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Figure 2
A sketch of the PES V(a) as a function of the rotational angle a of the BX3 octahedra. The atomic configurations generating these potentials are shown in Fig. 3[link]. (a) Dynamic tilting: the rotational degree of freedom is subject to a double-well potential V(a). From numerical calculations, the resulting ionic wave function φ(a) can be derived. In the case of a double well, states at the lowest energy show two distinct localizations in both potential minima and so does the particle density |φ(a)|2 (shaded in grey). However, the average tilting angle is at a = 0 – i.e. in between the two minima. The particle density (grey) is split and thus can explain large atomic MSDs or, according to the representation of the motion, large vibrational ellipsoids in structures with dynamical tilting. The vibrational energy spectrum is not equispaced in this case due to quasi-degeneracy. (b) Comparison of the vibrational DOS, double well (red) versus single well (green). For better visibility, smearing was applied. The energy spectrum is particularly dense for the double well, due to almost degeneracy of these energy states. This gives rise to particularly small transition energies and thus potentially to large polarizability. (c) Static tilting: the octahedral rotational degree of freedom is subject to a single potential with a minimum at a ≠ 0. The resulting ionic wave function φ(a) with the lowest energy shows a single localization at the potential energy minimum. The energy spectrum is equispaced.

IUCrJ
Volume 10| Part 3| May 2023| Pages 309-320
ISSN: 2052-2525
https://doi.org/10.1107/S2052252523002208