Parameterizing the surface free energy and excess adsorption of a hard-sphere fluid at a planar hard wall

he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy $\gamma$ and the excess adsorption $\Gamma$ are of central importance. For theoretical studies closed expression of $\gamma$ and $\Gamma$ can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for $\gamma$ and $\Gamma$, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for $\gamma$ and $\Gamma$ to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterizations show significant deviation at high density. In this work, we propose new parameterizations for $\gamma$ and $\Gamma$ that agree with the simulation data within statistical error over the entire fluid density range.