DFTB

The density functional tight-binding (DFTB) methods are accessible via the DFTB+ (DFTBP) program package. Generally, DFTB can be understood as an approximation to density functional theory,[44] based on a Taylor-expansion of the energy in terms of the electron density and density fluctuations

ETB[ρ] = E0[ρ0] + E1[ρ0, δρ] + E2[ρ0,(δρ)2] + ...

(7)

The energy expression for the most well known DFTB3 method is given by:

EDFTB3 = $${\frac{{1}}{{2}}}$$$$\sum_{{AB}}^{}$$VABrep + $$\sum_{{iAB}}^{}$$$$\sum_{\nu}^{}$$$$\sum_{\nu}^{}$$niCνiCμiH0μν + $${\frac{{1}}{{2}}}$$$$\sum_{{AB}}^{}$$ΔqAΔqBγABh + $${\frac{{1}}{{3}}}$$$$\sum_{{AB}}^{}$$(ΔqA)2ΔqBΓAB

(8)