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The ground state of the silicon atoms in the bulk solid is a closed
shell configuration. If a single up- or down-spin electron is excited
from the valence band to the conduction band, the wave function then
has a spin contamination, i.e. it is no longer an eigenstate of the
operator. It is possible to avoid this contamination
either by exciting simultaneously the electron with opposite spin, to
create a biexciton, or to use a superposition of determinantal
products to obtain a spin singlet state. This superposed trial
wavefunction is a generalisation of the trial wavefunction introduced
in chapter ,
A spin-singlet wavefunction for diamond-structure silicon can be
obtained from Eq.(), by the superposition of two
determinantal products,
where indicates a Slater determinant in which one of the
ground state orbitals has been replaced by an excited state orbital.
In the first product, the down-spin determinant contains the ground
state orbitals and the up-spin determinant has one of the ground state
orbitals replaced by an excited state orbital. In the second product
the up-spin determinant contains the ground state orbitals and the
down-spin determinant has one of the ground state orbitals replaced
with an excited state orbital.
Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996