## Main

Owing to their inherent modularity and resulting amenability to design, metal–organic materials1,2 such as metal–organic frameworks3,4 and porous coordination networks5,6 offer promise as energy-efficient physisorbents for gas separation and storage. Rigid microporous materials, which tend to exhibit fixed pore volumes and type I adsorption isotherms (Fig. 1a), have been classified as second-generation physisorbents7. A limitation of type I isotherms is that adsorption and desorption tend to occur at pressures outside the operationally relevant range, thus decreasing the working capacity8. Third- (soft, flexible frameworks characterized by stepped or S-shaped adsorption isotherms) and fourth-generation (porous materials with modifiable pore size, pore chemistry and self-switching pores) flexible metal–organic materials (FMOMs)7,9,10,11 offer more desirable type F sorption profiles (Fig. 1b). FMOMs exhibit structural transformations that can occur either between open and more open forms (Fig. 1b; type F-I) or between closed and open forms (Fig. 1b; type F-IV)12.

FMOMs are exemplified by stepped isotherms that arise when sudden switching occurs between a closed and an open phase with negligible sorption below the switching threshold pressure. Such materials are of potential utility as they offer higher working capacities for volatile gases that are normally stored in high-pressure cylinders (for example, O2, H2 and CH4) and C2H2, for which high-pressure storage is infeasible13,14,15,16,17,18,19,20. Nevertheless, nearly two decades have elapsed since the first reported switching sorbent21,22,23, and a recent review24 confirmed that fewer than 100 materials exhibit substantial flexible breathing behaviour. Among these, only 60 can be defined as switching sorbents (closed-to-open transformations)24,25,26,27,28,29,30,31,32,33,34. Rarer still are switching materials (type F-IV isotherms) with multiple steps, indicating additional transformations beyond the initial gate opening25,28,30,33. Despite the potential for enhanced working capacity in gas storage applications, FMOMs that exhibit type F-IV adsorption isotherms are relatively rare and remain to be classified by the International Union of Pure and Applied Chemistry24,35. Supplementary Table 5 shows the current benchmark switching materials. Despite the impressive uptake in some of these materials, owing to the large structural transformations associated with their switching behaviour, very few were found to exhibit recyclability with retained performance36.

Guest transport in porous materials occurs via three pathways: (1) rigid or flexible channels (Fig. 2, left); (2) pores interconnected via narrow rigid or dynamic apertures7,9,10,11 (Fig. 2, middle); and (3) diffusion between discrete cavities (Fig. 2, right). The nature of the dynamic behaviour observed in third- and fourth-generation systems has been ascribed to structural transformation through various mechanisms (for example breathing, swelling, linker rotation or subnetwork displacement)9,12. Establishing a mechanism can be a challenge as single crystals comprise many mechanically responsive unit cells and the strain associated with flexible transformations can induce crystal fracturing. Therefore, only a few FMOMs are known to exhibit single-crystal to single-crystal transformations20,33.

The concept of transient porosity must be invoked to explain guest transport in clathrates (that is, crystals with discrete voids but without connecting channels; Fig. 2, right). This was considered counter-intuitive until the prototypal example was published by Atwood et al.37 in 2002. In this seminal study, the bowl-shaped molecule p-tert-butylcalix[4]arene was shown to include a guest molecule in discrete cavities despite the absence of channels. Subsequently, other non-porous molecular materials exhibiting dynamic and cooperative guest transport were reported38,39,40,41,42,43,44,45.

Cooper et al.46 defined such porosity as being either intrinsic or extrinsic, with the former arising from cavities in the molecular building block itself and the latter being a consequence of solid-state packing. Although this definition is suitable for molecular systems, it does not easily translate to extended networks. The Kitagawa and Barbour groups have independently reported sorbate transport in FMOMs with connected pores47,48,49 or discrete voids50, the latter arising from a sorbent that has an as-synthesized phase with a channel-type structure.

Herein, we expand on the work of Barbour et al. by introducing an example of a FMOM, [Co(dpt)(1,3-bib)], 1, for which sorbate transport results from synergistic transient porosity that enables transformations between multiple non-porous phases. Specifically, 1 is a switching sorbent with non-porous, as-synthesized apohost (the guest-free framework) and gas-loaded clathrate phases. Furthermore, in addition to exhibiting a better working capacity compared with the previously reported [Co2(ndc)2(bpy)]n50, 1 exhibits switching in response to a number of different guests. Although the transformations in 1 are structurally subtle and associated with little to no strain on the framework, the switching is unambiguous and enables a working capacity that is higher than would be expected for a conventionally non-porous material. 1 also offers good recyclability and can serve as a prototypal structure for the development of future materials. In principle, this strategy can be evolved to include materials with much larger cavity sizes, to achieve a combination of high working capacity and sustained recyclability.

## Results and discussion

### Preparation and characterization of 1DMF

Solvothermal reaction of Co(NO3)2·6H2O with 2,5‐diphenylbenzene‐1,4‐dicarboxylic acid (dpt) and 1,3-bis(1H-imidazol-1-yl)benzene) (1,3-bib) in dimethylformamide (DMF) yielded diffraction-quality crystals of [Co(dpt)(1,3-bib)٠2DMF] (1DMF; Fig. 3). Single-crystal X-ray diffraction (SCXRD) showed that 1DMF crystallized in the monoclinic space group P21/n. The asymmetric unit (ASU) comprises one metal cation, one 1,3-bib ligand (anti-conformation), two independent half dpt ligands and two DMF guest molecules. One dpt ligand chelates the metal cation, whereas the second is mono-coordinate (Supplementary Fig. 1). The phenyl rings of the chelating dpt ligand were found to be disordered over two general positions with 0.74:0.26 site occupancy. The tetrahedral molecular building block is connected by the linker ligands to form a three-dimensional non-interpenetrated dmp topology net.

A Connolly map51,52 of the guest-accessible volume (using a 1.5 Å probe radius) in 1DMF indicated that at 100 K, it contains discrete solvent-filled voids of approximately 391 or 411 Å3 viewed down [100] (depending on the fragment of disorder used) (Supplementary Fig. 2). At 298 K, dpt ligands exhibit negligible disorder, with voids of 410 Å3 (Fig. 3). 1DMF is classified as a clathrate since it contains two intrinsic voids per unit cell, each accommodating four DMF molecules.

Thermogravimetric analysis confirmed that 1DMF lost all DMF guest molecules below 423 K and remained stable until framework decomposition at 603 K (Supplementary Fig. 13). Bulk-phase activation of 1DMF in air induced a colour change from purple to blue concomitant with a change in the powder X-ray diffraction (PXRD) pattern (Supplementary Figs. 910). The removal of DMF guest molecules from 1DMF resulted in a transformation to 1Hydrate. Comparison of the two structures at 100 K revealed that the previously chelating dpt carboxylate moiety became mono-coordinated, the resulting open metal site being filled by an aqua ligand (Supplementary Fig. 4). This transformation was accompanied by a reduction in the b and c axis lengths (from 14.62(3) to 12.86(2) Å and from 23.67(5) to 22.01(5) Å, respectively; Supplementary Table 1) and a 16% reduction in unit cell volume. Mapping of the guest-accessible volume showed that 1Hydrate contained discrete cavities of 42 Å3.

### Preparation and characterization of 1Apohost

To avoid the formation of 1Hydrate, a crystal of 1DMF was mounted in an environment gas cell, sealed and evacuated at 393 K overnight. A single-crystal to single-crystal transformation from 1DMF to 1Apohost (Fig. 3) was observed using SCXRD data recorded at 298 K. Although the space group was unchanged, activation induced 0.91(4) and 1.26(3) Å reduction in the b and c axes, respectively, and a 12% unit cell volume contraction (Supplementary Table 1). 1Apohost is similar to 1Hydrate in that the structural transformation arises from a change in the metal coordination environment (cobalt becoming 4-coordinate) and dpt linker rotation. We note that metal node isomerism involving coordination bond breakage is relatively rare but can play a key role in switching FMOMs53,54. The phenyl rings of the previously chelating dpt ligand were found to be disordered over two general positions with 0.54:0.46 site occupancies. However, unlike 1Hydrate, 1Apohost has no aqua ligands. Comparison of the torsion angle O1C13C14C15 in 1DMF and 1Apohost indicated that, upon activation, one of the dpt ligands had rotated by 61.0(1)° from a coplanar to a twisted orientation (Supplementary Figs. 5 and 6). Although the 1,3-bib ligand retains its anti-conformation, there is a reduction in the N–Co–N angle from 105.4(6)° in 1DMF to 101.4(8)° in 1Apohost. This combined motion reduces the void volume of 1Apohost to 84 Å3.

### Gas sorption of 1Apohost at 298 K and 1 bar

To investigate the gas-induced dynamic behaviour of 1, a series of sorption studies were conducted. A bulk sample of 1DMF was activated to afford 1Apohost; all sorption experiments used 1Apohost as the sorbent (Supplementary Fig. 11). Isotherms recorded at 298 K for CO2, C2H2, C2H4 and C2H6 showed that uptake to form a gas phase (where gas denotes the aforementioned gases) was induced by closed-to-open switching. The isotherms for C2H2, C2H4 and C2H6 exhibited steps at threshold pressures of 0.15, 0.20 and 0.24 bar, respectively (that is, type F-IV isotherms) (Fig. 4a,b). The CO2 isotherm was comparable in terms of its threshold pressure (0.3 bar), but the inflection was observed to be more gradual, corresponding to type F-III behaviour. This difference is emphasized in the first derivative of the adsorption curve (Supplementary Fig. 22), which can be contrasted with the sharper C2 gas profiles. We note that hysteresis between the adsorption and desorption branches of each isotherm was variable (Fig. 4a).

The CO2 isotherm displayed no discernible hysteresis; moderate hysteresis was observed for C2H4 and C2H6; and large hysteresis was seen for C2H2. The unusual isotherms exhibited by 1 do not conform to standard continuous isotherm models and were not conducive to accurate fitting by virial analysis (R2 < 70%) over the whole or partial loading ranges. Due to the low quality of parametrization, it was not feasible to determine physically meaningful isosteric heats of adsorption, as are conventionally reported for rigid adsorbents. Thermodynamic information on the nature of the transition was obtained from calculation of the enthalpy of gate opening (ΔHGO) from pure component data following the method of Li et al.55 (ESI, Section 7.4). ΔHGO was determined to be 25.2 kJ mol−1 for CO2, 33.7 kJ mol−1 for C2H2, 29.8 kJ mol−1 for C2H4 and 31.7 kJ mol−1 for C2H6. The similar values of ΔHGO exhibited by the C2 hydrocarbons and the lower value for CO2 help to explain the respective isotherm shapes and derivative profiles (Supplementary Fig. 28). The large enthalpy of gate opening in the presence of C2H2 is correlated with a lower threshold pressure, sharper derivative profile and greater degree of hysteresis. C2H4 and C2H6 show similar derivative profiles and intermediate threshold pressures, while CO2 shows the broadest derivative profile and highest threshold pressure, in agreement with their respective enthalpies of gate opening. The working capacities between 0.1 and 1 bar for CO2 and C2H2 at 298 K are 35.1 and 54.4 cm3 g−1, respectively. Sustained recyclability of 1Apohost was confirmed over 50 cycles using CO2 at 298 K in the range 0–30 bar (Supplementary Fig. 26).

### Structural insight into 1ʹCO2

To understand the flexible behaviour of 1Apohost induced by CO2, a gas-loading in situ SCXRD experiment was performed. After backfilling the environment gas cell with CO2 to the maximum pressure recorded for the corresponding isotherm (1 bar, at 298 K), the system was left to equilibrate for 3 h before being sealed (see Supplementary Information for details). SCXRD data were then recorded. Conversion of 1Apohost to CO2 occurred with an increase in the b and c axes (0.65(3) and 0.44(1) Å, respectively) and a 7% increase in the unit cell volume (Supplementary Table 1), resulting in discrete voids of 360 Å3. This transformation can once again be attributed to rotation and chelation of the dpt ligand (Supplementary Figs. 7 and 8). The 1,3-bib N–Co–N angle increased to 104.6(9)°. Although the CO2 guest could not be modelled crystallographically, the residual electron density analysis, as implemented by the SQUEEZE56 routine of PLATON57, indicated the presence of half a CO2 molecule per ASU.

### Cryogenic gas sorption isotherms of 1Apohost

Low-temperature isotherms (77, 195 and 189 K) were recorded using N2, CO2 and C2H2 to probe the phase behaviour of 1Apohost over a broad P/P0 (partial pressure) range. The 1Apohost to gas transition for CO2 occurred at a very low P/P0 (a similar transformation was also observed for N2 at 77 K; Supplementary Figs. 15 and 40) and both the CO2 and C2H2 isotherms exhibited additional steps (Supplementary Figs. 16 and 17). Examination of the isotherms using log plots established that the CO2 isotherm had three distinct inflections (Fig. 5a), whereas the C2H2 isotherm had two (Fig. 5c). In the CO2 isotherm, adsorption occurred after a step that we attribute to transformation of 1Apohost into CO2 with a threshold pressure of ~0.8 mbar (that is, equivalent to that observed at 298 K). A minor step (CO2 to 1ʹʹCO2; ~6.7 mbar) and a major step (1ʹʹCO2 to 1ʹʹʹCO2; ~525 mbar) were also observed. In the case of C2H2 adsorption, transformation of 1Apohost to 1ʹʹC2H2 occurred at ~0.1 mbar. An additional inflection was observed at ~2.4 mbar, corresponding to a transformation from 1ʹʹC2H2 to 1ʹʹʹC2H2. These multi-step isotherms can be classified as type F-IVm24.

### In situ PXRD characterization

Concurrent in situ PXRD data (selected patterns are presented in Fig. 5b,d; for additional patterns, see Supplementary Figs. 2934 and 41) were recorded during the 195 K CO2 and 189 K C2H2 sorption experiments and verified that the bulk-phase pattern of 1Apohost at each temperature was consistent with the calculated PXRD pattern of 1Apohost obtained from the SCXRD data. Upon exposure to 0.8 mbar of CO2, 1Apohost underwent a transformation to CO2 with a plateau at 3.7 mbar. Compared with 1Apohost, the PXRD pattern showed that most peaks had shifted towards a lower 2θ (consistent with unit cell expansion), some had disappeared (for example, 2θ = 24.7°) and new peaks had appeared (2θ = 24.3 and 25.5°). Furthermore, the experimentally obtained pattern at 3.7 mbar matched well with that generated from the SCXRD data (1 bar CO2 at 298 K), validating the formation of CO2. Progressive CO2 gas loading resulted in PXRD peaks shifting to lower 2θ positions. At a loading of 32 mbar, additional small peaks were observed at 13.4 and 29.8°. The lack of statistically significant additional peaks suggests that a minor structural change occurred during gas sorption to form 1ʹʹCO2.

Unit cell parameters from the Le Bail profile fitting demonstrated a progressive expansion of all three cell parameters and the unit cell volume (Supplementary Figs. 3539 and Supplementary Table 4). A comparison of the pattern obtained for 1ʹʹCO2 with that of 1DMF (Supplementary Fig. 32) indicated that the cavities of 1ʹʹCO2 resemble those of 1DMF.

Further loading resulted in a large step in the 195 K CO2 isotherm at 530 mbar (1ʹʹʹCO2). The PXRD pattern recorded at 960 mbar revealed the disappearance of two peaks (2θ = 15.3 and 16.0°) and the appearance of new peaks at 15.6, 18.0 and 19.3°. Although this phase was unlike the previous phases (Supplementary Fig. 31 and 33), this transformation was reversible, as evidenced by conversion to 1ʹʹCO2 and CO2 upon desorption.

In the case of C2H2, transformation of 1Apohost to 1ʹʹC2H2 (all PXRD peaks shifted to lower 2θ) occurred with a plateau at 2.4 mbar (Fig. 5d, yellow). This phase matched the PXRD of 1ʹʹCO2. Additional C2H2 loading induced peak shifting to lower 2θ values, consistent with unit cell expansion and transformation of 1ʹʹC2H2 to 1ʹʹʹC2H2 with saturation at 734 mbar. 1ʹʹʹCO2 and 1ʹʹʹC2H2 are not isostructural. Owing to the increased experimental single-point pore volume and expanded cell parameters (Supplementary Fig. 31 and Supplementary Table 3) for 1ʹʹʹCO2, we consider that the initially discrete cavities merge to form larger voids that accommodate more CO2 molecules.

### Structural insight into 1ʹʹCO2

Although the high-pressure CO2 294 K gas sorption isotherm (Supplementary Fig. 25) for 1 only shows the first transition from 1Apohost to CO2, we attempted to obtain the 1ʹʹCO2 phase crystallographically by exposing a crystal of 1Apohost to the maximum cylinder pressure attainable for CO2 at 298 K (56 bar). After allowing the crystal to equilibrate for 3 h, the environment cell was sealed and SCXRD data were then recorded. As evidenced by the 195 K CO2 isotherm and corresponding in situ PXRD, the conversion of CO2 to 1ʹʹCO2 occurs with a minor increase in the cell dimensions. The most notable parameter change is the unit cell volume, which increases by 157 Å3, resulting in discrete voids of 373 Å3 that appear to be expanding towards one another, hinting at the potential nature of guest transport (Fig. 3). As with CO2, the CO2 guest could not be reliably modelled crystallographically in 1ʹʹCO2. Residual electron density analysis indicated the presence of 1.4 molecules of CO2 per ASU. The calculated PXRD pattern generated from the structure of 1ʹʹCO2 is in good agreement with the bulk-phase pattern of 1ʹʹCO2 at 195 K CO2 (Supplementary Fig. 34).

### Computational insight into the mechanism of guest transport

To gain further insight into the experimentally observed transient diffusion mechanism(s), the spatial relationship between isolated cavities in the two crystal structures, CO2 and 1ʹʹCO2, was examined computationally. These experimentally obtained crystal forms have the same structural motifs, suggesting that the mechanism is isomorphic. It was found that each cavity–cavity geometry occurs with two neighbouring orientations; cavities are either diagonally adjacent, as shown in Fig. 3 for 1DMF, CO2 and 1ʹʹCO2, or are vertically stacked in a single direction (see the far right frame of Fig. 2). This strongly suggests that diffusion within these materials occurs via these pathways. Diagonally adjacent cavities are connected by narrow apertures that are sufficiently constricted to block transport. Guest transport appears unfeasible without the accommodating structural transformations highlighted in Fig. 6. Stacked voids form a corridor divided by dpt linkers (Fig. 6), which section them into discrete cavities.

To probe the viability of transport through these barriers, a rigid CO2 structure was loaded with a single CO2 molecule near the initially blocked channel. These mono-loaded structures were subjected to relaxation using density functional theory, implemented by the CP2K simulation package, to obtain an optimized initial position58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78. The position of the sorbate was then adjusted towards the barrier and a new relaxation was performed, wherein a single sorbate atom had the coordinate in the direction of the barrier held constant, relaxing the crystal to accommodate it. This adjustment was performed until the CO2 molecule had traversed the barrier into the adjacent cavity. The trajectory maximum barrier heights were found to represent only a small multiple of ambient thermal energy comparable to the CO2 sorption energy. A more detailed description of this methodology is included in the section ‘Computational Modelling’ of the Supplementary Information, where the collective diffusion coordinate is demonstrated explicitly via animations.

In the case of diagonally adjacent cavities, transport was characterized by small-scale shifting and ring rotation of proximal functional groups, which reverted to their initial configurations once they were no longer in the vicinity of the sorbate. The largest change in energy for the inter-cavity transport measured was 4.8 kJ mol−1, a barrier substantially lower than the enthalpy of gate opening for CO2HGO = 25.2 kJ mol−1) and less than twice the ambient thermal energy at 298 K. For stacked cavities, twisting of the dpt ligand occurs to facilitate transport, involving a rotation of the Co–dpt–Co axis, as well as a benzene pendant ring. Animation of the transport trajectory is included in the section ‘Computational Modelling’ of the Supplementary Information. Notably, the same linker rotates outward during the 1Apohost to CO2 transition, causing pairs of small cavities observed in a single unit cell of 1Apohost to merge into the two larger guest-filled cavities observed in a unit cell of CO2 (Fig. 3). Consequent to the gross mobility required, a higher energy barrier of 21.9 kJ mol−1 (less than nine times the ambient thermal energy) was observed. This barrier is of a higher energy than the diagonally adjacent cavity transport that is likely to be the most favourable diffusion mechanism. To probe the dynamic motion between cavities, a single cavity in an otherwise vacant CO2 crystal structure was loaded with 12 CO2 molecules via Grand Canonical Monte Carlo simulation and subjected to density functional molecular dynamics (DFTMD) simulations in the canonical ensemble at 473 and 623 K. Less than 1 ps at both temperatures produced thermal diffusion between diagonally adjacent cavities in a manner consistent with the more energetically favourable pathway described above. Animations of these molecular trajectories are provided as Supplementary Videos 16.

## Conclusion

1Apohost exhibits dmp topology with zero-dimensional spherical cavities and is unlike previous switching FMOMs, most of which feature gas-induced transformations requiring extreme network contortion9 or displacement9,12. Specifically, the type F-IVm sorption behaviour exhibited by 1Apohost arises from transient porosity that enables gas-induced intra-network distortion and transformations to phases with higher gas uptakes. We have shown an example of type F-IV adsorption behaviour in a seemingly non-porous coordination network that is a clathrate in each of four structurally characterized phases. These gas-induced transformations combine recyclability, optimal working capacity and high uptake without the need for extreme structural transformations. Sorbate diffusion between isolated cavities can take place along two discrete potential vectors, with travel through diagonally adjacent cells as the likely dominant mechanism. Small-scale collective molecular motions and ring rotation create a path through an otherwise inaccessible cavity. The second transport vector involves rotation of the dpt linker, with the more well-defined mechanism lending itself well to potential tuning of gate opening in future analogues. Furthermore, as the motion observed in this material arises from cooperative movement ascribed to both ligands, crystal engineering design principles could be used to iteratively expand the cavity and, in turn, the loading capacity while preserving the phenomenon of transient porosity.

## Methods

### Materials

Commercially available starting materials and solvents were purchased from Sigma–Aldrich, Merck and Fluorochem. All reactions were monitored using aluminium-backed silica gel Merck 60 F254 TLC plates and visualized using ultraviolet irradiation. All chemicals were used as received without additional purification.

### Synthesis of 1,3-bib

The synthesis of 1,3-bib was carried out in a single step, according to a previously reported procedure with minor modifications79. 1,3-dibromobenzene (10.0 g; 42.8 mol; 1.0 equiv.), imidazole (14.5 g; 213.0 mmol; 5.0 equiv.), CuI (1.63 g; 8.6 mmol; 20 mol%) and K2CO3 (29.4 g; 213.0 mmol; 5.0 equiv.) were all added to anhydrous DMF (150 ml) under an inert N2 atmosphere. The resulting reaction mixture was heated to reflux under an inert atmosphere for 72 h. After cooling to room temperature, the mixture was filtered. The filtered residue was washed with dichloromethane (2 × 150 ml) and the filtrate was transferred to a large separating funnel. The organic layer was washed with water (3 × 250 ml), separated and dried over MgSO4. The organic layer was concentrated under reduced pressure and the resulting solid material was finally purified by trituration from a dichloromethane/hexane mixture. The resulting 1,3-bib was isolated as a white solid (8.41 g; 94%).

### Synthesis of dpt

The synthesis of dpt was carried out in two steps, according to a previously reported procedure80. In step 1, 20 ml deionized water was degassed for 30 min using N2. 2,5-dibromo-p-xylene (2.00 g; 7.58 mmol; 1.0 equiv.), phenyl boronic acid (2.03 g; 16.7 mmol; 2.2 equiv.), Pd(OAc)2 (3.40 mg; 0.2 mol%), K2CO3 (5.24 g; 37.9 mmol; 5.0 equiv.) and n-Bu4NBr (4.87 g; 15.2 mmol; 2.0 equiv.) were all added. The resulting suspension was heated to 343 K for 4 h and stirred vigorously under an inert atmosphere. After cooling to room temperature, the reaction mixture was diluted with water (150 ml) and extracted with hexane. The organic phase was dried over MgSO4 and concentrated under reduced pressure to yield 2′,5′-dimethyl-p-terphenyl as a white solid (1.88 g; 96%). In step 2, 2′,5′-dimethyl-p-terphenyl (700 mg; 2.71 mmol; 1.0 equiv.) was added to 20 ml pyridine. Then, 2.2 g KMnO4 in 2.0 ml H2O was added and the reaction mixture was heated to reflux for 2 h. After reaching reflux, every 30 min, an additional 1.0 g KMnO4 in 2.0 ml H2O was added (a total of four times). After 6 h at reflux, a final 10 ml water was added to the reaction mixture, which was allowed to reflux overnight. The MnO2 precipitate was hot filtered from the reaction mixture and washed with near-boiling water (100 ml). The filtrate was carefully acidified using concentrated HCl, precipitating the dpt product as a white solid, which was collected by filtration, washed with 0.2 M HCl and finally dried in a 378 K oven overnight (732 mg; 85%).

### Crystallization

Crystals of 1DMF were grown solvothermally by combining 0.3 mmol (63.0 mg) dpt, 0.3 mmol (95.0 mg) 1,3-bib and 0.3 mmol (87.0 mg) cobalt nitrate hexahydrate in 10 ml DMF and heating at 393 K. Purple block crystals were obtained after 2 d.

### SCXRD

SCXRD data were recorded on a Bruker SMART APEX II81 and a Bruker QUEST APEX III equipped with an Mo or Cu sealed tube source. Both diffractometers employ an Oxford Cryosystems 700 Plus cryostat to control the temperature of the sample. Data reduction was carried out by means of standard procedures using the Bruker software package SAINT82. Absorption corrections and correction of other systematic errors were carried out using SADABS83. All structures were solved by direct methods using SHELXS-16 and refined using SHELXL-16 (ref. 84). X-Seed85 was used as the graphical interface for the SHELX program suite. Solvent-accessible voids can be visualized by calculating Connolly surfaces using MS-ROLL51,52, another program incorporated into X-Seed. Hydrogen atoms were placed in calculated positions using riding models.

### Activation procedure

A suitable crystal of the as-synthesized material was selected and glued onto a glass fibre with cyanoacrylate glue. The glass fibre was then inserted into an environmental gas cell (EGC), which consisted of a 0.3 mm Lindemann capillary secured to a steel nut with epoxy that was screwed into a valve body. The EGC allows for evacuation/pressurization of the immediate crystal environment and transportation to a diffractometer. The EGC was then connected to a Pfeiffer HiCube vacuum pump (pressure = ~3 × 10−3 mbar) and immersed in oil, which was heated to 393 K overnight. The valve was then closed and the EGC was removed from the activation apparatus. The evacuated crystal in an EGC was mounted onto a conventional goniometer and SCXRD data were recorded at 298 K.

The activated crystal in the EGC was attached to a CO2 cylinder via a gas manifold (regulator). The system was pressurized to 1 bar and left to equilibrate under static pressure for 3 h (multiple equilibration times were tested and this was found to be the best), after which the EGC was closed and loaded onto the diffractometer.

### PXRD

PXRD experiments were conducted using microcrystalline samples on a PANalytical Empyrean diffractometer (40 kV; 40 mA; CuKα1,2 λ = 1.5418 Å) in Bragg–Brentano geometry. A scan speed of 0.044509° s−1 (2.6° min−1), with a step size of 0.0262° in 2θ, was used at room temperature with a range of 5° < 2θ < 40°. Powder samples were evenly distributed on a zero-background holder after being ground with a mortar and pestle to minimize the effects of preferred orientation. Data analysis was carried out using X’Pert HighScore Plus86 (version 2.2e). Powder patterns were simulated from SCXRD structures using Mercury87.

### Thermogravimetric analysis

Thermogravimetric analysis was performed under N2 using a TA Instruments Q50 system. A sample was loaded into an aluminium sample pan and heated at 283 K min−1 from room temperature to 773 K.

### Differential scanning calorimetry

Differential scanning calorimetry was carried out using a TA Instruments Q2000 differential scanning calorimeter. Samples were prepared by crimping the sample pan and lid (a pin hole was placed in the lid to prevent pressure build-up). A reference pan was prepared in the same manner for each analysis. Analyses were generally carried out in the temperature range 253–523 K and a general experimental procedure consisted of two heating/cooling cycles while the heat flow into or out of the sample, relative to the reference, was measured as a function of time and temperature under a controlled atmosphere. N2 gas flowing at a rate of 50 ml min−1 was used to purge the furnace. The resulting thermograms were analysed using TA Instruments’ Universal Analysis program and Supplementary Fig. 14 was prepared with Microsoft Excel.

### Gas sorption isotherm measurements

Before performing the gas sorption experiments, a freshly prepared sample of 1DMF was placed in a quartz tube and degassed under high vacuum using a Smart VacPrep instrument at 343 K for 24 h to remove any remaining solvent molecules and yield 1Apohost. Isotherms were measured using a Micromeritics 3Flex sorption analyser. Gases were used as obtained from BOC Gases (Ireland), with the following certified purities: research-grade He (99.999%), CO2 (99.995%), C2H2 (98.5%), C2H4 (99.92%), C2H6 (99.0%) and N2 (99.998%). Bath temperatures of 77 and 195 K were maintained using liquid nitrogen and a dry ice–acetone slurry, respectively. A Julabo ME version 2 temperature controller was used to maintain bath temperatures in the 273 and 298 K experiments. Samples were activated between successive experiments overnight or for a minimum of 5 h at 343 K under high vacuum. High-pressure CO2 sorption experiments were performed using a Hiden Isochema XEMIS microbalance. Activated samples of 1Apohost were further outgassed under secondary vacuum for 3 h in situ before isotherms were run. Excess adsorption and desorption profiles were obtained after applying buoyancy correction using the crystallographically determined density of 1Apohost. Temperatures were maintained at 273 and 294 K using a Grant LT Ecocool 150 temperature controller. Equilibration was determined by a cut-off criterion of agreement within 0.01% of a pressure reading, with rolling averages of the previous ten pressure readings each collected after allowing the equilibration interval (10 s for the 195 K CO2 experiments and 77 K N2 experiments and 30 s for the 273 and 298 K experiments) to elapse. Equilibration data were recorded for the full range of pressure dosing during the 298 K CO2 and C2H2 experiments, with a sampling interval of around two pressure readings per second.

### Single-point pore volumes

Indicative single-point pore volumes were determined experimentally using the MicroActive software suite under the assumption of approximate validity of the Gurvich rule88,89, wherein the structural transformations follow a state approaching saturation of the preceding phase during 195 K CO2 adsorption experiments, as described in equation (1), where νpore. is the pore volume, $$n_{{\rm{CO}}_{2}}^{{\rm{Ads}}}$$ is the quantity of gaseous CO2 adsorbed, as determined at standard temperature and pressure, and $$\rho _{{\rm{CO}}_{2}}^{{\rm{Liq}}}$$ Is the density of liquid CO2.

$$\nu _{{{{\mathrm{pore}}}}} = \frac{{n_{{\rm{CO}}_{2}}^{{\rm{Ads}}}}}{{\rho _{{\rm{CO}}_{2}}^{{\rm{Liq}}}}}$$
(1)

The determined volumes are presented with 5% error bars (Supplementary Table 3) and show reasonable agreement with the assignment of phases based on in situ PXRD, as well as SCXRD-determined solvent-accessible volumes.

### Molar enthalpy of gate opening

The molar enthalpy of gate opening (ΔHGO) was calculated from the gate-opening pressures (PGO) determined from pure component isotherms at 273 and 298 K, using the Clausius–Clapeyron equation (R = the gas constant, T = absolute temperature) as described in equation (2). Enthalpies were found to be correlated with molar enthalpies of vaporization, in agreement with Li et al.55. Error bars represent 5% margins in Supplementary Fig. 27.

$${\Delta} H_{{\rm{GO}}} = {\rm{RT}}^2\left( {\frac{{\partial \ln P_{{\rm{GO}}}}}{{\partial T}}} \right)$$
(2)

### In situ PXRD

In situ coincident PXRD measurements were conducted on a Rigaku SmartLab with CuKα radiation, which was synchronized to a BELSORP-18PLUS volumetric adsorption instrument (MicrotracBEL). A helium-based cryosystem was connected to the sorption equipment to control the temperature range. The as-synthesized sample was soaked in MeOH for 3 d and then activated at 343 K under vacuum overnight using a copper plate holder. The activated sample of ~70 mg was transferred to the sorption instrument and treated again under vacuum at 353 K for 2 h. The second activation was performed to remove any adsorbed moisture during transfer. This is an essential step as the sample adsorbs water from the atmosphere. A CO2 sorption experiment was carried out up to 100 kPa at 195 K. In situ PXRD patterns were measured simultaneously at each equilibrium point of the adsorption and desorption isotherm. In addition to CO2, in situ PXRD patterns were measured at each equilibrium point of the adsorption isotherm for N2 at 77 K and C2H2 at 189 K. Powder patterns obtained from the in situ variable pressure PXRD experiment of 1Apohost at different CO2 adsorption loadings were indexed using the program EXPO2014 (refs. 90,91).

### Computational modelling

Computational modelling of the 1 crystal phases using electronic structure methods was undertaken via density function theory (DFT). Crystal structures were treated to full periodic relaxation using MOLOPT basis sets at the triple zeta level of theory and Perdew–Burke–Ernzerhof pseudopotentials. Dispersion was treated using a pair potential with the DFT-D3 correction of Grimme et al. These were implemented using the CP2K simulation package58,59,60,61,62,63,64,65,66,67,68,69,77,78. DFTMD simulations were implemented similarly using the canonical ensemble with a fixed particle number, volume and temperature (NVT) with a 0.5 fs timestep. The chosen thermostat was Nosé–Hoover, using a time constant of 100 fs. Classical modelling of CO2 sorption in 1 was undertaken to examine the sorptive behaviour and uptakes in these structures. These simulations involved Monte Carlo simulation of sorbates within a rigid crystal scaffold, as employed by the massively parallel Monte Carlo code92. Intermolecular forces were parametrized using the Universal Force Field93, the extended charge equilibration method94 and Thole–Applequist-type point polarizabilities95,96 taken from the work of van Duijnen and Swart97 to model the van der Waals, electrostatic and induced dipole effects, respectively. CO2-PHAST*98 was used for the sorbate parameters. X-ray crystal structures of 1Apohost, CO2 and 1ʹʹCO2 were relaxed using DFT, as described above. For all three, there was only minor alteration in atomic positions after optimization, providing stable optimized conformations even for the open CO2 and 1ʹʹCO2 structures. Classical simulation in the relaxed structures confirmed that they retained porosity, loaded sorbate into discrete pockets and supported CO2 uptakes equal to, or in excess of, the loadings reached in each structure to induce the next open phase as reported.

The potential for transient transport between neighbouring isolated cavities was examined along two potential pathways in the CO2 structure. An initial position was obtained from canonical Monte Carlo runs of CO2 sorption. A single sorbate position settled near the posited transport window was selected from each of the trajectories and settled into the local minima via simulated annealing. A single unit cell was then taken to probe transport between diagonally adjacent voids as each CO2 unit cell contains two cavities with that relative orientation. For the stacked cavities, a unit cell was replicated along the c axis to create a two-unit cell system with a single sorbate molecule (two cells were used as the stacked relative orientation is not observed within a single unit cell). These systems were then fully relaxed using CP2K. Using these relaxed initial positions, a series of sequential relaxations were performed wherein the optimized structure was modified, shifting the sorbate in the direction of the postulated transport channel, and re-relaxed subject to the constraint that a single sorbate oxygen atom was constrained in one direction (the b axis for the diagonally adjacent cavity and the a axis for the stacked cavity). This forced proximity to the channel while allowing the atom to shift in the remaining two dimensions to find the optimal route through. No further constraints were put on the other sorbate atoms or the crystal, permitting sorbate orientation and geometry to relax along with the structure. The constrained optimized structures were then taken and the CO2 was shifted further along the channel and re-relaxed. These iterations were repeated until a trajectory traversing each channel was obtained. Having determined the pathways, the energies of each sequential configuration were then compared with the initial position energy to determine the energy barrier as reported in the ‘Computational insight into the mechanism of guest transport’ section of the main text.

Dynamic molecular motion between cavities in the CO2 structure was modelled using a single unit cell with one cavity loaded with 12 CO2 molecules and the second cavity left empty. Initial positions of sorbate occupants were taken from grand canonical Monte Carlo simulation. The single-cavity-loaded structure was subjected to DFTMD simulations allowing all atomic positions to fluctuate at 473 and 623 K. The sorbate loading differential between cavities was found to provide sufficient motive impetus for sorbate molecules to diffuse through the barrier between diagonally adjacent cavities. Simulation across both temperatures reproduced the more energetically favourable mechanism of diffusion via rotation of the dpt linker.