Moments analysis of the dielectric function

For many purposes, the random-phase approximation (RPA) is an adequate approximation for dielectric screening when the latter is required within a calculation. Therefore, an efficient approximation to the RPA is similarly useful in a wide range of situations. In this talk, we will describe a model for the same based on knowledge of several approximate frequency moments of the irreducible polarizability function. These models rely, in part, on the Fourier transform of the two-point, one-electron density matrix. We test our model calculations against numerical density-function theory (DFT) calculations in isolated atoms, the homogeneous electron gas, and a wide variety of metals, semiconductors, and insulators.