Statistical Mechanics of Linear Molecules. VI. Solutions of the Percus–Yevick Integral Equation for a Hard-Core Model

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Abstract
The Ornstein–Zernike integral equation relating direct and indirect correlation functions has been generalized to linear molecules and solved numerically for a hard‐core diatomic model with the aid of the Percus–Yevick approximation. The generalized PY equation was decomposed into a set of coupled integral equations by expanding the correlation functions in series of spherical harmonics. Iterative solutions of the Fourier‐transformed form of these expressions were obtained after truncating the set. Correlation functions were calculated in this way as a function of density for two values of the molecular length and then used to evaluate compressibility factors from both the pressure and compressibility equations. It is found that the pair correlations at moderate densities obtained from the PY equation do not differ greatly from those calculated previously from density series. In addition, the various equations of state for this and similar hard‐core nonspherical models do not differ greatly from one another or from the hard‐sphere results, when the data are plotted as a function of reduced density using a reducing factor proportional to the molecular volume. A brief discussion is given of the limitations imposed upon these results by the mathematical approximations introduced.

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