DFTB

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.

References

^ 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
^ Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G. (1998). "Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties". Physical Review B. 58 (11): 7260–7268. Bibcode:1998PhRvB..58.7260E. doi:10.1103/PhysRevB.58.7260.
^ Yang; Yu, Haibo; York, Darrin; Cui, Qiang; Elstner, Marcus (2007). "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". The Journal of Physical Chemistry A. 111 (42): 10861–10873. Bibcode:2007JPCA..11110861Y. doi:10.1021/jp074167r. PMID 17914769.
^ Köhler, Christof; Seifert, Gotthard; Frauenheim, Thomas (2005). "Density functional based calculations for Fen (N⩽32)". Chemical Physics. 309: 23–31. doi:10.1016/j.chemphys.2004.03.034.

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[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] Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G. (1998). "Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties". Physical Review B. 58 (11): 7260–7268. Bibcode:1998PhRvB..58.7260E. doi:10.1103/PhysRevB.58.7260.

[3] Yang; Yu, Haibo; York, Darrin; Cui, Qiang; Elstner, Marcus (2007). "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". The Journal of Physical Chemistry A. 111 (42): 10861–10873. Bibcode:2007JPCA..11110861Y. doi:10.1021/jp074167r. PMID 17914769.

[4] Köhler, Christof; Seifert, Gotthard; Frauenheim, Thomas (2005). "Density functional based calculations for Fen (N⩽32)". Chemical Physics. 309: 23–31. doi:10.1016/j.chemphys.2004.03.034.

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