  We report a new model for highly mismatched semiconductor (HMS) alloys. Based
on the Anderson impurity Hamiltonian, the model generalizes the recent band
anti-crossing (BAC) model, which successfully explains the band bowing in
highly mismatched semiconductors. Our model is formulated in empirical
tight-binding (ETB) theory and uses the so called sp$^{3}$s* parameterization.
It does not need extra parameters other than bulk ones. The model has been
applied to BeSe$_{x}$Te$_{1 - x}$ alloy. BeTe and BeSe are wide-band gap and
highly mismatched semiconductors. Calculations show large band bowing, larger
on the Se rich side than on the Te rich side. Linear interpolation is used for
an arbitrary concentration $x$. The results are applied to calculation of
electronic and optical properties of BeSe$_{0.41}$Te$_{0.59}$ lattice matched
to Si in a superlattice configuration.
