Columnar shifts as symmetry-breaking degrees of freedom in molecular perovskites

We introduce columnar shifts-collective rigid-body translations-as a structural degree of freedom relevant to the phase behaviour of molecular perovskites ABX 3 (X = molecular anion). Like the well-known octahedral tilts of conventional perovskites, shifts also preserve the octahedral coordination geometry of the B-site cation in molecular perovskites, and so are predisposed to influencing the low-energy dynamics and displacive phase transitions of these topical systems. We present a qualitative overview of the interplay between shift activation and crystal symmetry breaking, and introduce a generalised terminology to allow characterisation of simple shift distortions, drawing analogy to the "Glazer notation" for octahedral tilts. We apply our approach to the interpretation of a representative selection of azide and formate perovskite structures, and discuss the implications for functional exploitation of shift degrees of freedom in negative thermal expansion materials and hybrid ferroelectrics. Columnar shifts are degrees of freedom in molecular perovskites of relevance to phase transitions, improper ferroelectricity, and negative thermal expansion.