Interaction site cluster series for the Helmholtz free energy and variational principle for chemical equilibria and intramolecular structures

Abstract

The interaction site cluster series is derived for the Helmholtz free energy of a molecular mixture in which molecules can interconvert by chemical reactions. This series expresses the free energy as a functional of the single‐molecule (intramolecular) distribution functions. Variations of this functional are studied. It is shown that when the total numbers of atoms in the mixture are fixed, the free energy functional is a minimum with respect to variations of the intramolecular distribution functions. Further, this variational principle is shown to be equivalent to the cluster series formulas derived earlier [J. Chem. Phys. 65, 2925 (1976)] for chemical equilibrium constants and intramolecular distribution functions of nonrigid molecules in condensed phases.