xTB

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xTB

Extended tight-binding (xTB) methods are similar in construction to the DFTB methods (see §4.13). AS DFTB, xTB is based on the tight-binding expansion

E^TB[ρ] = E⁰[ρ₀] + E¹[ρ₀, δρ] + E²[ρ₀,(δρ)²] + ...

(9)

xTB methods target specific properties such as Geometries, Frequencies, and Non-covalent interactions, which is reflected by the methods names: GFNn-xTB.[73] This level of theory can be used both in the DFTBP API, as well as with the dedicated XTB keywords. The energy expressions of the two most important xTB variants are given by

E^GFN1 = E_rep + $\displaystyle \sum_{{iAB}}^{}$ $\displaystyle \sum_{\nu}^{}$ $\displaystyle \sum_{\nu}^{}$ n_iC_νiC_μiH⁰_μν + E^D3_disp + E_srb + E_XB + E⁽²⁾_γ + E⁽³⁾_Γ

(10)

and

E^GFN2 = E_rep + $\displaystyle \sum_{{iAB}}^{}$ $\displaystyle \sum_{\nu}^{}$ $\displaystyle \sum_{\nu}^{}$ n_iC_νiC_μiH⁰_μν + E^D4_disp + E⁽²⁾_γ + E_AES + E_AXC + E⁽³⁾_Γ

(11)

Furthermore, a partially polarizable force-field variant of xTB, GFN-FF, exists that also can be used with the XTB keywords. Importantly, xTB methods are parametrized for all elements up to radon (Z≤86).