Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na-5 and Na-9(+), we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.