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.
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