title: Density functional formulation of the random-phase approximation for inhomogeneous fluids: Application to the Gaussian core and Coulomb particles.
abstract: Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
authors.affiliation: Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, China and School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Derek
authors.initials: D
authors.lastname: Frydel
authors.affiliation: Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Manman
authors.initials: M
authors.lastname: Ma