---
title: Time-Dependent Density Functional Theory (TDDFT)
url: https://www.emergentmind.com/topics/time-dependent-density-functional-theory-tddft
type: topic
---

# Time-Dependent Density Functional Theory (TDDFT)

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 [2204.10135] [1305.1388] [2509.10745].

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Source: https://www.emergentmind.com/topics/time-dependent-density-functional-theory-tddft