  We present a variational estimate for the binding energy of a Frenkel exciton
in the insulating cuprate superconductors. Starting from the three band Hubbard
model we perform a canonical transformation to O($t^2$), where $t$ is the bare
nearest neighbour copper-oxygen hopping integral. An effective Hamiltonian is
then derived to describe the hopping of the exciton through the copper oxide
plane. The critical parameter in the model is the nearest neighbour
copper-oxygen coulomb repulsion, $V$. It is found that a critical value of $V$
is needed to observe bound Frenkel excitons, and that these excitons have the
same symmetry as the parent copper orbital, $d_{x^2-y^2}$. We determine the
critical value of $V$ using a variational approach, and attempt to fit the
parameters of the model to known experimental results.
