Correlation Strength, Optical Conductivity and d-d excitons in high $T_c$ cuprates

A single site dynamical mean field analysis is presented of models of high $T_c$ copper-oxide superconductors, including oxygen orbitals and both $x^2-y^2$ and $3z^2-r^2$ $Cu$ d-orbitals. The optical conductivity, doping dependent effective mass and the $e_g$ portion of the d-d exciton spectrum are determined. The details of the oxygen-oxygen hopping are shown to be unimportant. A general connection between $d$ valence and the metal/charge transfer insulator phase boundary is outlined.