where F ex EDL = F ex C + F ex im describes first-order electrostatics and includes direct Coulomb term and image terms. All contributions to the excess free energy, except the short-range term, are calculated analytically from first principles using the Mean Spherical Approximation, the Fundamental Measure Theory, and Lifshitz theory of dispersion interactions. The solution densities are calculated self-consistently within cDFT via the minimization of the free energy functional with respect to the solution densities. The solution densities satisfy the following equation