Self-consistent construction of grand potential functional with hierarchical integral equations and its application to solvation thermodynamics

The construction of the density functional for grand potential is fundamental in understanding a broad range of interesting physical phenomena, such as phase equilibrium, interfacial thermodynamics, and solvation. However, the knowledge of a general functional accurately describing the many-body correlation of molecules is far from complete. Here, we propose a self-consistent construction of the grand potential functional based on the weighted density approximation (WDA) utilizing hierarchical integral equations. Different from our previous study [T. Yagi and H. Sato, J. Chem. Phys. 154, 124113, (2021)], we apply the WDA to the excess Helmholtz free energy functional rather than the bridge functional. To assess the performance of the present functional, we apply it to the solvation thermodynamics of Lennard-Jones fluids. Compared to the modified Benedict-Webb-Rubin equation of state, the present functional qualitatively predicts the liquid-vapor equilibrium. The solvation free energy obtained from the present functional provides a much better agreement with the Monte Carlo simulation result than the hypernetted chain functionals. It constitutes a general starting point for a systematic improvement in the accuracy of the grand potential functional.