Electron dynamics with real‐time time‐dependent density functional theory

Real‐time time‐dependent functional theory (RT‐TDDFT) directly propagates the electron density in the time domain by integrating the time‐dependent Kohn–Sham equations. This is in contrast to the popular linear response TDDFT matrix formulation that computes transition frequencies from a ground state reference. RT‐TDDFT is, therefore, a potentially powerful technique for modeling atto‐ to picosecond electron dynamics, including charge transfer pathways, the response to a specific applied field, and frequency dependent linear and nonlinear properties. However, qualitatively incorrect electron dynamics and time‐dependent resonant frequencies can occur when perturbing the density away from the ground state due to the common adiabatic approximation. An overview of the RT‐TDDFT method is provided here, including examples of some cases that lead to this qualitatively incorrect behavior.