On the classes of integral equations nonderivable by graph theory means: An improved molecular theory for classical liquids in equilibrium

Starting from the definition of molecular distribution functions a new hierarchy of integral equations for the equilibrium classical liquids is derived. An outline is given of why this hierarchy cannot be derived by graph theory means. In the theory, the sum of elementary diagrams is given explicitly as a functional of the higher order correlation functions. Analysing this functional the most general truncation scheme within the framework of the first order theories is presented. The pairwise additivity of the intermolecular potential is not assumed.