GW-Calculations of the Self-Energy of Electrons

For investigations on the physics of electrons in crystalline media it is of essential importance to know the dynamic self-energy function of the electrons. Knowing about this self-energy function is the basis of modern quasi-particle calculations and provides us with the possibility to calculate experimentally feasible quantities as, e.g., excitation energies of electrons and lifetimes of excited states. By an improved Green\'s function other important quantities as occupation numbers or momentum density distributions are accessible. This work investigates the dynamic self-energy function in simple and transition metals, based on the GW approximation as proposed in the 1960s by Lars Hedin. An algorithm for the calculation of the self-energy has been developed for detailed studies on the various aspects of the numerical determination of this function. Extensive investigations show the optimization of the parameters in order to achieve reliable results with justifiable numerical effort. After verification of the calculations on simple metals where corresponding results for the homogeneous electron gas are reasonable; the optimized GW algorithm has been applied to nickel.