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About DFTB

The Density Functional based Tight binding method is based on a second-order expansion of the Kohn-Sham total energy in Density-Functional Theory (DFT) with respect to charge density fluctuations. The zeroth order approach is equivalent to a common standard non-self-consistent (TB) scheme, while at second order a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements can be derived. These are modified by a self-consistent redistribution of Mulliken charges (SCC).

Besides the usual "band structure" and short-range repulsive terms the final approximate Kohn-Sham energy additionally includes a Coulomb interaction between charge fluctuations. At large distances this accounts for long-range electrostatic forces between two point charges and approximately includes self-interaction contributions of a given atom if the charges are located at one and the same atom. Due to the SCC extension, DFTB can be successfully applied to problems, where deficiencies within the non-SCC standard TB approach become obvious.

In the last few years, the DFTB method had been heavily extended to allow the calculation of optical and excited state properties. The GW formalism as well as time dependent DFTB had been implemented. Furthermore, DFTB had been used to calculate the Hamiltonian for transport codes, using Green functions techniques.

If you are interested in the details of the DFTB method,  you can study some selected references.

The DFTB method has several implementations. Some of them all listed on the implementation page.