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Octahedral distortion to D2d and D2h

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The octahedra of anatase and rutile TiO2 both have elongation along the z-axis (apical). Anatase experiences more angular distortion around the equatorial bonds. Why is anatase classified as D2d (meaning the dz^2, dxz and dyz states have an INCREASE in energy), while rutile is D2h (meaning these states have LOWER energy), if both have elongation along the z-axis and should therefore both have reduced repulsion between the central cation and the ligands?

A thought is that the angular distortion of the equatorial ligands somehow stabilizes the d orbitals with only xy components, but I don't know why these components would be more stabilized than those with z components, since the elongation along z should lower the repulsion.

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The solution offers personalized answer and covers all pertinent points for student's better understanding. It deals with some of the basic concepts of octahedral crystal field splitting, which may prove beneficial to other students.