Pair correlation in simple polar liquids

For a system of dipolar hard spheres, comparisons are made among new Monte Carlo results and the results of several approximation schemes developed to describe the pair correlation function in simple dipolar liquids. A self-consistent Ornstein-Zernike approximation (SCOZA) proposed by Høye and Stell gives results that appear to be nearly exact for all values of the dipole moment at which relevant Monte Carlo results are currently available ($\lambda =\frac{\beta {\mu }^2}{R^3}\le 2.75$, where $\beta =\frac{1}{\mathrm{kT}}$, $\mu$ is the dipole moment, and $R$ is the hard-sphere diameter). Results are also given for a linear approximation (LIN) as well as for a higher-order cluster series approximation ($L3\mathrm{}$) of Verlet and Weis and for an approximation of Høye and Stell (the PPA) based on the use of a Padé approximant for the thermodynamics. These provide much less overall accuracy, but each satisfactorily reproduces certain key features of $h\left(12\right)\mathrm{}$, the pair correlation function. The orientationally averaged PPA correlation function is highly accurate over a large range of $\lambda$ when used with appropriate thermodynamic input, while the angular components are much less adequate. The LIN and $L3\mathrm{}$ results require no thermodynamic and dielectric input and are of interest chiefly because of this, and because of the dielectric constants ${\epsilon }_{\mathrm{LIN}}$ and ${\epsilon }_{L3\mathrm{}}$ associated with them. The Wertheim expressions for $\epsilon$, ${\epsilon }_{\mathrm{LIN}}$, and ${\epsilon }_{L3\mathrm{}}$ are compared. Monte Carlo estimates seem to be closest to ${\epsilon }_{\mathrm{LIN}}$ for $\lambda \le 1$. For higher $\lambda$ there is some evidence that all three expressions may yield values of $\epsilon$ that are too low. All are clearly more accurate than the Onsager expression.