Many-body Diagrammatic Expansion for the Exchange-Correlation Kernel in Time-Dependent Density Functional Theory
Abstract
A diagrammatic expansion for the dynamic exchange-correlation kernel fxc of time dependent density functional theory is formulated. It is shown that fxc has no singularities at Kohn-Sham transition energies in every order of the perturbation theory. However, it may diverge with the system size in extended systems. This signifies that any approximate perturbative substitute for fxc requires a consistent perturbative treatment of the equation for the response function to avoid uncontrollable errors in the many-body corrections to excitations energies.
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