DFTB explained

The Density Functional Based Tight Binding method is an approximation to density functional theory, which reduces the Kohn-Sham equations to a form of tight binding related to the Harris functional. The original ^[1] approximation limits interactions to a non-self-consistent two center hamiltonian between confined atomic states. In the late 1990s a second-order expansion of the Kohn-Sham energy enabled a charge self-consistent treatment of systems ^[2] where Mulliken charges of the atoms are solved self-consistently. This expansion has been continued to the 3rd order in charge fluctuations ^[3] and with respect to spin fluctuations.^[4]

Unlike empirical tight binding the (single particle) wavefunction of the resulting system is available, since the integrals used to produce the matrix elements are calculated using a set of atomic basis functions.

Notes and References

1. Seifert, G., H. Eschrig, and W. Bieger. "An approximation variant of LCAO-X-ALPHA methods." Zeitschrift für Physikalische Chemie-Leipzig 267.3 (1986): 529-539
2. 10.1103/PhysRevB.58.7260 . Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. 1998. Elstner. M.. Porezag. D.. Jungnickel. G.. Elsner. J.. Haugk. M.. Frauenheim. Th.. Suhai. S.. Seifert. G.. Physical Review B. 58. 11. 7260–7268. 1998PhRvB..58.7260E.
3. 10.1021/jp074167r . Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method: Third-Order Expansion of the Density Functional Theory Total Energy and Introduction of a Modified Effective Coulomb Interaction. 2007. Yang. Yu. Haibo. York. Darrin. Cui. Qiang. Elstner. Marcus. The Journal of Physical Chemistry A. 111. 42. 10861–10873. 17914769. 2007JPCA..11110861Y.
4. 10.1016/j.chemphys.2004.03.034 . Density functional based calculations for Fen (N⩽32). 2005. Köhler. Christof. Seifert. Gotthard. Frauenheim. Thomas. Chemical Physics. 309. 23–31.