Detection of Core Hole Localization in X-ray Photoionization

In the quest to find further evidence of the core hole localization phenomenon we recently found in CF$_{\mathrm{4}}$, we present \textit{ab initio} calculations of molecular frame photoelectron angular distributions of electrons ejected from the core orbitals of the fluorine K-edge of various isomers of difluoroethylene (C$_{\mathrm{2}}$H$_{\mathrm{2}}$F$_{\mathrm{2}})$.$_{\mathrm{\thinspace }}$In the case of CF$_{\mathrm{4}}$, the probability of removing a core electron from any of the four F atoms is the nearly the same for all directions of photoejection of the electron. However, we found that for a particular decay channel, detecting an F$^{\mathrm{+}}$ ion makes the probability of having this ion be the atom that was core ionized nearly unity, because of a chemical effect related to the electronegativity of fluorine. C$_{\mathrm{2}}$H$_{\mathrm{2}}$F$_{\mathrm{2}}$ has two symmetry-equivalent fluorine atoms. Our work explores the extent to which the localization of core holes also takes place on one of two of the fluorine equivalent atoms following X-ray photoionization and is clearly visible in an experiment that averages around the axis of recoil of ion fragments after Auger decay.