Analytical approach to molecular liquids. V. Symmetric dissociative dipolar dumbbells with the bonding length σ/3≤L≤σ/2 and related systems

The exact asymptotic behavior of the particle–particle direct correlation function for dissociative dipolar dumbbells is discussed. It reveals the sense in which the complete association limit is like a critical point and suggests several approximations as well as the conditions under which they can be expected to be useful. The simplest of these is an extended mean spherical approximation (EMSA) that can be solved analytically for a model liquid of symmetric dissociative dipolar dumbbells with two centers (each bearing a point charge of opposite sign) a distance L apart, when σ/3≤L≤σ/2, where σ is the diameter of the spheres that consistute the dumbbells. The analytical expressions for the Born solvation free energy of a symmetric dipolar dumbbell in a symmetric dipolar dumbbell solvent and in a dipolar hard-sphere solvent are also obtained. Such expressions can be expected to be useful in investigating intramolecular electron-transfer reactions. Results for σ/2≤L≤σ that have a somewhat different conceptual status are obtained as well. They suggest a new interpretation of the Percus–Yevick solution to the sticky-sphere model considered by Baxter.