Two-δ- Function Generalized Plasma Pole Model for First Principle Calculations of Quasiparticle Energies in Many-Electron Systems

To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-δ-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single δ-function GPP model has the drawback of over simplifications and for the crystals without.the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-δ GPP model is an op timization of the two approaches. We analyze the two-δ GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these δ functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.