Cooperative CO2 adsorption mechanism in a perfluorinated CeIV-based metal organic framework

Adsorbents able to uptake large amounts of gases within a narrow range of pressure, i.e., phase-change adsorbents, are emerging as highly interesting systems to achieve excellent gas separation performances with little energy input for regeneration. A recently discovered phase-change metal–organic framework (MOF) adsorbent is F4_MIL-140A(Ce), based on CeIV and tetrafluoroterephthalate. This MOF displays a non-hysteretic step-shaped CO2 adsorption isotherm, reaching saturation in conditions of temperature and pressure compatible with real life application in post-combustion carbon capture, biogas upgrading and acetylene purification. Such peculiar behaviour is responsible for the exceptional CO2/N2 selectivity and reverse CO2/C2H2 selectivity of F4_MIL-140A(Ce). Here, we combine data obtained from a wide pool of characterisation techniques – namely gas sorption analysis, in situ infrared spectroscopy, in situ powder X-ray diffraction, in situ X-ray absorption spectroscopy, multinuclear solid state nuclear magnetic resonance spectroscopy and adsorption microcalorimetry – with periodic density functional theory simulations to provide evidence for the existence of a unique cooperative CO2 adsorption mechanism in F4_MIL-140A(Ce). Such mechanism involves the concerted rotation of perfluorinated aromatic rings when a threshold partial pressure of CO2 is reached, opening the gate towards an adsorption site where CO2 interacts with both open metal sites and the fluorine atoms of the linker.


S4
3. Gas sorption analysis N 2 , Ar and CO 2 isothermal physisorption measurements were performed on a Micromeritics ASAP 2020 analyser at 77 K, 87 K and 273 K, respectively. ( Figure S7) For CO 2 adsorption the temperature was kept constant thanks to a home-made patented glass coating cell 2 in which a coolant or heating fluid, connected to a thermostatic bath (JULABO F25), is recirculating. Prior to the measurement, the sample was heated overnight at 393 K under vacuum. Specific surface areas were determined by using the Brunauer−Emmett−Teller (BET) method, following the Rouquerol consistency criteria ( Figure S8-S10). 3 Cumulative pore volume and pore size distribution were derived from adsorption isotherms by applying the NL-DFT method with the Microactive software provided by Micromeritics, using: (i) a cylindrical pore geometry and considering the model "Argon on Oxides at 87 K" for Ar adsorption at 87 K; (ii) a cylindrical pore geometry and considering the model "N 2 Cylindrical Pores Oxides Surfaces" for N 2 adsorption at 77 K; (iii) a slit pore geometry and considering the model "CO 2 -GCMC CO 2 Carbon " for CO 2 adsorption at 273 K (Figure S11-S14).
High pressure CO 2 adsorption-desorption isotherms up to 5 bar were measured with a Quantachrome iSorb High Pressure Gas Analyser at 298, 313, 328 and 343 K (Figure 2a). About 200 mg of sample was used for the adsorption studies. The sample was degassed at 393 K under dynamic vacuum for 12 h prior to analysis and at 393 K for 1 h in between subsequent measurements. The adsorption branches were fitted using the following version of the Dual Site Langmuir-Freundlich equation, implemented in OriginLab: Where q is the gas loading at pressure P, q 1 and q 2 are the saturation loadings for each site, K 1 and K 2 are the affinity constants for each site, n 1 and n 2 are the indices of heterogeneity for each site. We note that the physical meaning of the model might not be representative of the actual CO 2 adsorption phenomenon occurring in F4_MIL-140A(Ce), but it provides an excellent fit of the experimental data nonetheless (see Figures S1-S4 and Table S1). Using these fitted isotherms, the isosteric heat of adsorption (Qst) was extracted using the linear version of the Clausius-Clapeyron equation in the loading range 0.1-2.2 mmol g -1 ( Figure S6). Figure S1. Dual site Langmuir Freundlich (DSLF) fit (grey line) of the CO 2 adsorption isotherm collected at 298 K (black circles) up to 5 bar.   Table S1. Dual site Langmuir Freundlich fitting parameters of the CO 2 adsorption isotherms collected at 298 K, 313 K, 328 K and 343 K up to 5 bar.

Temperature
(K) q 1 k 1 n 1 q 2 k 2 n 2 R 2 Figure S5. Plot of logP at which the first derivative of the adsorption isotherm reaches the maximum value as a function of the temperature (black circles) and linear fitting (red line). The very good correlation (R 2 = 0.9973) suggests that the threshold pressure for phase change in the 298-343 K temperature range may be straightforwardly predicted. Figure S6. Plot of isosteric heat of CO 2 adsorption (Qst) versus loading obtained from the isotherms collected at 298 K, 313 K, 328 K and 343 K up to 5 bar. The "bump" between 1.5 and 2.0 mmol g -1 loading is probably an artefact originating from the uncertainty in the fitting in that region, where the isotherms display a change of gradient near saturation and few or no experimental data are available (See Figures S1-4). Figure S7. Volumetric adsorption isotherms in the 0 < p/p0 < 0.03 pressure range (semi-logarithmic isotherms in the same pressure range displayed in the inset (a) and volumetric adsorption/desorption isotherms in the whole pressure range of: Ar at 87 K (dark red), N 2 at 77 K (orange) and CO 2 at 273 K (grey) on F4_MIL-140A(Ce) (b).
S9 Figure S8. Linear BET fit in the 0.0032<p/p 0 <0.036 pressure range for Ar at 87 K. Figure S9. Linear BET fit in the 0.0032<p/p 0 <0.036 pressure range for N 2 at 77 K. S10 Figure S10. Linear BET fit in the 0.0028<p/p 0 <0.031 pressure range for CO 2 at 273 K. S11 Figure S11. NL-DFT Pore Size Log Goodness of Fit Graph obtained by applying the NL-DFT analysis to the adsorption isotherm, employing a cylindrical pore geometry and considering the model "Argon on Oxides at 87 K" present in the Microactive software. Figure S12. NL-DFT Pore Size Log Goodness of Fit Graph obtained by applying the NL-DFT analysis to the adsorption isotherm, employing a cylindrical pore geometry and considering the model "N 2 Cylindrical Pores Oxides Surfaces" present in the Microactive software. S12 Figure S13. NL-DFT Pore Size Log Goodness of Fit Graph obtained by applying the NL-DFT analysis to the adsorption isotherm, employing a slit pore geometry and considering the model "CO 2 -GCMC CO 2 Carbon" present in the Microactive software. Figure S14. Cumulative pore volume graph derived from NL-DFT analysis of Ar at 87 K (dark red) N 2 at 77 K (orange) and CO 2 at 273 K (grey).  Figure S8), obtained from NL-DFT analysis of the adsorption isotherm employing a cylindrical pore geometry and considering the model "NLDFT-Argon on Oxides at 87 Kelvin" present in the Microactive software. d Calculated using the cumulative pore volume graph ( Figure S8), obtained from NL-DFT analysis of the adsorption isotherm employing a cylindrical pore geometry and considering the model "N2 -Cylindrical Pores-Oxides Surfaces" present in the Microactive software. e Calculated using the cumulative pore volume graph ( Figure S8), obtained from NL-DFT analysis of the adsorption isotherm employing a slit pore geometry and considering the model "CO2 -GCMC Carbon" present in the Microactive software. f Derived from the pore size distribution graph ( Figure 2B) obtained from the NL-DFT analysis of the adsorption isotherm, employing a cylindrical pore geometry and considering the model "NLDFT-Argon on Oxides at 87 Kelvin" present in the Microactive software. g Derived from the pore size distribution graph ( Figure 2B) obtained from the NL-DFT analysis of the adsorption isotherm, employing a cylindrical pore geometry and considering the model "N2 -Cylindrical Pores-Oxides Surfaces" present in the Microactive software. h Derived from the pore size distribution graph ( Figure 2B) obtained from the NL-DFT analysis of the adsorption isotherm, employing a slit pore geometry and considering the model "CO2 -GCMC Carbon" present in the Microactive software.

In situ IR spectroscopy
IR spectroscopy was performed on a Bruker Vertex 70 instrument equipped with a MCT (mercury cadmium tellurium) cryo-detector. All the spectra were recorded in a spectral range of 4500-250 cm -1 with a resolution of 2 cm -1 and an average of 32 scans. Before the analysis, F4_MIL-140A(Ce), as self-supported pellet, was activated in vacuum at 393 K for 12 h. Both CO and N 2 interactions with the sample were studied by dosing a proper amount of gas (~60 mbar) into the cell and cooling down to 77 K with liquid nitrogen. The spectra reported for both the experiments were collected in outgassing through subsequent expansions until complete degas was achieved ( Figure S16).
The sample was completely evacuated at 393 K overnight ( Figure 3) and spectra in contact with CO or N 2 were recorded at 77 K. The interaction of CO with F4_MIL-140A(Ce) gives rise to three main bands at 2155, 2130 and 2106 cm -1 . The most intense band at 2155 cm -1 can be assigned to CO adsorbed on Ce 4+ sites. 4 Bands at similar frequencies have also been attributed to the interaction of CO with mildly acidic OH groups. 5,6 However, the absence of changes in the OH stretching region at 3645 cm -1 suggests that the latter hypothesis is not realistic (see inset of figure S16). The weak band at 2130 cm -1 is tentatively assigned to CO interacting with Ce 3+ sites, whose presence in F4_MIL-140A(Ce) in small amounts was previously revealed, 7 although another hypothesis is the presence of physisorbed CO into the pores which is usually reported to be in the 2145-2131 cm -1 region. 5,8 Since the rate of disappearance of the band at 2130 cm -1 is the same as that of the 2155 cm -1 band upon CO desorption, and this is not the first signal that starts disappearing, the latter hypothesis is to be considered unlikely. The band at 2106 cm -1 is due to the isotopic shift of the 13 C- 16 O interacting with Ce 4+ . The ratio between the band at 2155 cm -1 and this latter one is 1.023, which is nearly equivalent to the isotopic shift factor reported in the literature. 9 N 2 is a much weaker basic probe than CO and becomes IR active due to a decrease in symmetry caused by the interaction with Brønsted or Lewis acid sites. The interaction of N 2 at 77 K with F4_MIL-140A(Ce) causes the appearance of a band at 2328 cm -1 , whose assignment is not straightforward, due to the few data reported in literature. Bands in the range 2332-2328 cm -1 are usually assigned to N 2 interacting with hydroxyls and are accompanied by the appearance of signals in the O-H stretching region. 10 Since no significant changes are observed in this latter region, the 2328 cm -1 band probably testifies the interaction of N 2 with Ce 4+ acidic sites ( Figure S16). This last interpretation is in agreement with what previously assumed for CO bands and is a proof of a specific interaction of N 2 with the sample. The 2328 cm -1 value is in fact comparable to those observed for N 2 adsorbed on MIL-100(Cr) (2290 cm -1 ) 11 and V 2 Cl 2.8 (btdd) (2342 cm -1 ). 12 This result clearly demonstrates N 2 is not an inert molecular probe for this MOF with open metal sites and it could be responsible for the higher BET surface area measured with N 2 than with Ar. Figure S16. IR spectra of F4_MIL-140A(Ce) after adsorption of 60 mbar of CO at 77 K (left) and after adsorption of 60 mbar of N 2 at 77 K (right) and following outgassing. The spectra were plotted subtracting the spectrum of the evacuated material. In the inset the row data of the hydroxyl region is shown.

Periodic density functional theory (DFT) simulations
Vibrational and energetic features of F4_MIL-140A(Ce), also in presence of relevant adsorbates, were simulated at the DFT level of theory with the CRYSTAL17 code. 13,14 In detail, the B3LYP hybrid GGA functional 15,16 was exploited in conjunction with a double-ζ quality basis set (C and O from ref. 17 ; F from ref. 18 and Ce from ref. 19 ). An effective core potential was adopted to describe the 26 electrons located in the inner shells of Ce. A larger Ahlrichs TZV2p basis 17 described atoms belonging to adsorbed molecules (H 2 O, CO 2 , CO and N 2 ). Dispersive interactions were empirically included in the Hamiltonian according to the Becke-Johnson dumped version of the Grimme's D3 scheme. 20,21 The truncations for the mono-and bi-electronic integral (TOLINTEG) were set to {7 7 7 7 14}. The sampling in the reciprocal space (SHRINK) was set to {2 2}, for a total of 6 irreducible k-points sampled in the 1 st Brillouin zone. Such computational setup provided a satisfactory structural and electronic description of Ce-MOFs. 22 Initially, the structure of the dehydrated F4_MIL-140A(Ce) (experimental structure as initial model) was geometry optimised. Symmetry was fully exploited in the calculations. Subsequently, adsorbed molecules were introduced and the obtained structures optimised. H 2 O was put in direct interaction with the exposed Ce site of the evacuated MOF through a lonepair of the O atom of the molecule (initial Ce-O distance was set to 2.2 Å). CO 2 interaction with F4_MIL-140A(Ce) was modelled considering two distinct adsorption sites: i) in direct interaction with Ce, by forming a linear adduct (initial Ce-O distance 2.4 Å); ii) positioned within the MOF channels, as proposed by Zhao and coworkers. 23 Vibrational frequencies and IR intensities were computed for all relaxed structures and the absence of imaginary modes verified (i.e. all relaxed models are energy minima). Enthalpies and Gibbs free energies, computed at T = 298.15 K and p = 1013 mbar, were also obtained for the minima structures. Adsorption energies (ΔE), enthalpies (ΔH) and Gibbs free energies (ΔG) per adsorbed molecule were calculated as it follows: Where X MOF+mol refers to the F4_MIL-140A(Ce) + molecule adduct structure, X MOF to the dehydrated MOF and X mol to the isolated molecule. The obtained values were corrected for the basis set superposition error (BSSE) through the counterpoise method. 24 Table S3. Cell parameters for the DFT-optimised structures of F4_MIL-140A(Ce), as such and interacting with H 2 O and CO 2 (the latter, both directly with the metal site or with the microporous channel).

In situ powder X-ray diffraction (PXRD)
The in situ PXRD study described took place at Beamline P02.1 (PETRA III, DESY, Hamburg). 25 PXRD patterns were collected using 60.0 keV (0.207124 Å) radiation. The sample was held in a 0.5 mm internal diameter glass capillary, which was mounted on a custom-built spinner device which allows for rotating a gas filled capillary mounted on a commercial Huber goniometer head by 360° forth and back. The temperature of the sample was controlled between 25 and 140 °C with an Oxford Hot-Air Blower. The beamline was equipped with a Perkin Elmer XRD1621 CN3 -EHS detector (200×200 µm 2 pixel size, 2048 x 2048 pixel area). The detector was positioned at 1000 mm from the sample stage. Each PXRD pattern was collected in the 0.0071-16.3041 °2θ range, with a 0.0067 °2θ step size and a total acquisition time of 30 s. The resulting 2D images were azimuthally integrated to 1D diffraction patterns using the software Fit2D. 26 The data were analysed by Rietveld refinement as implemented in the software TOPAS 6.0. 27 Wavelength, instrument peak shape parameters and zero-point error were refined based on data collected on LaB 6 standard material. First, a Pawley refinement was carried out to model background, profile shape parameters and lattice parameters. In both cases, a slightly better result was obtained when refining using a P2 1 /c space group, rather than the more symmetric C2/c space group observed for the as-synthesised MOF and used for all DFT simulations. However, given the very small differences in Rwp (2.38 in C2/c vs 2.03 in P2 1 /c for the evacuated MOF; 2.50 in C2/c vs 2.16 in P2 1 /c for the CO 2 loaded MOF), we decided to proceed with Rietveld refinement using the highest symmetry space group, which contains half as many crystallographically independent atoms and requires to refine less parameters. This choice is also supported by SSNMR data, which show that only two crystallographically independent linkers exist.
Rietveld refinements of the dehydrated and CO 2 loaded forms of F4_MIL-140A(Ce) were performed using structural models obtained from the DFT optimisations described above. Rietveld refinement was performed to model the atomic coordinates and atomic displacement parameters. For the CO 2 loaded F4_MIL-140A(Ce), the pattern collected at 40 °C under 1188 mbar CO 2 was refined. The aromatic ring of linker B was modelled by employing a rigid group. To correctly describe the geometry of the aromatic ring, one dummy atom named XX, whose occupancy factor was set to zero, was employed in the rigid group and placed at the centre of the aromatic ring. The position of XX was restrained to the special position (0, y, 0.25) by fixing the translational parameters of the rigid group along the x and z axis. Rotational parameters along the x and z axis were kept fixed at 90 and 0°, respectively, whereas rotation along the y axis was left free to refine. All the other atoms were refined individually, using 20 distance restraints and 16 angle restraints for each structure. To correctly describe the geometry of the aromatic ring of linker A, another dummy atom named YY, whose occupancy factor was also set to zero, was employed. The position of YY was restrained to the special position (0.25, 0.25, 0.5), and three distance and three angle restraints were applied that involved this atom. In the case of the CO 2 loaded MOF, an additional restraint was applied to ensure flatness of the aromatic ring belonging to linker A. The atomic displacement parameter for Ce was refined independently, while those of the light atoms were constrained to the same value. In the CO 2 loaded MOF, the occupancy of the CO 2 molecule was set to 0.9, in agreement with the observed loading at 40 °C under 1188 mbar CO 2 (2.25 mmol, versus a loading at saturation of 2.5 mmol) and the atomic displacement parameters of the constituting C and O atoms were constrained to refine to the same value, independently from those of the light atoms belonging to the framework. At the end of the refinement, all the parameters were refined together until convergence. Details of the refinements are reported in Table S4.

In situ X-ray absorption spectroscopy (XAS)
Ce K-edge XAS data were collected on the BM23 28 beamline of the European Synchrotron Radiation Facility (ESRF) of Grenoble, France. The storage ring was operating in the 32-bunch mode with a target current of 150 mA. The measurements were conducted in transmission mode using a Si(311) double-crystal monochromator. Intensity of the X-ray beam was measured by the means of three ion chambers (30 cm, 1 kV) placed before the sample (I 0 , filling 0.28 bar Kr + 1.72 bar He), after the sample (I 1 , filling 1.35 bar Kr + 0.65 bar He) and after the CeO 2 reference sample (I 2 filling 1.35 bar Kr + 0.65 bar He). This experimental setup allowed us to reference the energy to the edge of the reference sample and thus calibrate the energy for each spectrum.
Samples were measured in the form of self-supporting pellets, whose optimized weight were calculated with the XAFSmass code. 29 A home-built gas dosing setup equipped with mass-flow controllers allowed us to dose He/CO 2 mixtures at carefully selected amounts in order to collect adsorption isotherms. Total flow was set to 50 mL min -1 . The temperature was set to 328 K.
EXAFS data analysis was carried out by the means of the Demeter package 30 : Athena for the raw data treatment (normalization, extraction) and Artemis for fitting of the EXAFS spectra. FEFF6 31 was used to calculate phase shifts and scattering amplitudes.    (2) *This parameter accounts as a correction factor for an isotropic elongation/contraction of all crystallographic Ce-C CO2 distances.

Solid state nuclear magnetic resonance (SSNMR)
SSNMR measurements were carried out on a Bruker Avance Neo spectrometer working at Larmor frequencies of 500.13, 470.59, and 125.77 MHz for 1 H, 19 F, and 13 C nuclei, respectively, equipped with a double-resonance cross-polarization magic angle spinning (CP/MAS) probe head accommodating rotors with external diameter of 4 mm.
The SSNMR characterization was performed on as-synthesised, evacuated, and CO 2 -loaded F4_MIL-140A(Ce) samples. For preparing the evacuated sample, the unsealed rotor containing the as-synthesised sample was heated overnight under vacuum (0.1 mbar) at the temperature of 423 K in a home-built cell and then sealed under N 2 atmosphere. For CO 2 loading, the home-built cell containing the evacuated sample packed into the rotor was loaded with CO 2 at 1 bar pressure and the rotor was sealed under the gas atmosphere. The cell is indeed provided with a mechanical lever operated from outside enabling the capping of the rotor without disturbing the cell atmosphere. 1 H-13 C and 19 F-13 C cross-polarization (CP) and heteronuclear correlation (HETCOR) experiments were performed at a MAS frequency of 15 kHz. 19 F-13 C CP-MAS spectra were recorded using contact times (ct) ranging from 0.2 to 10 ms using a recycle delay of 2 s for the evacuated and as-synthesized samples and of 12 s for the CO 2 -loaded one; 800 scans were accumulated for all samples. The 1 H-13 C CP-MAS experiment on the as-synthesized sample was acquired using a ct of 2 ms, 10000 scans and a recycle delay of 2 s. For the as-synthesized and evacuated samples, 19 F-13 C HETCOR experiments with FSLG decoupling 32 in the indirect dimension were performed recording 64 rows, accumulating 80 scans with a recycle delay of 2 s and using ct values of 0.5, 1.5 or 3 ms. For the CO 2 -loaded sample, 72 rows were acquired, accumulating 320 scans with a recycle delay of 10 s and using ct values of 0.2 and 2 ms. 13 C spectra were recorded on CO 2 -loaded F4_MIL-140A(Ce) by Direct Excitation (DE) with background suppression and high power 19 F decoupling under both MAS (15 kHz) and static conditions. The MAS spectra were acquired with recycle delays of 150 and 2 s and accumulating 800 and 200 scans, respectively. For the static spectrum, a recycle delay of 2 s was employed to selectively observe the CO 2 signal and 25000 scans were accumulated.
All spectra were acquired at room temperature using air as spinning gas. The chemical shift for all nuclei was referenced to the 13 C signal of adamantane at 38.46 ppm.
The line shape of the CO 2 powder pattern in the static 13 C DE spectrum was simulated using the NMR-WEBLAB online software 33,34 using δ 11 = δ 22 = 230 ppm and δ 33 = -85 ppm for the CO 2 principal chemical shift tensor components, in agreement with the literature, 35,36 and a Lorentzian line width of 30 ppm. The wobbling in a cone model in the fast motion limit was used with a cone angle of 75° and a flip angle of 120° (flipping between 3 sites). It must be pointed out that the same line shape could be obtained by wobbling among ≥3 sites.    For as-synthesised F4_MIL-140A(Ce), the deconvolution of signals of CF, Cq and COOcarbons in 19 F-13 C CP-MAS spectra ( Figure S49) highlights the presence of three CF peaks at 142.6, 143.5 and 145.3 ppm. On the basis of the 19 F-13 C HETCOR spectra shown in Figure S50, 13 C signals at 142.6 and 143.5 ppm, giving strong correlation peaks with 19 F signals at about -145 and -143 ppm, respectively, are ascribed to CF carbons (C7 and C8) belonging to linker B. Indeed, these CF carbons seem to be bonded to two inequivalent Cq carbons (C6 and C9) resonating at different 13 C chemical shifts (118.7 and 117.6 ppm), as expected in the presence of a two-fold symmetry axis. Carboxylic carbons resonating at 166.9 and 165.2 ppm also belong to ring B and can be tentatively ascribed to positions C10 and C5. On the other hand, the 13 C signal at 145.3 ppm, correlating with the 19 F signal at about -143 ppm, is attributable to CF carbons (C3 and C4) belonging to linker A spatially close to Cq carbons (C2) resonating at 117.6 ppm and carboxylic carbons at 163.7 ppm (C1). Figure S51. Expansions of the 19 F-13 C HETCOR spectra of evacuated F4_MIL-140A(Ce) with signal assignment. Spectral regions of carboxylic (ct = 3 ms), fluorinated (ct = 0.5 ms), and quaternary (ct = 0.5 ms) carbons are shown from left to right. A and B are the two independent linkers in the crystal structure sitting on an inversion centre and on a two-fold axis, respectively.
As far as evacuated F4_MIL-140A(Ce) is concerned, deconvolution of the 19 F-13 C CP-MAS spectra ( Figure  S49) highlights the presence of two CF peaks at 146.0 and 143.6 ppm, which can be ascribed to linkers A (C3 and C4) and B (C7 and C8), respectively. Indeed, based on the correlation peaks visible in the 19 F-13 C HETCOR spectrum ( Figure S51), the 13 C peak at 143.6 ppm (C7 and C8) correlates with two distinct 19 F signals at about -143 and -141 ppm, which are also associated to COOcarbons resonating at about 167.3 ppm (C5 and C10) and to two inequivalent Cq carbons resonating at 115.8 (C6) and 117.4 (C9) ppm, in agreement with the presence of a two-fold symmetry axis. On the other hand, the 13 C peak at 146.0 ppm (C3 and C4) correlates with the 19 F signal at about -142 ppm, also associated with COOand Cq carbons resonating at 168.4 (C1) and 115.8 (C2) ppm, respectively, which is compatible with the presence of an inversion centre in the linker. In the case of CO 2 -loaded F4_MIL-140A(Ce), the deconvolution of the 13 C DE-MAS spectra ( Figure S49) shows the presence of two CF peaks at 145.7 and 143.6 ppm, each arising from 2 CF carbons of linker A and 2 of linker B. In fact, in the 19 F-13 C HETCOR spectrum recorded with ct = 0.2 ms ( Figure S52, central panel), in which the sole carbons bonded to fluorines are observed, the 13 C peak at 143.6 ppm correlates with two distinct 19 F signals at about -142 and -139 ppm, whereas the 13 C peak at 145.7 ppm only correlates with the 19 F signal at -142 ppm. The signals at -139 and -142 ppm indeed arise from 2 and 6 fluorine atoms, respectively. When the 19 F-13 C HETCOR spectrum is recorded with ct = 2 ms, a correlation peak also appears between the 19 F signal at -139 ppm and the 13

Adsorption microcalorimetry
The differential molar heat of adsorption was evaluated on F4_MIL-140A(Ce) by means of a heat flow microcalorimeter (Calvet C80 by Setaram) connected to a high-vacuum (≈ 10 -4 mbar) glass line equipped with a Varian Ceramicell 0-100 mbar gauge and a Leybold Ceramicell 0-1000 mbar gauge. The sample was activated in vacuum at 120 °C for 12 h before being placed into the calorimeter under isothermal conditions. The measurement was performed at 303 K (30 °C) and not at 298 K (25°C) due to technical limitations. This procedure allows the determination of both integral heats evolved (−Q int ) and adsorbed amounts (N ads ) for small increments of the adsorptive pressure. The heats of adsorption obtained for each small dose of gas admitted over the sample (−q diff ) are reported as a function of coverage, in order to obtain the (differential) enthalpy changes. The differential heat plot was obtained by taking the middle point of the partial molar heat (ΔQ int /ΔN ads , kJ mol −1 ) vs. N a histogram relative to the individual incremental dose. A volumetric isotherm was performed at the same temperature by means of a Micromeritics ASAP 2020 instrument and were compared with the one measured at 298 K (25 °C) and 313 K (40 °C) in the pressure range 0-1.2 bar showing an intermediate CO 2 uptake ( Figure S54).

Appendix: Coordinates of DFT-computed crystal structures
Structures of DFT models (all in C2/c space group) are provided hereafter, according to the following format: • MODEL NAME a b c β (unit cell parameters) N i x i y i z i (atom type N and fractional coordinates for the i th atom in the asymmetric unit)