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, $h_{\lambda }(\mathbf{r},{\mathbf{r}}^{\prime })$, where $\lambda$ determines the interaction strength. To obtain $h_{\lambda }(\mathbf{r},{\mathbf{r}}^{\prime })$ we use the Ornstein-Zernike equation, and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. As the two equations do not form a closed set, an approximate closure relation is required and it determines a type of an approximation. In the present work we investigate the random phase approximation (RPA) closure. We determine that this approximation is identical to the variational Gaussian approximation derived within the framework of the field-theory. We then apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.

References in corpus (1)

• Introduction to statistical field-theory: from a toy model to a one-component plasma

Cited by in corpus (11)

• The double-layer structure of overscreened surfaces by smeared-out ions
• General theory of charge regulation within the Poisson-Boltzmann framework: study of a sticky-charged wall model
• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• A self-consistent field theory of density correlations in classical fluids
• Mean-field theory of active electrolytes: dynamic adsorption and overscreening
• Two-component Gaussian core model: strong-coupling limit, Bjerrum pairs, and gas-liquid phase transition
• Inhomogeneous fluid of penetrable-spheres: application of the random phase approximation
• Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
• Electrostatic contribution to colloidal solvation in terms of the self-energy modified Boltzmann distribution
• Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach
• Modified Poisson-Nernst-Planck model with Coulomb and hard-sphere correlations