Post-pulse dipole instability in adiabatic TDDFT: fact or artifact?

Recent real-time TDDFT calculations have reported an unexpected delayed growth of molecular dipole oscillations some time after an extreme-ultraviolet (XUV) pulse is applied. We show that numerical and analytical arguments suggest that this instability is an artifact of an incorrect non-linearity introduced by the computational approach: Propagation with an adiabatic exchange-correlation approximation within the time-dependent Kohn-Sham equations of time-dependent density functional theory (TDDFT) tends to amplify initially small and pure sinusoidal oscillations in a system. On the other hand, when this same adiabatic approximation is used within the recent response-reformulated RR-TDDFT,the instability is absent. The absorbing boundary condition plays a crucial role consistent with our argument. We demonstrate this explicitly on the N2 molecule subject to an XUV pulse, with a range of adiabatic functionals.