  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.
