Perturbation Correction for the Free Energy and Structure of Simple Fluids

Abstract

Separation of an arbitrary potential $\ensuremath{\phi}$ into a short-range, repulsive part ${\ensuremath{\phi}}_{0}$ and a weak correction ${\ensuremath{\phi}}_{1}$ affords the possibility of describing the $\ensuremath{\phi}$-system properties as corrections to the assumed-known ${\ensuremath{\phi}}_{0}$ reference system. We derive here an expression for such a correction of the classical Helmholtz free energy that is the analog of a result familiar from the development of the hypernetted-chain integral equation. Other corrections are obtained therefrom, including a corrected pair-distribution function proposed earlier. All results are easily adapted for numerical calculation.