction energy into a hard and soft part, we also have here an element of ambiguity as to the exact manner in which this split may be achieved. For instance for ethane, we assume that the ethane-water interaction may be written as the sum of the two methyl-water interactions, as schematically depicted in figure 7.4. Next, we proceed to split the total binding energy of the solute X— Y into two parts, 

As in the previous section, we have again an average of a product of two functions. This, in general, may not be factorized into a product of two average quantities. If this could have been done, then relation (7.130) could have been written as a sum of two terms, i.e., 

Such a group additivity, though very frequently assumed to hold for AA X Y (as well as for other thermodynamic quantities), has clearly no justification on a molecular basis, even when the split of the potential function in expression (7.128) is exact. 

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