where W denotes the dynamically screened Coulomb interaction. This is determined by first computing the polarization P in the random-phase approximation (RPA), then with it the microscopic dielectric function as a convoluting of P with the bare Coulomb interaction v, i.e., ϵ = 1 -vP . Finally, W is obtained as W = ϵ -1 v, i.e., after inversion of ϵ and subsequent convolution with the bare Coulomb interaction. The frequency integration in Eq. ( ) can be performed fully analytically (FA) based on contour deformation techniques or with the use of a generalized plasmon-pole model (PPM), which extends the RPA result for ω = 0 (static polarization) and the associated static dielectric function to the dynamic one.