Understanding structural distortions in hybrid layered perovskites with the <i>n</i> = 1 Ruddlesden–Popper structure

A symmetry mode analysis yields 47 symmetrically distinct patterns of octahedral tilting in hybrid organic-inorganic layered perovskites that adopt the n = 1 Ruddlesden-Popper (RP) structure. The crystal structures of compounds belonging to this family are compared with the predictions of the symmetry analysis. Approximately 88% of the 140 unique structures have symmetries that agree with those expected based on octahedral tilting alone, while the remaining compounds have additional structural features that further lower the symmetry, such as asymmetric packing of bulky organic cations, distortions of metal-centered octahedra or a shift of the inorganic layers that deviates from the a/2 + b/2 shift associated with the RP structure. The structures of real compounds are heterogeneously distributed amongst the various tilt systems, with only 9 of the 47 tilt systems represented. No examples of in-phase ψ-tilts about the a and/or b axes of the undistorted parent structure were found, while at the other extreme ∼66% of the known structures possess a combination of out-of-phase φ-tilts about the a and/or b axes and θ-tilts (rotations) about the c axis. The latter combination leads to favorable hydrogen bonding interactions that accommodate the chemically inequivalent halide ions within the inorganic layers. In some compounds, primarily those that contain either Pb²⁺ or Sn²⁺, favorable hydrogen bonding interactions can also be achieved by distortions of the octahedra in combination with θ-tilts.