RPA Dielectric functions: Streamlined approach to relaxation effects, binding and high momentum dispersion

The implementation of dielectric functions based on the Random Phase Approximation (RPA), including those by Lindhard, Kaneko, and Levine-Louie, is presented systematically, incorporating the effects of electron relaxation (finite width) and lattice interactions. A straightforward approach is proposed to introduce electron relaxation time and binding effects without needing Mermin corrections or Kramers–Kronig (KK) relations. This method yields the same dielectric function as the Mermin-corrected Lindhard and Kaneko models in several limiting cases (optical, high momentum transfer, and static limits). Moreover, the result adheres to the Bethe and F sum rules and the real and imaginary part are Kramers–Kronig pairs. Still, it shows some variation at intermediate energy and momentum transfer. Additionally, the description of dispersion at high momentum transfer is refined to account for relativistic effects. A small library containing the implementation of these dielectric functions is provided as supplementary material.