Using first-principles calculations, we show that CsBX$_3$ halides with B=Sn or Pb undergo octahedral rotation distortions, while for B=Ge and Si, they undergo a ferro-electric rhombohedral distortion accompanied by a rhombohedral stretching of the lattice. We show that these are mutually exclusive at their equilibrium volume although different distortions may occur as function of lattice expansion. The choice between the two distortion modes is in part governed by the Goldschmidt tolerance factor. However, another factor explaining the difference between Sn and Pb compared with Ge and Si is the stronger lone-pair character of Ge and Si when forced to be divalent as is the case in these structures. The lone-pair chemistry is related to the off-centering. While the Si-based compounds have not yet been synthesized, the Ge compounds have been established experimentally. As a final test of the importance of the tolerance factor we consider RbGeX$_3$, which has smaller tolerance factor than the corresponding CsGeX$_3$ because Rb is smaller than Cs. We find that it can lower its energy by both rotations or rhombohedral off-centering distortions but the latter lower the energy slightly more efficiently.
A Unified Description of Electron-Phonon Coupling and Ion Migration in Metal Halide Perovskites
Nanjing University of Posts and Telecommunications（南京邮电大学）；The University of Queensland（昆士兰大学）；University of Cambridge（剑桥大学）；Université catholique de Louvain（天主教鲁汶大学）；Xi’an Jiaotong University（西安交通大学）；Southeast University（东南大学）
Coupled Structural and Electronic Requirements in Alpha-FASnI3 Imposed by the Sn(II) Lone Pair
Laboratory of Computational Chemistry and Biochemistry, Institute of Chemical Sciences and Engineering, Swiss Federal Institute of Technology (EPFL)（洛桑联邦理工学院化学科学与工程研究所计算化学与生物化学实验室）
Band-like Carriers in a Soft, Anharmonic Lattice: Lead-Halide Perovskites
Pohang Accelerator Laboratory, POSTECH（浦项加速器实验室，浦项科技大学）；YUHS-KRIBB Medical Convergence Research Institute, College of Medicine, Yonsei University（延世大学医学院佑山-韩国生命科学研究院医学融合研究所）；Department of Physics, University of Seoul（首尔大学物理系）；Global Institute of Future Technology, Shanghai Jiao Tong University（上海交通大学未来技术学院）
Operando Raman probing of mode selective electron phonon coupling in two dimensional halide perovskites
Institut national de la recherche scientifique（国家科学研究学院）；Eindhoven University of Technology（埃因霍温理工大学）；CNR NANOTEC, c/o Department of Chemistry, University of Bari（巴里大学化学系附属意大利国家研究委员会纳米技术研究所）；Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente（特温特大学科学与技术学院及MESA+纳米技术研究所）
Ligand-Controlled Phonon Dynamics in CsPbBr3 Nanocrystals Revealed by Machine-Learned Interatomic Potentials
Georgia Institute of Technology（佐治亚理工学院）；Queens College, City University of New York（纽约市立大学皇后学院）；The Graduate Center, City University of New York（纽约市立大学研究生中心）
