A Snapshot of Time-Dependent Density-Functional Theory

TL;DR

This perspective surveys TDDFT as a time-dependent extension of DFT, emphasizing both foundational aspects and cutting-edge real-time and linear-response developments. It highlights nonadiabatic xc functionals, RR-TDDFT, and excitonic approaches for solids, along with computational advances that broaden practical reach. The real-time frontier covers ultrafast nonlinear dynamics, HHG, electronic stopping power, pump–probe spectroscopy, magnetism, and photon-field coupling via QEDFT, illustrating a wide-ranging impact on chemistry and condensed-matter physics. Despite substantial progress, the authors stress the need for rigorous foundations, robust validation, and effective electron–nuclear and light–matter coupling to realize quantitatively predictive nonequilibrium TDDFT.

Abstract

Time-dependent density-functional theory (TDDFT) is an extension of ground-state density-functional theory which allows the treatment of electronic excited states and a wide range of time-dependent phenomena in the linear and nonlinear regime, including coupled electron-nuclear dynamics. TDDFT is a vibrant field with many exciting applications in physics, (bio)chemistry, materials science and other areas. This perspective gives an overview of recent developments and successes, formal and computational challenges, and hot topics in TDDFT.

Figures (13)

• Figure 1: Number of papers per year using or citing TDDFT, from Web of Science (accessed on September 12, 2025).WOS
• Figure 2: Dipole power spectrum of two interacting electrons on a Hubbard trimer. The inset shows the site occupation of the ground state $(n_0)$ and first excited state $(n_1)$. The TDKS spectra with exchange-only and adiabatically exact approximation only reproduce the two single excitations but fail to capture the higher-lying double excitations.
• Figure 3: Time-dependent dipole moment $d(t)$ for the Hubbard trimer, driven at the first resonance. (a) Exact solution of the 2-electron Schrödinger equation. (b) TDKS with exchange-only approximation. (c) TDKS with the adiabatically exact xc potential. The horizontal dashed lines indicate the exact dipole moments of the ground state $(-1.49)$ and the first excited state $(-0.43)$.
• Figure 4: Schematic summary of nonadiabatic TDDFT methods and their pros and cons. See text for more details and references.
• Figure 5: Dipole moment $\mu_z$ associated with the resonantly driven charge transfer in the LiCN molecule, calculated using TDKS and RR-TDDFT. LiCN, a linear molecule, has a dipole moment in the degenerate second and third excited states opposite to that of the ground state, and a laser pulse at the excitation frequency should induce a large change in $\mu_z$ (see curve labeled "Exact"). The adiabatic PBE Perdew1996 and tBNL Baer2005Livshits2007 functionals fail with TDKS, but achieve complete dipole switching within the RR scheme. Adapted with permission from APS from Ref. Dar2024, © 2024.