As mentioned above, the elements of the Hamiltonian matrix are fitted
to first-principal calculations for different equilibrium structures
[98]. To describe the properties of non-equilibrium structures,
as amorphous solids or liquids, the hopping integrals and the
repulsive energy should be rescaled with respect to the interatomic
distance. The rescaling functions proposed by Goodwin *et. al.*
[103] greatly improve the transferability of the tight binding
model to stuctures not included in the parametrization. These
functions are now widely used, in the slightly improved form proposed
by Xu *et. al.* [102]

(7.19) |

for the rescaling of the hopping integrals, and

(7.20) |

for the repulsive potential. In the rescaling functions found by Goodwin em et. al., the parameters