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We present a variational estimate for the binding energy of a Frenkel excitonin the insulating cuprate superconductors. Starting from the three band Hubbardmodel we perform a canonical transformation to O($t^2$), where $t$ is the barenearest neighbour copper-oxygen hopping integral. An effective Hamiltonian isthen derived to describe the hopping of the exciton through the copper oxideplane. The critical parameter in the model is the nearest neighbourcopper-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 thesame symmetry as the parent copper orbital, $d_{x^2-y^2}$. We determine thecritical value of $V$ using a variational approach, and attempt to fit theparameters of the model to known experimental results.Comment: Latex document. Figures on request

A variational estimate of the binding energy of charge transfer excitons in the cuprate superconductors