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Self consistency

Charge transfer phenomenon is particularly important in materials with significant ionic bonding or defects, in surfaces and in small clusters. To account for this effect, the tight binding Hamiltonian must dependent on the electronic distribution in a self-consistent way. In the case of metals or isolated materials, any local excess charge should be neutralised by screened Coulombic interactions, so that each atom must be charge neutral. The self-consistency may then be well described by local charge neutrality [101]. In this scheme, the on-site energies are varied on all sites by an amount of $\Delta \varepsilon_i$ according to


\begin{displaymath}\varepsilon_{i\alpha} \rightarrow \varepsilon_{i\alpha}
+\Delta \varepsilon_i.
\end{displaymath} (7.21)

The value of $\Delta \varepsilon_i$ is found iteratively, until the number of electrons on each atom is equal to the ionic charge, that is


\begin{displaymath}\sum_\alpha[
\underbrace{2\sum_{n({\rm occ.})}C_{i\alpha}^{(n...
...f \ electrons \ on \ atom} \ i}
- N_{i\alpha}^{\rm atom}] = 0
\end{displaymath} (7.22)

for each site i. The variation imposed on the on-site energies may be physically explained by the fact that an excess (deficient) electronic charge on one atom should raise (decrease) the on-site energy due to the raise (decrease) of the electrostatic potential on this atom. This change on the electrostatic potential induces a charge transfer that equalizes the Fermi level and restores the neutrality of the atoms.


next up previous contents
Next: Force calculations Up: The tight binding model Previous: The rescaling functions
David Saada
2000-06-22