# 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.