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The rescaling functions

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]


\begin{displaymath}h(r) = (r_0/r)^n \exp \{n[-(r/r_c)^{n_c} + (r_0/r_c)^{n_c}] \},
\end{displaymath} (7.19)

for the rescaling of the hopping integrals, and


\begin{displaymath}\phi(r) = \phi_0(d_0/r)^m \exp \{m[-(r/d_c)^{m_c}
+ (d_0/d_c)^{m_c}] \}
\end{displaymath} (7.20)

for the repulsive potential. In the rescaling functions found by Goodwin em et. al., the parameters nc and rc were the same as mc and dc respectively. All the parameters appearing in the rescaling functions are obtained by fitting first principle results of energy versus nearest-neighbour interatomic distance for different crystalline phases, given equilibrium sets of hopping integrals for these structures. In this way, the tight binding model is transferable to different atomic environements.


next up previous contents
Next: Self consistency Up: The tight binding model Previous: The bond energy model
David Saada
2000-06-22