Predicting Distortion Magnitudes in Prussian Blue Analogues

Based on simple electrostatic and harmonic potential considerations, we derive a straightforward expression linking the composition of a Prussian blue analogue (PBA) to its propensity to undergo collective structural distortions. We demonstrate the existence of a threshold value, below which PBAs are undistorted, and above which PBAs distort by a degree that is controlled by a geometric tolerance factor. Our analysis rationalises the presence, absence, and magnitude of distortions in a wide range of PBAs.