DFTB

{{Context|date=May 2020}}

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 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 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 {{Cite journal | doi=10.1103/PhysRevB.58.7260 | title=Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties| year=1998| last1=Elstner| first1=M.| last2=Porezag| first2=D.| last3=Jungnickel| first3=G.| last4=Elsner| first4=J.| last5=Haugk| first5=M.| last6=Frauenheim| first6=Th.| last7=Suhai| first7=S.| last8=Seifert| first8=G.| journal=Physical Review B| volume=58| issue=11| pages=7260–7268| bibcode=1998PhRvB..58.7260E}} where Mulliken charges of the atoms are solved self-consistently. This expansion has been continued to the 3rd order in charge fluctuations {{Cite journal | doi=10.1021/jp074167r |title = 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|year = 2007|last1 = Yang|last2 = Yu|first2 = Haibo|last3 = York|first3 = Darrin|last4 = Cui|first4 = Qiang|last5 = Elstner|first5 = Marcus|journal = The Journal of Physical Chemistry A|volume = 111|issue = 42|pages = 10861–10873|pmid = 17914769|bibcode = 2007JPCA..11110861Y}} and with respect to spin fluctuations.{{Cite journal | doi=10.1016/j.chemphys.2004.03.034 | title=Density functional based calculations for Fen (N⩽32)| year=2005| last1=Köhler| first1=Christof| last2=Seifert| first2=Gotthard| last3=Frauenheim| first3=Thomas| journal=Chemical Physics| volume=309| pages=23–31}}

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.