Zeolitic Imidazolate Frameworks (ZIFs) represent a thriving subclass of metal–organic frameworks (MOFs) owing to the large variety of their topologies, of which some of them are common with zeolites, and the ability to modulate the chemistry of their frameworks as well as the hydrophobicity/hydrophilicity balance, making them perfect examples of the isoreticular chemistry concept. One peculiar structural feature of ZIFs is their potential for structural transitions by rotation (or swing) of their linkers under external stimuli (guest adsorption, mechanical constraints, etc.). This singular characteristic, often denominated “swing effect” or “gate opening”, is related to flexible ZIFs. Our study focuses on the influence of the functional group (−CH3, −Cl, −Br) borne in position 2 by the imidazolate linker on the flexible/stiff nature of three isoreticular ZIFs with SOD topology. In the first part, we report the structures of ZIF-8_Cl and ZIF-8_Br, two halogenated analogs of the well-known ZIF-8 (herein named ZIF-8_CH3), thanks to synergistic contributions of powder X-ray diffraction and 13C MAS NMR spectroscopy. In both cases, a disorder of the linker is noted and characterized by two quasi-equal occupancies of the two linker subsets in the asymmetric unit. Experimental nitrogen sorption measurements, performed at 77 K for the three isoreticular ZIFs, combined with first-principles molecular dynamics simulations bring to light the flexibility of ZIF-8_CH3 and ZIF-8_Cl and the stiffness of ZIF-8_Br.