Improved local-field corrections to the G_ {0} W approximation in jellium: Importance of consistency relations
We study the effects of local vertex corrections to the self-energy of the electron gas. We find that a vertex derived from time-dependent density-functional theory can give accurate self-energies, provided, however, a proper decay at large momentum transfer (large q) is built into the vertex function. (The local-density approximation for the vertex fails badly.) Total energies are calculated from