Cluster approach for the density functional theory study of organic cation vibrations in hybrid halide post-perovskite 3-cyanopyridinium lead tribromide

Internal vibrations of organic cations in halide perovskites and their analogues could be used to study the crystal structure of these novel semiconductor materials. In this work, we have studied the vibration properties of the 3-cyanopyridinium (3cp⁺ = [3-CN-C5H5NH]⁺) cation in the hybrid organic–inorganic halide post-perovskite (3cp)PbBr₃. For DFT modeling of the experimental Raman spectrum, we have constructed three different models: free cation, minimal stoichiometric cluster and nanocluster. Calculations of a free cation adequately describe most of the internal vibrations. To describe high-wavenumber hydrogen stretching vibrations, and first of all N–H vibrations, it is necessary to use sufficiently large clusters. We show in the cluster approach for crystal field description that it is necessary to include in the cluster not only halogens but also their nearest environment. In this case, agreement with experiment is reached, and further considerations can be put forward about the strength of the hydrogen bond and its role in stabilising the crystal.