TDDFTB

TDDFTB, or time-dependent density functional tight-binding, is an approximate quantum-chemical method for calculating electronic excited states in large systems. It extends density functional tight-binding (DFTB) to the time-dependent regime by applying linear-response theory to the ground-state DFTB electronic structure, yielding excitation energies and oscillator strengths with much lower computational cost than standard TD-DFT.

The method uses a minimal valence basis and a parameterized Hamiltonian derived from a second-order expansion of the DFT energy around a reference density. The excited-state problem is formulated in a Casida-like linear-response framework, where the exchange-correlation kernel is approximated within the DFTB scheme and expressed through two-body interaction parameters obtained from ground-state DFTB data. Solving the resulting eigenproblem provides singlet and triplet excitation energies and their transition strengths.

TDDFTB is particularly suited for large molecules, polymers, and nanostructures, where it can handle systems containing hundreds to thousands of atoms with modest computational resources. It is implemented in software such as DFTB+, and it benefits from well-established DFTB parameter sets.

Limitations include dependence on the underlying parameterization and the approximate kernel, which can limit accuracy for certain excitations. In general, valence-type excitations are reproduced reasonably well, while Rydberg and charge-transfer states are more challenging unless additional corrections or long-range improvements are incorporated. Users should validate TDDFTB results against higher-level methods or experimental data for the specific system and property of interest.