DFTB

DFTB, short for Density Functional Tight Binding, is a semi-empirical quantum mechanical method derived from density functional theory (DFT). It aims to retain the essential physics and accuracy of DFT while reducing computational cost by using a tight-binding-like Hamiltonian and a minimal, atom-centered basis set.

The method expands the DFT total energy in deviations of the electron density from a reference state to second order (with higher-order variants available). It relies on precomputed two-center integrals (Slater-Koster parameters) and a repulsive potential to describe interatomic interactions. Self-consistent charge DFTB (SCC-DFTB) allows partial charges to respond to the environment, improving descriptions of bond formation and charge transfer. Parameters are typically derived from DFT calculations for chosen functionals and basis sets, providing practical transferability within chemical families.

DFTB has several levels, such as DFTB0, DFTB2, and DFTB3, corresponding to the order of the density expansion and the inclusion of corrections. The most widely used implementation is DFTB+, which supports SCC-DFTB and various extensions. Modern variants include dispersion corrections and time-dependent extensions (TD-DFTB) for excited-state properties.

Applications of DFTB span large-scale systems, from nanostructures and surfaces to polymers and biomolecules, where conventional DFT is computationally demanding. It is valued for rapid geometry optimizations, molecular dynamics simulations, and screening studies, enabling exploration of systems containing thousands to hundreds of thousands of atoms.

Limitations include dependence on parameter sets and transferability, reduced accuracy for systems poorly represented in reference data, and challenges for strongly correlated or highly excited-state scenarios. results are often validated against higher-level methods when critical accuracy is required.