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A new model to calculate electronic states of the diamond
vacancies has been developed using many body techniques. This
model is based on physical assumptions of previous molecular
models but does not use configuration interaction. Present model
allows an accurate and unified treatment of electronic levels and
related eigen functions for diamond vacancies, in addition to
transition energies of the first dipole-allowed transitions in the
neutral $(V^{0})$ and negatively charged $(V^{-})$ vacancies, GR1
and ND1 band. For the first time, we calculated their optical
transition intensities. For obtaining these results, we solved a
generalized form of the Hubbard Hamiltonian, which consists of all
electronelectron interaction terms on atomic orbital basis.
Spatial symmetry of the defect, $T_{d}$ symmetry, is included in
the form of the Hamiltonian, and the eigen states have
automatically the correct spin and symmetry properties. We discuss
the possibility of the reduction of the wide gap between
theoretical and semiempirical wisdom by including deformation of
the dangling orbital or delocalization of the vacancy electrons to
the next nearest neighbor (NNN) atoms of the vacancies. Our
prediction for low lying the $3_{T_{1}}$ level of the neutral
vacancy in diamond is consistent with experimental expectations.
We report the variation of the ground and excited states of the
GR1 and ND1 lines with hopping parameter t and also the electronic
configurations of these states.
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