Time-Dependent Density Functional Theory (TDDFT)

• TDDFT is a quantum mechanical framework that extends ground-state DFT to analyze electronic excitations and time-dependent phenomena.
• It maps an interacting electron system to a non-interacting Kohn–Sham system to reproduce the exact time-dependent density.
• TDDFT is applied in linear-response for vertical spectra and in real-time for broadband spectral analysis, strong-field dynamics, and nonequilibrium processes.

Time-dependent density-functional theory (TDDFT) extends ground-state Kohn–Sham density functional theory to electronic excitations and electron dynamics, and provides a formally exact framework for the quantum many-body dynamics of electrons in terms of the time-dependent density rather than the underlying many-body wavefunction. In its standard formulation, for a fixed initial state, a time-dependent external potential and the resulting time-dependent density are in one-to-one correspondence up to a purely time-dependent gauge, and the interacting system is mapped to a noninteracting time-dependent Kohn–Sham system constructed to reproduce the exact density. In practice, TDDFT has two principal realizations: linear-response TDDFT in the frequency domain, which is the de facto tool for vertical electronic spectra, and explicitly time-dependent or real-time TDDFT, which propagates the Kohn–Sham system after an external perturbation and is used for broadband spectra, strong-field dynamics, and nonequilibrium processes (Herbert, 2022, Ullrich et al., 2013, Ullrich, 12 Sep 2025).