Graph theoretical analysis as an aid in the elucidation of structure-property relations of perovskite materials.

Halide perovskite materials are intensively studied with respect to their optoelectronic properties, in the quest for novel stable and reliable solar cell materials. Computational methods complement experimental data adequately but the associated computational costs and the extremely large number of potential materials, call for shortcuts that can narrow down our search, in the form of trustable structure-property correlations. Here, we employ graph theory to extract quantitative descriptors of the crystal structure, and correlate them with physical properties. In particular, we use atom-atom proximity to define adjacency relations and to map the structure of selected halide perovskite compounds to graphs preserving their topology. These graphs are processed according to the concept of equitable partition or, alternatively, on the basis of chemical composition, to derive the corresponding quotient graphs. We calculate the spectra of all these graphs and compute an appropriately defined compression ratio that compares the original graph with its equitable partition and quantifies the symmetry and regularity of the former. Important spectral information as the Perron-Frobenius and Fiedler eigenvalues, as well as the compression ratio, are compared with measured physical properties and interesting correlations come to the fore. These observations may pave the way to novel structure-property relation schemes allowing the prediction of properties and, ideally, identify the best materials for optoelectronic devices. [ABSTRACT FROM AUTHOR]