Small practical cluster models for perovskites based on the similarity criterion of central location environment and their applications†
Developing universal theoretical models for perovskites (often denoted as ABX3) can contribute to the rational design of novel perovskite photovoltaic materials. However, few models can be successfully applied to study the intrinsic electronic structure due to the poor accuracy and unaffordable computational cost. Herein, we report the innovative construction of small practical cluster models through the similarity criterion of the central location environment, which retains only the central A-site as the original cation while the others are substituted by Cs to keep the clusters electrically neutral. The central cation has a chemical environment similar to that of the bulk perovskite. The binding energy between A and the BX framework, geometric structures (B–X distances and B–X–B angles), and the electronic structures (the gap and the spatial distribution of HOMO and LUMO, electron distribution) of these clusters have been investigated and compared with the corresponding properties of bulk materials. The results suggest that the cluster model with twelve B-atoms suitably describes these properties. The geometric structures and gaps are closer to the bulk situations than the quasi-one-dimensional and quasi-two-dimensional cluster models with all-primitive cations, respectively. Other organic cations, such as NH3(CH2)nCH3 (n = 1, 2, and 3 for EA, PA, and BA, respectively), and (NH2)2CH (FA) can, therefore, mimic perovskite materials. Clusters with different sizes of A indicate that PA and BA will distort the quasi-cubic structures, which is consistent with the judgment of the tolerance factor of bulk materials. The reliable cluster model provides the research foundation for some basic issues of perovskites, such as vibrational spectroscopy and hydrogen bonding strength, to gain detailed insight into the interactions between A and the BX framework.