Many-body expansion of interaction energy

A next question could be is the interaction energy pair-wise additive, i.e. is the interaction energy a sum of paim ise interactions  

It has to be an infinite order perturbation theory with a large radius ot convergence. 

If this were true, it would be sufficient to calculate all possible interactions of pairs of molecules in the configuration identical to that of the total system and our problem would be solved. 

For the time being let us take the example of a stone, a shoe and a foot. The owner of the foot will certainly remember the three-body interaction, while nothing special happens when you put a stone into the shoe, or your foot into the shoe, or a small stone on your foot (two-body interactions). The molecules behave like this - 

In me case ot three mteractmg molecules, there is an ellect ot a strictly three-bocfy character, which cannot be reduced to any two-body interactions. Similarly for larger numbers of molecules, there is a non-zero four-body effect, because all cannot be calculated as two- and three-body interactions, etc. 

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