Repulsive contributions#
Effective coulombic repulsion#
The xTB Hamiltonian is using an effective coulomb-like repulsion term
\[E_\text{rep} =
\frac12
\sum_\text{A}^{N_\text{at}}
\sum_\text{B}^{N_\text{at}}
\frac{Z_\text{AB}}{R_\text{AB}^{r_\text{AB}}}
\exp[-\alpha_\text{AB}\cdot R_\text{AB}^{k_\text{AB}}]
,\]
where RAB is the interatomic distance and ZAB, αAB, rAB and kAB are pairwise parameters for each species pair. The pairwise parameters are usually formed from element-specific parameters to limit the actual amount of free parameters. The effective nuclear charges are formed by
\[Z_\text{AB} =
Z_\text{A} \cdot Z_\text{B}
.\]
Repulsion exponents are obtained as geometric mean from element specific exponents by
\[\alpha_\text{AB} =
\sqrt{\alpha_\text{A}\alpha_\text{B}}
.\]
Finally, the exponents, rAB and kAB, of the distance dependent contributions are usually set globally for all element-pairs.