What does TDDFT compute that ground-state DFT cannot?

It yields electronic excitation energies, oscillator strengths, and frequency-dependent response properties, giving access to absorption and emission spectra rather than only ground-state structure and energetics.

Why are charge-transfer states a known weakness?

Standard semilocal functionals lack the correct long-range exchange behavior, so excitations that move charge over large distances are systematically underestimated unless range-separated functionals are used.

Time-Dependent Density Functional Theory

Time-dependent density functional theory extends the density-based formalism to systems in time-varying fields, providing the standard route to molecular excited states and optical spectra.

Definition

The extension of density functional theory to time-dependent external potentials, from which electronic excitation energies and response properties are obtained.

Scope

Covers the Runge-Gross theorem that grounds the time-dependent formalism, the linear-response (Casida) approach for computing excitation energies and oscillator strengths, the adiabatic approximation, and characteristic limitations such as the poor description of charge-transfer and doubly excited states.

Core questions

How does the Runge-Gross theorem extend density functional theory to the time domain?
How are excitation energies extracted from the linear response of the density?
What does the adiabatic approximation assume and when does it fail?
Why are charge-transfer excitations problematic for standard functionals?

Key theories

Runge-Gross theorem: Establishes a one-to-one correspondence between the time-dependent density and the time-dependent external potential, providing the formal basis for the time-dependent theory.
Casida linear-response formulation: Recasts the calculation of excitation energies and intensities as an eigenvalue problem in the space of single excitations, making excited-state calculations routine.

Clinical relevance

Time-dependent density functional theory is the most widely used method for predicting UV-visible absorption and emission spectra of medium and large molecules, supporting the design of dyes, photocatalysts, and fluorescent probes.

History

Founded by the Runge-Gross theorem of 1984 and made practical for molecules by Casida's linear-response formulation in the mid-1990s, the method became the dominant tool for excited-state chemistry once efficient implementations spread through the major quantum-chemistry packages.

Debates

Adiabatic approximation and charge-transfer failures: The standard adiabatic, frequency-independent kernel misses double excitations and badly underestimates charge-transfer excitation energies, motivating range-separated functionals and approaches.

Key figures

Erich Runge
Eberhard Gross
Mark Casida

Seminal works

runge1984
casida1995

Frequently asked questions

What does TDDFT compute that ground-state DFT cannot?: It yields electronic excitation energies, oscillator strengths, and frequency-dependent response properties, giving access to absorption and emission spectra rather than only ground-state structure and energetics.
Why are charge-transfer states a known weakness?: Standard semilocal functionals lack the correct long-range exchange behavior, so excitations that move charge over large distances are systematically underestimated unless range-separated functionals are used.