Flexible Yttrium Coordination Geometry Inhibits “Bare-Metal” Guest Interactions in the Metal-Organic Framework Y(btc)

Abstract

Y(btc) (btc = 1,3,5-benzenetricarboxylate) is a metal-organic framework that exhibits significant adsorption of industrially-relevant gases such as H₂, CH₄, and O₂. Previous studies have noted a surprising lack of close interactions between the adsorbed guest molecules and Y, despite the apparent availability of a “bare-metal” binding site. We have extended our previous work in a detailed investigation of the adsorption behaviours of CO₂, CD₄, and O₂ in Y(btc) over a range of concentrations using in situ neutron powder diffraction methods. The O–Y–O bond angles enclosing the bare-metal site are found to change considerably depending on the type and quantity of guest molecules present. Multiple binding sites are found for each guest species, and the largest changes in O–Y–O angles are accompanied by changes in the filling sequences of the binding sites, pointing to an important interplay between guest-induced framework distortions and binding site accessibility. These results suggest the potential for coordinatively flexible rare-earth metal centres to promote guest-selective binding in metal-organic frameworks.

1. Introduction

The atomic-scale understanding of gas-sorption mechanisms in porous solid sorbents has become a focus of major research efforts in recent times, driven in particular by the need for efficient gas separators in many energy-related applications. Porous crystalline materials such as metal-organic frameworks (MOFs) are often targeted for these applications due to their favourable properties: good gas selectivity and capacity, ease of handling compared to liquid sorbents, as well as adequate mechanical, thermal, and chemical stabilities. Importantly, these materials are highly tuneable, and significant opportunities exist for engineering their chemistries toward particular sorbent applications. Key framework features which improve adsorption properties need to be identified and optimised for the development of better future materials. For example, many studies have shown that the presence of coordinative-unsaturated metal centres tends to enhance total uptake of gases such as hydrogen [1,2,3], methane [4] and ammonia [5], among others, and can also contribute to guest selectivity in the presence of gas mixtures [6]. These “bare” metal sites interact strongly with many guest molecules, yielding higher binding energies and often resulting in denser arrangements of guests in the pores of the sorbent material. Unfortunately, the operative stability of bare metal-containing MOFs is often compromised by their ability to readily adsorb guests from the air, such as water and gaseous species, which can lead to permanent degradation of their crystallinity and adsorptive function [7,8,9]. By contrast, the excellent moisture stability of the well-known Zr₆O₄(OH)₄(BDC)₆ (where BDC = benzene-1,4-dicarboxylate), also known as UiO-66(Zr) material, has been partially attributed to the absence of coordinatively unsaturated Zr in the Zr₆O₄(OH)₄(CO₂)₁₂ oxide cluster, preventing hydrolytic attack by water molecules [8].

Bare-metal sites are typically created in MOFs by the removal of coordinated solvent molecules from the material following its initial synthesis. In these cases, the preferred coordination geometry of the metal centre and the fixed network topology of the linker molecules both serve to maintain the overall structure of the MOF without significant changes to the framework geometry in the vicinity of the metal centre. However, MOFs containing rare-earth metals may display more flexibility in their coordination geometry upon removal of the solvent due to the greater number of satisfactory geometries adopted by these large metal ions [10,11,12]. One such example is Y(btc) (btc = 1,3,5-benzenetricarboxylate), a MOF which displays appreciable uptake of H₂ [13], CH₄ and O₂ [14]. Y(btc) is a structural analogue of Tb(btc) (also known as MOF-76 [15]) and consists of parallel 4₁-type helices of Y atoms linked by the bridged carboxylate groups of three btc ligands, resulting in square channels which extend along the c axis in the tetragonal space group P4₃22 (Figure 1). The distance between corresponding atoms on opposite walls of the square channels is ~10.3 Å, equivalent to the a parameter of the unit cell. Structural studies have demonstrated significant relaxation of the linker geometry around the Y centre upon removal of the coordinated water-of-crystallisation, yielding a bare-metal site which may be less accessible to guest molecules [14]. In the same study, CD₄ was found to display no significant interaction with the Y centre at 1 CD₄:Y loading, while O₂ interacted weakly with Y only at the least populated of its three observed binding sites. Similarly, no interaction with the bare-metal site was reported for any of the four observed binding locations of D₂ in the material [13].

The linear CO₂ molecule has a smaller minimum diameter than CH₄ and is more polarisable than either H₂ or O₂, giving it the opportunity for better access to, and more favourable interactions with, the restricted Y bare-metal site in Y(btc). Furthermore, the capture of CO₂ by porous sorbents is of special relevance to the energy industry, due to the drive to minimise carbon dioxide emissions from the waste streams of existing fossil-fuel technologies such as coal plants [16,17], as well as ensuring the viability of natural gas reserves. We have therefore undertaken a detailed investigation of the adsorption behaviour of CO₂ in Y(btc), extending a previous investigation of CH₄ and O₂ adsorption in the material by exploring the guest concentration effects on both the binding and the framework structure. As with the previous investigations of gas adsorption in Y(btc), neutron scattering methods were used for structural characterisation of the host-guest system, as scattering from the heavy yttrium dominates the X-ray data and inhibits the location of lighter framework and guest atoms. In the context of this new work and of results previously reported for O₂, CH₄, and H₂ [13,14], we present an analysis of the Y coordination environment in Y(btc) and its behaviour in the presence of different guest species and concentrations, with a view to understanding how MOF sorbent functionality is influenced by the use of coordinatively flexible rare-earth metal centres.

2. Results

2.1. Carbon Dioxide Adsorption

2.1.1. Adsorption Isotherms

Gas adsorption isotherms measured for Y(btc) at 298 K demonstrated good uptake of CO₂, the measured value of around 5 mmol·g⁻¹ at 10 bar being almost twice the uptake of CH₄ and four times that of O₂ or N₂ at the same pressure and temperature (Figure 2). Uptake kinetics for all gases were very rapid, with equilibration achieved within ~2 min after each dose was applied to the sample. Water adsorption in Y(btc) was found to be fully reversible and the isothermal curve was reproduced after a second adsorption cycle, highlighting the relatively-good stability of the material to moist environments (Figure S1).

2.1.2. Binding Site Locations

The structure of the empty Y(btc) framework was initially refined against neutron powder diffraction (NPD) data collected for the CO₂-loaded material. Three crystallographically-distinct CO₂ adsorption sites were determined, all of which were observed to be partially occupied after the first dose of 1 CO₂:Y (that is, one mole of CO₂ per mole of Y(btc)) (

Table 1. Crystallographic details for CO₂ sites within Y(btc) at a dose of 1 CO₂:Y.

Binding Site	Atom	Wyckoff Site	Site Symmetry	Fractional Coordinates			Fractional Occupancy	Uiso (10−2 Å2)
				x (a)	y (b)	z (c)
ACO2	C1a	8d	1	0.818(4)	0.819(8)	0.359(5)	0.52(2)	21.3(2)
	O1a	8d	1	0.831(7)	0.852(7)	0.4347(4)	0.52(2)	21.3(2)
	O1b	8d	1	0.853(7)	0.808(8)	0.2850(4)	0.52(2)	21.3(2)
BCO2	C2a	4a	.2.	0.693(1)	0	0.25	0.199(17)	17.5(3)
	O2a	8d	1	0.673(8)	0.007(1)	0.1670(2)	0.199(17)	17.5(3)
CCO2	C3a	4a	.2.	0	0.945(1)	0.5	0.111(11)	4.6(2)
	O3a	8d	1	0.915(8)	0.950(8)	0.553(1)	0.111(11)	4.6(2)

). Y(btc)·CO₂ refinement results can be found in the Supporting Information (Tables S1 and S2).

Figure 3 shows the arrangement and orientation of all symmetry-generated locations for each of the three CO₂ adsorption sites within a single Y(btc) unit cell. The molecules located at sites B_CO2 and C_CO2 lie along the [y, 0, 1/4] and [0, y, 1/2] 2-fold axes, respectively, and therefore occur with half the multiplicity of site A_CO2. Site occupancy restrictions arising from close interactions between these adsorption sites are discussed in Section 2.1.3.

The binding site with the highest CO₂ population, A_CO2, is located approximately 3.1 Å above one carboxylate-functionalised arm of the btc ligand and 4.1 Å from the nearest available bare-metal site. It is interesting to note that one of the shortest host-guest distances is between the A_CO2 O atom nearest to the Y bare-metal site and the carboxylate O atom coordinated to the same Y atom. Although electrostatic repulsion is generally expected between two oxygen atoms, it appears likely that the coordinatively unsaturated Y atom draws electron density more strongly from the coordinated atoms, decreasing their partial negative charges to the point where a weak O–O distance of 3.14(10) Å is permitted between them. The other nearest-neighbour distances between A_CO2 and Y(btc) are attributed to typical electrostatic interactions between electron-deficient and electron-rich atoms, with observed distances in the intermediate-to-weak range of 2.86–3.42 Å.

The second-most populated CO₂ adsorption site, B_CO2, is located approximately 2 Å above the pseudo‑plane of two adjacent btc ligands and interacts symmetrically with four carboxylate functional groups. As a result of the relative positioning and distance from each of these groups, the observed host-guest interactions are attributed to electrostatic interactions dominated by the quadrupolar nature of the CO₂ guest. The O atoms of the CO₂ molecule are positioned 3.17(9) Å from the C atom of the nearest carboxylate group, and 2.94(8) Å from the adjacent C atom on the 6-membered ring. These electron-deficient C atoms provide a favourable environment with which the electron-rich O guest atoms can interact. Similarly, O atoms from two of the nearby carboxylate groups appear to sandwich the electron-deficient C atom of CO₂, forming a ring of favourable electrostatic host-guest interactions below the guest molecule. Nevertheless, while site B_CO2 appears more favourable based on the quantity of electrostatic host-guest interactions, the observed occupancy factor of 0.199(17) CO₂:Y at a loading of 1 CO₂:Y is less than half that of site A_CO2.

The third observed adsorption site, C_CO2, displays the longest host-guest distances and the lowest site occupancies after both CO₂ doses. This site is located 3.628(10) Å and 4.21(3) Å from the nearest and next-nearest btc carboxylate groups, respectively. These distances are generally considered too large to result from significant host‑guest interactions, so it is proposed that this site arises from the formation of a bilayer with previously adsorbed CO₂ molecules. When the gas-loaded system is viewed along the c axis, it can be seen that site C_CO2 is closest to the pore centre (Figure 3b), further supporting this hypothesis.

It should be noted that none of the three CO₂ adsorption sites display any significant interaction with the available Y bare-metal sites, with the closest interaction distances occurring for sites A_CO2 and C_CO2 at 4.16(9) and 4.640(10) Å, respectively. It is typically expected that the bare-metal sites of a coordination framework should provide guest molecules, particularly quadrupolar CO₂ molecules, with a favourable interaction site. This result will be discussed further below.

The total refined occupancies across the observed CO₂ sites after both doses of CO₂ equated to 80%–85% of the amount of CO₂ dosed, indicating that up to 20% of guests were disordered within the framework and could not be located crystallographically. The relative occupancies of each site remained largely unchanged between the first and second doses, with all occupancy factors increasing by around 100% when the total CO₂ dosage was doubled.

2.1.3. Intermolecular Interactions and Occupancy Restrictions

As seen in Figure 4, several of the possible CO₂ binding sites lie in close proximity to one another, and this is expected to impose some occupancy restrictions. The shortest guest-guest distance of 2.063(1) Å occurs between two symmetrically-equivalent C_CO2 sites, restricting the maximum occupancy of this site to 50% (0.5 CO₂:Y). The highest observed C_CO2 occupancy factor, ~26%, lies well within this upper bound. The nearest intermolecular distance between sites A_CO2 and C_CO2 (2.10(8) Å) also restricts the co-occupation of these sites to 50%. As the multiplicity of site A_CO2 is 8, the maximum 50% occupancy of this site corresponds to 1 CO₂:Y. This value is approached after the second dose of CO₂.

The nearest interactions between sites A_CO2 and B_CO2 occur at a distance of 2.35(2) Å. These two sites are aligned in an offset‑parallel orientation relative to one another that takes advantage of the electrostatic interactions between the slightly positively-charged C and slightly negatively-charged O atoms. Although an end‑to‑side interaction (similar to that observed in solid CO₂) would more effectively exploit the quadrupolar nature of the CO₂ molecule, the observed arrangement appears to represent an optimal guest-guest configuration given the space constraints inside the Y(btc) pore and the presence of additional host-guest electrostatic interactions.

2.2. Methane and Oxygen Adsorption at High Dosage

Each NPD measurement described in [14] for CD₄ and O₂ at 1 guest:Y dosing was immediately followed by a second dose of 1 guest:Y applied to the same sample, for a total dose amount of 2 guest:Y. NPD data were also collected after the second dose of each gas. The fractional occupancies at all binding sites previously identified for CD₄ and O₂ increased after the second dose, but no new binding sites were identified for either gas (

Table 2. Unit-cell parameters and site-occupancy factors determined using Rietveld analysis of NPD data for empty and guest-loaded Y(btc).

Guest:Y	a (Å)	c (Å)	Fractional Occupancy				Rwp (%)
			Site A	Site B	Site C	Total
None 1	10.2998(1)	13.8635(2)	-	-	-	-	3.46
1 CD4 1	10.2970(2)	13.8581(3)	0.39(4)	0.274(8)	-	0.67(5)	4.85
2 CD4	10.2949(3)	13.8432(4)	0.740(5)	1.006(12)	-	1.75(6)	5.81
1 O2 1	10.2974(3)	13.8600(5)	0.722(16)	0.220(14)	0.198(10)	1.14(4)	5.58
2 O2	10.29363(15)	13.8522(2)	1.32(2)	0.337(14)	0.440(12)	2.09(5)	3.97
1 CO2	10.2976(2)	13.8639(3)	0.52(2)	0.199(17)	0.111(11)	0.86(5)	4.85
2 CO2	10.2709(7)	13.8579(6)	0.966(12)	0.37(2)	0.260(11)	1.59(4)	7.04

¹ From [14].

). Full refinement results for the guest-loaded systems with 2 guest:Y loading can be found in the Supporting Information (Tables S3 and S4).

A reversal of binding site preference upon increased loading was observed for CD₄, with site B_CD4 (interacting with the carboxylate groups and first aryl carbon atom) displaying a higher occupancy than site A_CD4 (interacting with carboxylate only) after the second dose. Similarly, the preference for guest binding at sites B_O2 (near carboxyl and aryl carbons) and C_O2 (Y bare metal site) was reversed after the second O₂ dose, though site A_O2 (carboxylate groups and first aryl carbon) remained the dominant binding site, containing more than half of the adsorbed O₂.

Adsorption of all guests results in a slight contraction of the unit cell of Y(btc) (Table 2). The a parameter decreases slowly and uniformly with increased loading of CO₂, CD₄ and O₂, except for a sharp decrease of ~0.25% between the first and second CO₂ dose. The c parameter also decreases uniformly by a similar magnitude, with the largest overall change occurring for O₂ (~0.15% decrease after the second dose).

2.3. The Yttrium Coordination Sphere

The possible region for guest binding between the Y atom and the guest-accessible pore space is enclosed by carboxylate O atoms belonging to four different btc ligands. The opposite pairs of these O atoms are crystallographically equivalent and correspond to sites designated O1 and O3. The angles formed by these atom pairs and the Y centre change considerably upon removal of the water of crystallisation from the as-synthesised framework, with the btc ligands closing in around the vacated binding site (

Table 3. Opposing O–Y–O angles which enclose the bare-metal Y site in the hydrated, dehydrated and guest-loaded Y(btc) materials. O1 and O3 refer to the relevant framework O atoms [13,14].

Guest:Y	O1–Y–O1 (°)	Change from Dehydrated (%)	O3–Y–O3 (°)	Change from Dehydrated (%)
Hydrated	167.9(3)	-	137.6(3)	-
Dehydrated	139.3(5)	-	120.8(5)	-
1 CO2	143.1(11)	3.8	115.9(8)	−4.9
2 CO2	143(3)	3.7	115.7(19)	−5.1
1 CD4	141.9(10)	2.6	114.3(8)	−6.5
2 CD4	147.2(11)	7.9	114.6(9)	−6.2
1 O2	141.9(7)	2.6	117.3(6)	−3.5
2 O2	147.5(8)	8.2	121.4(6)	0.6

). The subsequent addition of other guest molecules causes a partial re-opening of the O1–Y–O1 angle, even though the direct interactions between the guests and Y at this location are minimal [14]. Interestingly, the angle opening becomes more pronounced at higher loadings of CD₄ and O₂, but does not change significantly with increased CO₂ loading. The O3–Y–O3 angle, by contrast, contracts further upon the addition of guests to the empty framework. The only exception occurs at the 2O₂:Y loading where the angle becomes slightly larger than that of the empty framework, probably due to the small amount of O₂ binding to the bare Y site at high loadings [14]. A graphical representation of the changing YO₆ coordination environment is shown in Figure 5.

3. Discussion

The four guest species D₂, CO₂, CD₄, and O₂ display markedly different adsorption behaviour in Y(btc). In the absence of direct binding to the bare-metal site, the polar carboxylate groups tend to offer the most favourable adsorption sites and dominate guest occupation at low dosage amounts. However, the precise locations and orientations of these binding sites are unique to each guest, and the order of subsequent site filling also varies among the different species.

D₂ occupies four distinct binding sites, and is the only guest for which these sites are filled in a sequential fashion. Luo et al. [13] found that Site A, which lies near the carboxylate C atoms, is more than 65% occupied before any significant population is observed at Site B, which is closer to the aryl rings. Following the addition of further D₂, Site A saturates and Site C near the carboxylate O atoms populates almost to the level of Site B; B and C then co-fill to saturation. Site D appears to interact primarily with the carboxylate O atoms and other bound D₂ molecules, and is only slightly populated at loadings higher than 4 D₂:Y.

By contrast, CO₂ partially occupies three different binding sites after a single dose of 1 CO₂:Y, though Site A_CO2 (near the carboxylate groups) is dominant. All three site populations increase proportionally when the total loading is increased to 2 CO₂:Y. The very similar O–Y–O angles observed after the first and second doses of CO₂ (Table 3) indicate that the framework geometry is not greatly affected by the overall increase in CO₂ loading, which may explain the unchanging relative favourability of the three binding sites.

CD₄ occupies only two binding sites in Y(btc). The population at Site A_CD4 is only slightly higher than at Site B_CD4 for 1 CD₄:Y, but at higher loadings there is a reversal of preference and Site B_CD4 saturates before Site A_CD4. The more rapid increase in the occupancy of B_CD4 may indicate that this site is the more energetically favourable adsorption site, but is sterically hindered due to its location in the acute angle between the btc ligands. As additional CD₄ is introduced, the energetic barrier associated with this steric deterrent could be exceeded by guest-guest repulsions, allowing higher occupancy to be achieved. The considerable change in the O1–Y–O1 angle between the first and second doses of CD₄ tends to support the theory that ligand repositioning on increased loading alters the local CD₄ binding environment.

O₂, like CO₂, binds at three different sites which are all partially occupied at 1 O₂:Y loading, with one site dominating strongly. However, the dominant adsorption site A_O2 is associated more closely with the carboxylate C and adjoining aryl C atoms than with the carboxylate O atoms favoured by A_CO2. Furthermore, the two less favourable sites (B_O2 and C_O2) show a reversal of preference at high loading which is not observed for B_CO2 and C_CO2. This is probably due to the very different local environments of the respective sites: C_O2 is a bare-metal binding site, whereas the CO₂ molecules at all sites show significant interactions with the ligands only. It is notable that the greatest “opening” of the O–Y–O angles (especially O3–Y–O3) is observed for the second O₂ dose, and this increase in the steric accessibility of the bare Y site is almost certainly linked to the increased favourability of this site at the higher dosing level. A slight decrease of the distance between C_O2 and the Y centre from 3.77(6) Å at 1 O₂ to 3.72(4) Å at 2 O₂ is also observed, signifying stronger metal-guest interactions.

Finally, the water adsorption isotherm measured at 298 K (Figure S1) shows a large step, which is also consistent with the initial inaccessibility of the bare Y site. Up to a partial pressure (P₀) of 0.08 the water uptake is comparatively low, and attributed to adsorption only on exterior surface sites. The steep adsorption step, equivalent to approximately 4 water molecules per formula unit, probably occurs when the chemical pressure is sufficient to overcome the energetic barrier to opening the structure.

It is clear that the opening of the O–Y–O angles is important for promoting the accessibility of binding sites which are energetically favourable for otherwise sterically-hindered guest molecules. Whilst O₂ is able to induce this opening at higher concentrations, allowing the guest to interact with the Y, CO₂ is not able to force access to the bare-metal site. Similarly, CD₄ does not interact closely with Y even at high guest loadings, but remains preferentially sandwiched between btc units in a corner position, likely as a consequence of its tetrahedral shape as shown for other MOFs [18].

The demonstrated ability of the btc ligands around Y to undergo guest-specific rearrangement leading to changes in site binding enthalpy has important implications for tailoring sorbent selectivity in MOFs. Guest-induced structural changes are generally common in flexible MOFs [19,20] and can extend even to extreme modifications such as topotactic switching of interpenetration schemes [21], leading to fundamental changes in pore size and shape. Although the effects of the guest-induced site opening in Y(btc) observed in our work are relatively subtle, they represent an avenue for the tuning of adsorptive behaviour which has been largely unexplored so far. The utilisation of these coordinatively flexible metal centres may offer new strategies in MOF design, especially when combined with existing guest-responsive structural features, potentially leading to important applications in carbon capture and fuel storage.

4. Materials and Methods

4.1. Sample Preparation

A mixture of Y(NO₃)₃·6H₂O (5.22 g, 13.6 mmol) and 1,3,5-benzenetricarboxylic acid (1.06 g, 5.04 mmol) was dissolved at room temperature in a 1:1:1 (by volume) mixture of N,N‑dimethylformamide, ethanol and water (240 mL). This solution was divided equally into four 100 mL Parr Teflon-lined vessels which were heated at a rate of 1.1 K·min⁻¹ to 363 K and maintained at this temperature for 18 h. The resulting clear, needle‑shaped crystals were allowed to cool to room temperature before being isolated by vacuum filtration and washed with ethanol (100 mL). The combined sample was ground to a fine white powder and desolvated by heating in a glass sample tube at 573 K under high vacuum (~10⁻⁵ mbar).

4.2. Isothermal Adsorption Measurements

Gas adsorption isotherms for N₂ (supplied at 99.99% purity) and water vapour were measured using the IGA‑002 gravimetric system (Hiden-Isochema, Warrington, UK). The freshly-synthesised sample was loaded into a stainless steel basket and heated to 523 K under high vacuum (<10⁻⁶ mbar) for 7 h, after which the mass (~67 mg) remained stable. Adsorption isotherms were measured at 298 K with the system temperature maintained within 0.1 K. At each data point the pressure in the sample chamber was set and the mass allowed to equilibrate before moving to the next data point. In the case of water isotherms, the maximum equilibration time allowed per pressure point was 5 h, at which point the measurement was continued. The equilibrium mass was corrected for the buoyancy of the sample and balance components.

4.3. Neutron Diffraction

Neutron powder diffraction (NPD) data were collected using the high-resolution neutron powder diffractometer ECHIDNA [22] at the Australian Nuclear Science and Technology Organisation (ANSTO). The desolvated sample (1.376 g) was transferred to a 6 mm-diameter cylindrical vanadium can inside a helium-filled glovebox and loaded onto a custom-designed gas-delivery centrestick, which has been described elsewhere [23,24]. At all times, the sample was maintained in vacuo or in a helium atmosphere to prevent unwanted adsorption of gaseous species from the air. The sample stick was inserted into a top-loading cryofurnace for the duration of the experiment, and the sample was repeatedly dosed and reactivated in situ via a thermally-isolated capillary line.

Each dose of a known amount of gas was introduced to the sample at 250 K and slowly cooled to below the condensation/deposition point, at which point the pressure in the system decreased to almost zero. The sample was then cooled over 1 h to the measurement temperature of 10–15 K. No evidence was found any of in the diffraction patterns for the presence of frozen gases, implying that all of the gas was adsorbed by the sample. Diffraction data were acquired over the angular range 17° < 2θ < 137° with an incident neutron wavelength of 2.4425(1) Å, determined using a LaB₆ (NIST SRM 660b) standard reference material. A correction for the Debye-Scherrer ring curvature was applied before data reduction. The sample was re-activated prior to the introduction of new guest species by heating at 350 K under vacuum (~10⁻⁵ mbar) for approximately 1 h.

4.4. Structural Analysis

Rietveld structural refinements were performed using the program GSAS [25] with the EXPGUI [26] interface. A pseudo-Voigt peak profile function incorporating axial divergence asymmetry (CW neutron Type III, as defined in GSAS) was used, and a 12-term shifted Chebyshev background function was refined. Fractional coordinates and isotropic atomic displacement parameters (ADPs) were refined for all framework atoms. Fourier difference maps were generated in GSAS after initial refinement of the empty framework structure and visualised using VESTA [27] in order to identify the CO₂ adsorption sites. The CO₂ guests were modelled as complete molecules with variable site occupancies in subsequent refinement cycles.