Using test particle sum rules to improve approximations in classical density functional theory: White-Bear and White-Bear mark II versions of the Lutsko functional

In a recent paper [M. Gül et al., Phys. Rev. E 110, 064115 (2024)2470-004510.1103/PhysRevE.110.064115], we showed that test particle sum rules, which address the excess chemical potential and isothermal compressibility, could be used to develop accurate classical density functionals for hard-sphere (HS) fluids. Here we extend our approach to the construction of HS functionals building upon the state-of-the-art White-Bear (WB) and White-Bear mark II functionals. Employing the same test particle sum rules, we determine the two free parameters in the Lutsko [J. F. Lutsko, Phys. Rev. E 102, 062137 (2020)2470-004510.1103/PhysRevE.102.062137] formulation of fundamental measure theory by minimizing the relative errors between different routes to the two thermodynamic quantities. The resulting optimized Lutsko WB functionals, especially Lutsko WB mark II, are generally more accurate and consistent than those obtained in earlier treatments.