Recent real-time, time-dependent density functional theory (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 nonlinearity introduced by the computational approach: Propagation with an adiabatic exchange-correlation approximation within the time-dependent Kohn-Sham equations of 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 TDDFT, the instability is absent. The absorbing boundary condition plays a crucial role consistent with our argument. We demonstrate this explicitly on the ${\mathrm{N}}_2$ molecule subject to an XUV pulse, with a range of adiabatic functionals.

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• Electronic excitation & ionization
• Electronic structure of atoms & molecules
• Ultrafast phenomena
• Density functional theory
• Time-dependent DFT