  Core excitation from terminal oxygen O$_T$ in O$_3$ is shown to be an
excitation from a localized core orbital to a localized valence orbital. The
valence orbital is localized to one of the two equivalent chemical bonds. We
experimentally demonstrate this with the Auger Doppler effect which is
observable when O$_3$ is core-excited to the highly dissociative
O$_{T}$1s$^{-1}$7a$_1^1$ state. Auger electrons emitted from the atomic oxygen
fragment carry information about the molecular orientation relative to the
electromagnetic field vector at the moment of excitation. The data together
with analytical functions for the electron-peak profiles give clear evidence
that the preferred molecular orientation for excitation only depends on the
orientation of one bond, not on the total molecular orientation. The
localization of the valence orbital "7a$_1$" is caused by mixing of the valence
orbital "5b$_2$" through vibronic coupling of anti-symmetric stretching mode
with b$_2$-symmetry. To the best of our knowledge, it is the first discussion
of the localization of a core excitation of O$_3$. This result explains the
success of the widely used assumption of localized core excitation in
adsorbates and large molecules.
