‘‘Onsager-molecule’’ approach to liquid structure: Derivation of the universal bridge functions

The direct [{φ}(r){→}S(k)] and inverse [S(k){→}{φ}(r)] problems of liquid pair structure can be solved by a hypernetted-chain (HNC) integral equation provided the bridge functions B(r) are known. The asymptotic high-density properties of the HNC equation are mapped on the Onsager lower bound to the potential energy, which features ``atoms'' and ``molecules'' as mathematical constructs (e.g., the confined-atom Thomas-Fermi model for dense bulk matter). This asymptotic HNC Onsager ``state'' provides a starting point for analyzing the structure of dense fluids---like the ideal-gas state for dilute fluids. Using only the asymptotic properties of the HNC equation and the single assumption that B(r) is nonsingular, I present the first direct calculation of the bridge functions for a highly correlated fluid and derive their universal characteristics.