Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $\delta$. New correction (``$\eta$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $W\delta < \omega < W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.