SCCDFTB

Self-Consistent Charge Density Functional Tight-Binding (SCC-DFTB) is an approximate quantum mechanical method derived from density functional theory. It belongs to the family of tight-binding methods and is designed to model large systems with reduced computational cost compared with full Kohn–Sham DFT.

In SCC-DFTB, the total energy is obtained by a second-order expansion of the DFT energy around a reference density, with additional terms to account for charge fluctuations. A self-consistent charge (SCC) term introduces atomic charges q_I that describe redistribution of electron density in response to bonding. The energy includes a Coulomb-like interaction term between charges, often written as a function of gamma_{IJ} q_I q_J, plus an empirical repulsive energy and a reference Hamiltonian matrix built from two-center integrals. The method is solved iteratively until the charges converge, providing a self-consistent description of charge redistribution within a tight-binding framework.

Parameterization is essential: parameters for element pairs and the gamma functions are fitted to reference data, and different parameter sets exist for various classes of elements. This underpins the method’s transferability and accuracy for specific systems.

Applications include structural optimization and molecular dynamics of organic molecules, polymers, surfaces, and nanostructures. SCC-DFTB enables simulations of systems containing thousands of atoms with reasonable efficiency, delivering reliable geometries and trends in relative energetics when appropriate parameter sets are used. Limitations include dependence on parameter quality, and reduced accuracy for systems with strong electronic correlation or for certain excited-state properties.

Implementation is available in software such as DFTB+, with extensions like SCC-DFTB3 that aim to improve accuracy by incorporating higher-order corrections.