Interpolation Formula for Radial Distribution Functions

A Padé approximant is used as an interpolation formula to obtain the density dependence of radial distribution functions. The equation is of the form $$g\exp {\text{(u\hspace{0.17em}/\hspace{0.17em}kT)\hspace{0.17em}=\hspace{0.17em}(1\hspace{0.17em}+\hspace{0.17em}a}}_1{\mathrm{\rho \hspace{0.17em}+\hspace{0.17em}a}}_2{\rho }^2{\text{)\hspace{0.17em}/\hspace{0.17em}(1\hspace{0.17em}+\hspace{0.17em}b}}_1{\mathrm{\rho \hspace{0.17em}+\hspace{0.17em}b}}_2{\rho }^2\mathrm{),}$$ where $g$ is the radial distribution function, $u$ is the pair potential energy, $k$ is Boltzmann's constant, $T$ is the absolute temperature, and $\rho$ is the number density. Padé constants are determined for the Gaussian and hard‐sphere models of a fluid.