Time-Dependent DFT
Also known as: TDDFT, TDDFT/DFT
Time-Dependent Density Functional Theory (TDDFT) extends DFT to excited states and time-dependent phenomena. Formulated by Runge and Gross in 1984, TDDFT enables calculation of excitation energies, optical spectra, and charge-transfer processes with moderate computational cost, making it invaluable for photochemistry and materials science.
Key highlights
- Excitation energies within ~0.3–0.5 eV of experiment for many molecules.
- Moderate computational cost; O(N^3) to O(N^4) scaling.
- Natural treatment of frequency-dependent response.
- Applicable to valence and Rydberg excitations.
- Well-developed software implementations (Gaussian, ORCA, TURBOMOLE).
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
TDDFT is used for computing excitation energies, optical absorption spectra, and emission properties of molecules and materials. It is fast enough for systems with 100–1000 atoms, making it popular in photochemistry and drug design.
Strengths & limitations
- Excitation energies within ~0.3–0.5 eV of experiment for many molecules.
- Moderate computational cost; O(N^3) to O(N^4) scaling.
- Natural treatment of frequency-dependent response.
- Applicable to valence and Rydberg excitations.
- Well-developed software implementations (Gaussian, ORCA, TURBOMOLE).
- Excitation energies systematically underestimated for charge-transfer states.
- Double excitations poorly described; requires higher-order approximations.
- Kernel approximation (adiabatic LDA/GGA) ignores memory effects.
- Triplet-singlet transitions difficult; transition dipoles can be inaccurate.
- No guaranteed lower bound on excitation energies (unlike variational methods).
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What is the Casida equation and how does it relate to TDDFT?
The Casida equation is the eigenvalue equation for excitations in linear-response TDDFT. It relates excitation energies to the response of the electron density. Solving the Casida matrix gives excitation energies and transition dipole moments.
Why does TDDFT fail for charge-transfer excitations?
Standard LDA and GGA kernels lack range-dependence in the exchange-correlation potential. Charge-transfer states require long-range interactions that these kernels miss. Range-separated hybrids (CAM-B3LYP) or long-range corrected functionals improve charge-transfer accuracy.
How do I include solvent effects in TDDFT?
Use implicit solvation models (PCM, CPCM, SMD) that surround the solute with a dielectric continuum. The solvent polarization shifts excitation energies and broadens spectra, essential for solution-phase spectroscopy.
Can TDDFT describe double excitations?
Standard linear-response TDDFT includes double excitations only indirectly through the kernel. For systems where double excitations are important, configuration interaction (CI) or coupled cluster methods are more appropriate.
How accurate are TDDFT excitation energies?
Typically within 0.3–0.5 eV of experiment for single excitations. Charge-transfer states can be off by 1–2 eV. Double excitations are often missed. For demanding applications, benchmark against experiment or higher-level methods.
Sources
- 1.Runge, E., Gross, E. K. (1984). Density-functional theory for time-dependent systems. Physical Review Letters, 52, 997–1000.
- 2.Casida, M. E. (1995). Time-dependent density-functional response theory for molecules. In Recent Advances in Density Functional Methods. World Scientific.
- 3.Huix-Rotllant, M., et al. (2020). Assessment of time-dependent density functional theory for excited states. In Handbook of Excited State Spectroscopy. World Scientific.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Time-Dependent DFT. ScholarGate. https://scholargate.app/quantum-computing/time-dependent-dft