Revisiting the real space density functional theory of hard sphere freezing in the Percus-Yevick approximation

A team of researchers studied the freezing transition of a hard sphere fluid, using classical density functional theory (DFT). The researchers used the DFT with a free energy perturbation to the second order, the Percus-Yevick (PY) approximation to the liquid-state direct correlation function (dcf), and a real space representation of the solid density, as a sum of Gaussians. An alternative derivation was also presented that evaluated the real space perturbation integrals in a different manner, focusing on an intermediate function that is analogous to the indirect correlation function of the Ornstein-Zernike theory. An updated set of numerical values were formulated for the coexistence densities and Lindemann parameter of the hard sphere system that is consistent with the equations of the team of researchers.