Fig. 5: Characterisation of MMF crystal structures by principal component analysis based on interatomic distances in Pd^II-macrocycles.

a Internuclear distances (d₁–d₆) of six atomic pairs (N/C···Cl) used as variables. b PCA score plot of 50 MMF crystal structures with various effectors (variance; PC1 = 68%, PC2 = 29%). Typical structures are labelled with the accommodated effectors, and all structures are categorised into three clusters I–III. c The characteristics of three structural clusters: the void volume in the unit-cell, interactions around allosteric sites, and effectors accommodated. The pink lines in (c) represent atom pairs that are close enough to interact, while the grey lines represent unbound atom pairs. The pink arrows indicate structural misalignment due to specific interactions with effector molecules in each cluster. All seven effectors in cluster II can also afford cluster III, which is generally the most stable structure. The molecules enclosed by the rectangular dashed box in (c) are solid effectors housed in the solution. For solid effectors, the crystal structures obtained in 1,2,3,4-tetrahydronaphthalene solutions were used for PCA analysis.