Blindness of the exact density response function to certain types of electronic excitations: implications for time-dependent density-functional theory.

Examples of electronic excitations are presented and discussed that do not contribute to the sum-over-state expression of the frequency-dependent density-density response function and thus do not lead to poles of the latter. As a consequence, these excitations principally cannot be described by time-dependent density-functional theory (TDDFT) response methods or any other method relying on the poles of the density-density response function. For these excitations, the DFT response approach commonly used in molecular physics or quantum chemistry is shown to not properly represent a DFT method and to yield differences of Kohn-Sham eigenvalues as excitation energies. The discussed examples are simple valence-valence excitations in the neon atom and the nitrogen molecule.