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In this physical review B paper, the authors mentioned that the local symmetry of anatase TiO2 is D2d point group. Also, in this applied physics letters paper, the authors mentioned that the symmetry of the Ti$^{4+}$ ion in anatase TiO2 is D2d point group, and illustrated this using the conventional cell of anatase TiO2.

My question is how the D2d point group is determined? By inspecting the atomic structure of anatase TiO2, I understand the point group of the Ti$^{4+}$ ion is D2d, but I believe this is neither the best nor the correct way to determine the point group.

Another question is, can we simply report that the local symmetry of anatase TiO2 is D2d point group, like what the authors did in the physical review B paper linked above? Does it mean that the D2d point group is inherient to all Ti/O sites as well as the interstitial sites in anatase TiO2? I have this question because in another physical review letters paper, the authors analyzed whether the s-d coupling between the s orbital of an interstitial Cu atom and the d orbitals of Cd/Te atoms exists based on the local symmetry of CdTe. Since the Cu atom is located at an interstitial site within CdTe, I don't understand how the local symmetry of CdTe can be used to perform the analysis.

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