Sizable dynamics in small pores: CO₂ location and motion in the α-Mg formate metal–organic framework

Abstract

Metal–organic frameworks (MOFs) are promising materials for carbon dioxide (CO₂) adsorption and storage; however, many details regarding CO₂ dynamics and specific adsorption site locations within MOFs remain unknown, restricting the practical uses of MOFs for CO₂ capture. The intriguing α-magnesium formate (α-Mg₃(HCOO)₆) MOF can adsorb CO₂ and features a small pore size. Using an intertwined approach of ¹³C solid-state NMR (SSNMR) spectroscopy, ¹H–¹³C cross-polarization SSNMR, and computational molecular dynamics (MD) simulations, new physical insights and a rich variety of information have been uncovered regarding CO₂ adsorption in this MOF, including the surprising suggestion that CO₂ motion is restricted at elevated temperatures. Guest CO₂ molecules undergo a combined localized rotational wobbling and non-localized twofold jumping between adsorption sites. MD simulations and SSNMR experiments accurately locate the CO₂ adsorption sites; the mechanism behind CO₂ adsorption is the distant interaction between the hydrogen atom of the MOF formate linker and a guest CO₂ oxygen atom, which are ca. 3.2 Å apart.

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Introduction

Carbon dioxide (CO₂) is the most abundant greenhouse gas in the Earth's atmosphere, but increasing levels of CO₂ emissions in the recent decades and the accompanying climate change^1,2 have negatively impacted human health,^3,4 increased the risk of extinctions,^5,6 and is acidifying the oceans.⁷ In recent years, widespread concerns over elevated atmospheric CO₂ concentrations have spurred interest in CO₂ capture,^8–10 sequestration,^11,12 and storage¹³ as potential solutions for climate change, but significant challenges persist. For example, techniques such as amine scrubbing of flue gas have been utilized to capture CO₂ generated during fossil fuel combustion, but are associated with high input energies and significant financial cost.^14,15 Catalysis has also been investigated as a potential solution with limited success; techniques such as catalytic hydrogenation of CO₂ remain economically unfeasible.¹⁶

Solid adsorbents, including zeolites and metal–organic frameworks (MOFs), have proven to be promising media for CO₂ capture and storage.^17–20 MOFs feature metal nodes or metal–inorganic secondary building units (SBUs) interconnected in three dimensions by organic linkers, forming highly porous structures that are well-suited for many industrially related applications²¹ such as gas adsorption,^22–24 separation,^25–27 and catalysis.^28–30 In particular, MOFs can be used for CO₂ capture and adsorption under a variety of conditions,^{19,24,25,31,32} as shown, for example, by the research groups of Eddaoudi^33–40 and Llewellyn.^41–48 Despite the abundance of MOFs suitable for CO₂ storage, new knowledge of CO₂ dynamic motions and their links to the CO₂ adsorption capacity of MOFs continues to be unlocked and unraveled; in particular, CO₂ motion and diffusivity in MOFs^49,50 is an active research area, with disseminated works by Jobic^41,49–53 and Maurin,^46,51,54,55 as well as Sholl^56–60 and Krishna.^61–68 Unlocking a deeper, more comprehensive understanding of adsorbed CO₂ dynamics within a variety of MOF systems and topologies is crucial for the rational design and development of future porous materials.

The α-magnesium formate (α-Mg₃(HCOO)₆) MOF is relatively straightforward and inexpensive to prepare,⁶⁹ is structurally stable across a wide range of temperatures as well as moderate pressures (i.e. ≤2 GPa),⁷⁰ and has demonstrated the ability to adsorb CO₂ gas with a very high isosteric heat of adsorption exceeding 25 kJ mol⁻¹.⁷¹ In the structure of α-Mg formate (Fig. 1(a)), Mg is octahedrally coordinated to six oxygen atoms originating from bound formate ligands. There are two types of chemically independent oxygen atoms present,^69,72 corresponding to oxygen atoms bound to either one or two Mg centers; in contrast, there are four crystallographically unique Mg sites. The extended lattice of α-Mg formate (Fig. 1(b)) is built by interconnecting edge-sharing MgO₆ octahedra, which give rise to MgO₆ chains interconnected by vertex-sharing MgO₆ octahedra, forming zig-zag shaped MOF channels that measure ca. 4.5 × 5.5 Å and propagate along the crystallographic b axis (Fig. 1(c)). All Mg centers in the α-Mg formate MOF are fully coordinated to six oxygen atoms and cannot directly interact with guest species. In contrast, the hydrogen atoms of the formate linkers are oriented toward the interior of the MOF channels, presenting a convenient interaction site for guest species; these hydrogen atoms may serve as the CO₂ adsorption sites in α-Mg formate.

Fig. 1 The local chemical environment of Mg in (α-Mg₃(HCOO)₆) is shown in (a), featuring six oxygen atoms arranged in an octahedral fashion. The polyhedra represent the MgO₆ octahedra. In (b), the extended crystal lattice of α-Mg formate as viewed down the crystallographic b axis is depicted. The zig-zag shaped porous channels which propagate along the crystallographic b axis of α-Mg₃(HCOO)₆ are shown in (c), from a viewpoint perpendicular to the b axis.

Several studies have been performed to investigate host–guest interactions in α-magnesium formate.^{70,71,73–77} Exceptional selective adsorption of C₂H₂ over other guest molecules including CO₂, H₂, N₂, O₂ and CH₄ takes place within α-magnesium formate, owing to interactions between the C₂H₂ hydrogen atoms and oxygen atoms from the framework.⁷⁸ The adsorption sites and dynamics of H₂, pyridine, benzene and N,N-dimethylformamide (DMF) guests adsorbed in α-Mg formate have been probed through the use of ¹H and ²H solid-state NMR (SSNMR).^77,7913C SSNMR is highly sensitive to molecular-level motions and has shown great utility for the investigation of CO₂^80–86 and CO^87,88 guest adsorption and dynamics in MOFs. Herein, variable temperature (VT) ¹³C and ¹H–¹³C cross-polarization (CP) SSNMR experiments are paired with molecular dynamics (MD) simulations to comprehensively investigate CO₂ adsorption locations and dynamics, along with host–guest interactions, in α-magnesium formate.

Experimental section

Synthesis

α-Mg₃(HCOO)₆ was synthesized following a solvothermal variation of the reported oil bath procedure;⁶⁹ the solvothermal route is summarized here. 0.77 g of Mg(NO₃)₂·6H₂O (Sigma-Aldrich, 99%) was dissolved in a mixture of 0.23 mL formic acid (HCOOH, Alfa Aesar, 97%) and 10 mL N,N dimethylformamide (DMF, Caledon, 99.9%) within a 30 mL cylindrical glass vial. The capped glass vial was then placed in a 110 °C oil bath for 72 h. The white crystalline “as-made” product was recovered by vacuum filtration and washed repeatedly with DMF. In order to remove all guests (i.e. residual DMF and excess formate linkers) from the MOF pores, the as-made sample was placed on a watch glass and heated in a 150 °C oven for 24 hours, yielding the “activated” MOF sample with empty channels.

Gas adsorption

Due to the low 0.96% natural abundance of the NMR-active ¹³C isotope,⁸⁹ isotopically enriched ¹³CO₂ (Sigma-Aldrich, 99% ¹³C) was used as the guest species. For simplicity, ¹³CO₂ is herein denoted as CO₂. A home-built Schlenk line integrated with a vacuum pump and a pressure gauge was used to perform a second activation process, followed by CO₂ loading of the MOF. First, ca. 0.14 g of the activated α-Mg₃(HCOO)₆ MOF was packed into the bottom of an L-shaped glass tube 5 mm in outer diameter, and then the MOF sample was secured in place by a small amount of glass wool. The L-shaped glass tube was attached to the Schlenk line, heated at 150 °C, and kept under dynamic vacuum (≤1 mbar) for 5 h in order to complete the sample activation process. A round-bottomed flask containing pressurized CO₂ was then attached to the Schlenk line, and a known amount of CO₂ gas was released into the Schlenk line and the attached glass tube, which together have a measured combined volume of 82.7 mL. The gas loading level in the MOF is described using the molar ratio between CO₂ guests and Mg. In this study, the gas loading level was 0.1 CO₂/Mg. The L-shaped glass tube was then immersed into liquid nitrogen in order to freeze CO₂ gas within the MOF sample; a flame-sealing procedure was used to isolate the glass tube containing the CO₂-loaded MOF sample from the Schlenk line in order to perform NMR experiments.

Powder X-ray diffraction (pXRD)

Powder X-ray diffraction experiments were used to verify the MOF identity and purity. All pXRD measurements were performed on a Rigaku diffractometer operating using Co Kα radiation (λ = 1.7902 Å). Samples were examined through 2θ values ranging from 5 to 45°, using increments of 0.02° and a scan rate of 10° per min. The experimental pXRD patterns are shown in Fig. S1 (ESI†), and are in good agreement with simulated patterns based on the reported crystal structure.⁶⁹

SSNMR characterization

SSNMR experiments were performed on a Varian Infinity Plus spectrometer, which was equipped with a 9.4 T Oxford Instruments superconducting magnet and a double channel (HX) 5 mm Varian/Chemagnetics static probe. The experimental temperature was adjusted between 173 and 393 K using a Varian VT temperature control unit, and experimental temperature readings were calibrated using the ²⁰⁷Pb chemical shift of solid Pb(NO₃)₂.⁹⁰ All direct-excitation ¹³C SSNMR experiments were performed using the DEPTH⁹¹ or DEPTH-echo⁸³ pulse sequences, utilizing an optimized 90° pulse length of 3.00 μs, along with calibrated recycle delays of 3 s for acquisitions at temperatures ≥293 K, and recycle delays of 5 s for experimental temperatures <293 K. Each ¹³C SSNMR spectrum was assembled from 1280 or 2560 scans, except for the 293 K spectrum, which was constructed from 12 800 scans. Static ¹H–¹³C CP experiments were carried out on both activated and CO₂-loaded α-Mg formate samples to investigate the adsorption site locations; individual spectra were acquired at temperatures of 173 K and 293 K using CP mixing times of 0.5, 3, 6, 8, and 10 ms. At CP experimental temperatures ≥293 K, a 1 s recycle delay was employed, while the recycle delay was 1.2 s at temperatures <293 K. All VT ¹H–¹³C CP experimental spectra were assembled from 1024 individual scans. The chemical shifts of all ¹³C spectra were referenced to tetramethylsilane (TMS) using the methylene carbon resonance of ethanol at δ_iso = 56.83 ppm⁹² as a secondary reference.

Chemical shift (CS) tensor convention

The ¹³C powder patterns in this study are broadened and dominated by the chemical shift (CS) interaction. The CS interaction can be modeled by a second-rank tensor defined by the three orthogonal components δ₁₁, δ₂₂ and δ₃₃, which are ordered such that δ₁₁ ≥ δ₂₂ ≥ δ₃₃. There are three NMR parameters that are used to describe SSNMR powder pattern lineshapes and the CS tensor: the isotropic chemical shift (δ_iso, δ_iso = (δ₁₁ + δ₂₂ + δ₃₃)/3), the span (Ω, Ω = δ₃₃ − δ₁₁), and the skew (κ, κ = 3(δ₂₂ − δ_iso)/Ω). The WSolids⁹³ and Dmfit⁹⁴ software packages were used to analytically simulate the experimental spectra and extract the observed, or apparent, ¹³C NMR parameters. The EXPRESS⁹⁵ software package was used to simulate the effects of different types and rates of dynamic motion on the observed ¹³C SSNMR spectra and ¹³C NMR parameters, given that the known parameters for static, stationary CO₂ are δ_iso = 125 ppm, Ω = 335 ppm, and κ = 1.⁹⁶ The localized rotation of CO₂ molecules is modeled by a sixfold “wobbling” motion, and the non-localized two-site jumping or “hopping” CO₂ motion is modeled by a twofold exchange. The rate of all motions is considered to be “fast” (i.e. ≥10⁷ Hz).

Molecular dynamics (MD) simulations

The α-Mg formate 3 × 4 × 3 supercell was constructed as a simulation box, where the unit cell parameters and coordination were obtained from reported values.⁶⁹ The amount of CO₂ was set to 45 molecules, according to the employed gas loading ratio of 0.1 CO₂/Mg for SSNMR experiments. The dispersive interactions between CO₂ and α-Mg formate were modeled using a Lennard-Jones (L-J) 12-6 potential. The L-J and point charge parameters for α-Mg formate and CO₂ were obtained from literature values,^74,97 while the interactions between different atoms were calculated using Lorentz–Berthelot mixing rules. The cutoff for dispersive interactions was set to 16 Å, and the Ewald summation method was used to account for long-range electrostatic interactions. The MD simulation incorporated a canonical ensemble (i.e. a NVT ensemble) using Hoover thermostats. Temperatures from 173 to 393 K were considered in the simulations. The simulations ran for 10 ns to ensure that the entire system was fully equilibrated, followed by 10 ns of production running to obtain the CO₂ trajectory, where the time step was set to 2 fs. All MD simulations were performed using the DL_POLY 2.20 package.⁹⁸

Results and discussion

¹³C VT SSNMR experiments

¹³C VT SSNMR experiments were performed on CO₂-loaded α-Mg formate at temperatures ranging from 173 K to 393 K, yielding spectra that feature a single broad powder pattern and are profoundly influenced by the experiment temperature (Fig. 2(a)). In addition to the broad powder pattern, there is also a sharp resonance at ca. 125 ppm present in spectra acquired at temperatures ≥333 K.

Fig. 2 (a) The experimental ¹³C SSNMR spectra of CO₂ adsorbed in α-Mg formate at temperatures ranging from 173 K to 393 K are shown. The red asterisk (*) and the red dashed line indicate the contributions from mobile CO₂ undergoing rapid isotropic motion. A deconvolution of the 393 K ¹³C SSNMR spectral lineshape is shown in (b), highlighting the contributions of the powder pattern associated with adsorbed CO₂ along with the second sharp resonance originating from mobile CO₂.

The sharp resonance originates from mobile CO₂ undergoing rapid isotropic motion (i.e. tumbling), which removes the ¹³C chemical shift anisotropy (CSA) and gives rise to a narrow resonance; this is consistent with our prior observations of free CO₂ in MOFs,^82,83,85 and is near the reported ca. 132 ppm isotropic chemical shift (δ_iso) of CO₂.⁹⁶ In contrast, the broad ¹³C powder pattern arises from CSA, and thus the corresponding CO₂ molecules are not undergoing rapid isotropic tumbling. Given that CO₂ in this system must be either freely isotropically tumbling through space or adsorbed within α-Mg formate, the broad powder pattern is assigned to adsorbed CO₂. Furthermore, the observation of a single broad powder pattern indicates that adsorbed CO₂ resides in only one type of local environment, meaning that one unique CO₂ adsorption site, multiple symmetry-equivalent adsorption sites, or multiple CO₂ adsorption sites in quite similar local environments are present.

Analytical simulations of the ¹³C SSNMR spectra were performed in order to obtain the observed ¹³C NMR parameters, with a detailed 393 K simulation shown in Fig. 2(b), and the entire set of simulations shown in Fig. 3. The δ_iso, span (Ω), and skew (κ) values extracted from simulations are summarized in Table 1, and illustrated in graph form in Fig. 4. Simulations of the broad powder pattern began with a fixed value of δ_iso = 125 ppm at all temperatures and required little adjustment despite changes in the experimental lineshape; this value is very similar to that of static, stationary CO₂,⁹⁶ confirming that the broad resonance corresponds to adsorbed CO₂. At the lowest experimental temperature of 173 K, the ¹³C powder pattern is at its broadest, corresponding to Ω = 69(2) ppm and κ = 0.64(2). The discrepancy between these values versus the NMR parameters for solid, static CO₂ (Ω = 335 ppm, κ = 1 at 20 K)⁹⁶ indicates that the ¹³C CSA of adsorbed CO₂ guests in α-Mg formate is being partially averaged by some phenomenon. Both Ω and κ decrease as temperatures rise from 173 K to 333 K, however, Ω and κ then increase with experimental temperature from 313 K to 393 K. The strong dependence of observed Ω and κ (i.e. the partial averaging of ¹³C CSA) with temperature indicates that adsorbed CO₂ undergoes restricted dynamic motion in α-Mg formate.

Fig. 3 The (a) experimental and (b) analytically simulated ¹³C SSNMR spectra of CO₂ adsorbed in α-Mg formate at temperatures from 393 to 173 K are depicted. Note that there is no contribution from free CO₂ to the experimental lineshape at temperatures below 333 K. In (c), the simulated contributions of only the adsorbed ¹³C powder pattern are shown.

Table 1 The observed, or apparent, ¹³C NMR parameters of CO₂ adsorbed in α-Mg formate

Temperature (K)	δ iso (ppm)	Span (Ω, ppm)	Skew (κ)
393	127(1)	36(1)	−0.56(2)
373	127(1)	33(1)	−0.70(2)
353	127(1)	32(1)	−0.81(2)
333	126(1)	31(1)	−0.81(2)
313	126(1)	30(1)	−0.83(3)
293	125(1)	30(1)	−0.58(2)
273	125(1)	32(1)	−0.31(1)
253	125(1)	34(1)	−0.05(1)
233	125(1)	39(1)	0.24(1)
213	125(1)	47(2)	0.43(1)
193	124(1)	57(2)	0.58(2)
173	124(1)	69(2)	0.64(2)

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Fig. 4 This chart illustrates the observed, or apparent, CS tensor parameters associated with CO₂ adsorbed in α-Mg formate at experimental temperatures ranging from 173 to 393 K, see Table 1 for the measured values. Note the pronounced increase in span and skew as the temperature is reduced from 313 K to 173 K, and also as the temperature is increased from 313 to 393 K; the temperature where trends in span and skew begin to reverse (313 K) is indicated with a red dashed line, which could represent some phase change or change in unit cell dimensions, such as negative thermal expansion.

The reduction in apparent Ω values as the temperature rises from 173 K to 313 K indicates that CO₂ molecules gain a higher degree of mobility with increasing temperature. In comparison, the increase in Ω from 313 to 393 K suggests that CO₂ mobility is more restricted at higher temperature within this temperature range, which is not intuitive. It is important to emphasize that this unexpected trend of decreased guest gas motion at higher temperatures has not been observed in SSNMR experiments examining guest gases in a variety of other MOF systems,^{77,80–83,85,87} raising the possibility of a subtle high-temperature structural change in α-Mg formate that acts to reduce CO₂ mobility. Although high-temperature structural changes have not yet been documented in α-Mg formate, there is precedence in other MOF systems. For example, MOF-5 was reported to exhibit negative thermal expansion (NTE),⁹⁹ meaning that the MOF-5 unit cell shrinks as the temperature increases. It is possible that α-Mg formate also exhibits NTE at higher temperature, leading to slightly smaller channels and restricted CO₂ movements. Unfortunately, to the best of our knowledge, no previous studies have been performed to investigate the possibility of temperature-induced structural changes in α-Mg formate.

In order to understand what the ¹³C NMR parameters and their temperature dependence physically represent in terms of CO₂ motion, the location of the adsorption sites within this MOF must be first established. There are six crystallographically unique formate hydrogen atoms in α-Mg formate;^69,79 three of these hydrogen atoms are positioned along the MOF channel interior, permitting direct interactions with guest species and serving as likely CO₂ adsorption sites. In order to investigate the spatial connectivity between the framework hydrogen atoms and the carbon atoms of adsorbed CO₂ molecules, static ¹H–¹³C CP SSNMR experiments were performed on CO₂-loaded samples of α-Mg formate.

Exploring the specific CO₂ adsorption sites in α-Mg formate

The CP experiment is mediated by the ¹H–¹³C dipolar interaction, which is dependent on the internuclear distance between ¹H and ¹³C spin pairs; only ¹³C nuclei which are proximate to ¹H nuclei will engage in strong ¹H–¹³C dipolar coupling and give rise to a ¹³C NMR resonance of high intensity.^100,101 During the ¹H–¹³C CP experiment, spin polarization is transferred from ¹H nuclei to ¹³C nuclei via simultaneous rf irradiation at both Larmor frequencies for some duration of time in the ms regime, which is known as the mixing time or contact time. The duration of contact time is crucial: shorter contact times act as a spectral filter and generally favor the detection and enhancement of framework-based ¹³C resonances, given that C and H are directly bound to each other within the linker. Longer contact times typically discriminate in favor of the signals of ¹³C nuclei that are more distant from ¹H. Accordingly, the ¹H–¹³C CP experiments performed in this study were carried out using a variety of contact times, ranging from 0.5 to 10 ms, in order to investigate the location of CO₂ adsorption sites within α-Mg formate.

The ¹H–¹³C CP SSNMR spectra of activated and ¹³CO₂-loaded α-Mg formate obtained using a variety of CP contact times are illustrated in Fig. 5. Although the framework carbon atoms of α-Mg formate were not ¹³C enriched, they are directly bound to hydrogen atoms (i.e. highly proximate), and thus their corresponding resonances are readily detected in ¹H–¹³C CP experiments. The background ¹³C lineshape originating from the framework carbon atoms consists of a wide, intense resonance centered at ca. 180 ppm with two broad overlapping features located at ca. 130 ppm and 220 ppm (Fig. 5). When a short contact time of 0.5 ms is implemented, the ¹H–¹³C CP spectra of CO₂-loaded α-Mg formate at both 173 and 293 K appear essentially identical to those of the empty activated frameworks (Fig. 5, bottom); no resonances originating from adsorbed CO₂ are detected due to the relatively long distances and concomitant weak dipolar coupling between framework ¹H atoms and ¹³C atoms of CO₂ molecules that is further weakened by molecular motions.

Fig. 5 The experimental static ¹H–¹³C CP SSNMR spectra obtained using various CP contact times at temperatures of (a) 173 K and (b) 293 K are depicted in the form of blue and red spectral traces. The red traces are ¹H–¹³C CP SSNMR spectra of empty activated α-Mg formate, while the blue spectra are the ¹H–¹³C CP SSNMR spectra of CO₂-loaded α-Mg formate. The black traces at the top of the figure are the direct-excitation ¹³C SSNMR spectra of CO₂-loaded α-Mg formate obtained at 173 K and 293 K, shown for comparison purposes to illustrate how the ¹³C powder pattern of adsorbed CO₂ is clearly detected in ¹H–¹³C CP experiments.

As contact times are extended at 173 and 293 K, an additional ¹³C powder pattern emerges between ca. 100 and 160 ppm (Fig. 5, yellow box), which exhibits an intensity that increases with contact time. When a contact time of 10 ms is used, this additional resonance is strikingly similar in lineshape to that observed from CO₂ in the direct-excitation ¹³C SSNMR spectrum of CO₂-loaded α-Mg formate (Fig. 5, top), indicating that ¹H–¹³C CP to CO₂ is now efficient. Recall that as the contact time is increased, CP becomes more efficient across longer internuclear distances, and ¹³C atoms that are progressively further from ¹H are detected. In α-Mg formate, the resonance associated with CO₂ gradually emerges from the background signal of the activated framework as longer contact times are used, revealing that the hydrogen atoms from the framework and carbon atoms from CO₂ molecules are indeed dipolar coupled. These spectra serve as clear evidence that adsorbed CO₂ molecules in α-Mg formate are proximal to the hydrogen atoms of the framework at all experimental temperatures, and strongly suggest that these hydrogen atoms serve as the CO₂ adsorption sites.

Of special note is the temperature-dependent relative intensity of the ¹H–¹³C CP resonance that corresponds to adsorbed CO₂ in this system. At 173 K and using a contact time of 10 ms, the ¹³CO₂ resonance is intense and easy to distinguish from the broad ¹³C framework powder pattern. In contrast, the ¹³CO₂ resonance obtained at 293 K and a contact time of 10 ms is relatively less intense and harder to discern from the underlying background powder pattern in ¹H–¹³C CP SSNMR experiments. The temperature-dependent intensity of the ¹³CO₂ resonance is another strong indication that adsorbed CO₂ molecules are in motion within α-Mg formate. When one or both nuclei participating in CP experiments are undergoing dynamics, the ¹H–¹³C dipolar vector is continually altered; this modulation significantly reduces the effective ¹H–¹³C dipolar coupling, rendering the ¹³C resonance challenging or impossible to detect in CP experiments. At 293 K, CO₂ is relatively mobile in α-Mg formate, which reduces the effective ¹H–¹³C dipolar interaction and corresponds to a relatively less intense ¹³C resonance in ¹H–¹³C CP SSNMR experiments. In contrast, CO₂ mobility is reduced in α-Mg formate at low temperatures (vide supra), which gives rise to a relatively stronger effective ¹H–¹³C dipolar interaction and a more intense ¹³C resonance in ¹H–¹³C CP SSNMR spectra.

¹H–¹³C CP SSNMR data have yielded unambiguous proof that adsorbed CO₂ is proximal to the H atoms lining the pores of α-Mg formate; however, further complementary characterization is required to understand exactly where CO₂ is positioned and what motion it undergoes in this system. To further probe the location of adsorbed CO₂ within α-Mg formate, its potential interactions with framework hydrogen atoms, and the number of CO₂ adsorption sites, computational molecular dynamics (MD) simulations were performed.

MD simulations, atomic position distributions, and CO₂ adsorption site locations

The distribution of carbon atoms of CO₂ within α-Mg formate at 253 K, as predicted by MD simulations, is shown from three different crystallographic perspectives in Fig. 6. The most striking feature of these simulations is that they suggest two separate localized CO₂ adsorption sites exist in this MOF. In order to reconcile MD simulations and VT ¹³C SSNMR results, there are two possibilities: either the two adsorption sites are symmetry-related and there is only one crystallographically unique CO₂ adsorption site, or both adsorption sites are indeed crystallographically distinct but situated in strikingly similar local environments in α-Mg formate.

Fig. 6 Several different projections of the distribution of carbon atoms of CO₂ in α-Mg formate at 253 K, as predicted by molecular dynamics (MD) simulations, are shown. The lightly shaded areas represent the MOF channels. The distribution is shown as projected on (a) the yz plane, (b) the xz plane, and (c) the xy plane. The colors of C, H, O, and Mg atoms in the structure are gray, white, red and green, respectively.

There is an interesting asymmetry about the distribution of carbon atoms when viewed in the yz plane (Fig. 6(a)) and the xy plane (Fig. 6(c)), which almost appears as “tails” leading towards an adjacent adsorption site. As the temperature is increased, MD simulations predict that these “tails” of carbon atom distributions increase in intensity at the expense of intensity in the main elliptical region of probability density (Fig. S2, ESI†). The interpretation of spreading this carbon probability density between the adsorption sites is that (i) CO₂ must be mobile within α-Mg formate, and (ii) CO₂ mobility generally increases with experimental temperature. Both of these findings are in good agreement with the results from ¹³C and ¹H–¹³C CP SSNMR experiments (vide supra).

MD simulations also provide the distribution of CO₂ oxygen atoms in the α-Mg formate MOF. In Fig. 7(a), four sets of localized intensity pairs are depicted, corresponding to four pairs of oxygen atoms associated with CO₂ molecules (i.e. there are four CO₂ molecules pictured in Fig. 7(a)). Each individual defined region of intensity represents one of the two oxygen atoms belonging to a single CO₂ molecule. For clarity, CO₂ molecules are superimposed over the distribution of oxygen atoms in Fig. 7(b). There again appear to be two adsorption sites in a single channel (Fig. 7, lightly shaded region), but much like in the case of the carbon atom distributions, the adsorption sites associated with these two pairs of oxygen distributions must be either symmetry related or reside in similar local environments in order to agree with the ¹³C VT SSNMR results. Equally as important, the localized regions of individual oxygen distributions are relatively large and assume a decidedly asymmetric shape, implying the existence of some localized CO₂ motion upon the adsorption site. The last notable fact that can be drawn from Fig. 7 is that the two oxygen atoms of a single CO₂ molecule have different degrees of mobilities, as evidenced by the unique and dissimilar shapes of their probability distributions; this again indicates that some localized CO₂ motion is likely present.

Fig. 7 The xy plane projection of the distribution of oxygen atoms of CO₂ in α-Mg formate at 253 K is shown in (a), as predicted by molecular dynamics (MD) simulations; the lightly shaded areas highlight the MOF channels. In (b), CO₂ molecules are superimposed over the distribution of oxygen atoms for clarity. Note that the relatively large localized distributions of oxygen atoms imply some type of localized CO₂ motion on the adsorption site. The colors of C, H, O, and Mg atoms in the structure are gray, white, red and green, respectively.

An extended view of the oxygen atom distribution positioned perpendicular to the b-axis of α-Mg formate (i.e. perpendicular to the MOF channels) also provides insight into CO₂ adsorption locations and motion within this system (Fig. 8). From these simulations, it can again be seen that CO₂ molecules reside at two well-defined adsorption sites located within the zig-zag shaped channels. Furthermore, as in the case of carbon, there is some residual oxygen probability that seems to connect adjacent adsorption sites, hinting that there is non-localized motion of CO₂ between adsorption sites; this motion must be in addition to the localized motion upon each adsorption site indicated by the asymmetric and distinct shape of the individual oxygen atom distributions in Fig. 7. In order to further investigate the motion of CO₂ in this MOF, the exact location of CO₂ must first be ascertained.

Fig. 8 The projection of the distribution of oxygen atoms of CO₂ in α-Mg formate at 253 K along the b axis, as predicted by molecular dynamics (MD) simulations; a legend is provided in top right.

Position and angle of CO₂ relative to the adsorption site

MD simulations were used to probe the orientation of adsorbed CO₂ with respect to the adsorption site, along with the relevant distances involved in the adsorptive interaction. A recent report has shown that dimethylformamide (DMF) guests in α-Mg formate participate in weak C–H⋯O hydrogen bonding with the framework formate linkers.⁷⁹ In addition, previous reports have consistently indicated that CO₂ adsorption in MOFs occurs through some variation of side- or end-on binding to the CO₂ oxygen atoms.^{23,81,85,102–105} Since ¹H–¹³C CP SSNMR experiments have indicated proximity between H atoms in the MOF and ¹³C atoms in CO₂ (vide supra), it is highly likely that CO₂ interacts with the MOF hydrogen atoms lining the pores of α-Mg formate via the CO₂ oxygen atoms in end- or side-on C–H⋯O attractive interactions.

Within α-Mg formate, only three of the six crystallographically unique formate hydrogen atoms are oriented toward the pore interior and are accessible to CO₂ molecules, while the three other unique hydrogen atoms are “hidden” within the zigzag chains and inaccessible to guests (see Fig. S4, ESI†). According to MD simulations, both of the CO₂ adsorption sites are located in close vicinity to the formate hydrogen atoms within the MOF pores, implying that these sites play a prominent role in CO₂ adsorption. The calculated radial distribution functions and corresponding internuclear distances from MD simulations are shown in Fig. 9. The radial distribution functions predict only very small changes in H(formate)–O(CO₂) and H(formate)–C(CO₂) distances from 173 to 393 K. The distance between the closest hydrogen atom and the oxygen atom of CO₂ is ca. 3.2 Å and the C–H⋯O vector is linear, confirming that hydrogen bonding or a distant attractive interaction between formate linkers and CO₂ guests is the driving adsorptive interaction in this MOF. The distance between the formate hydrogen atom and the carbon atom of CO₂ is ca. 3.9 Å, while the H⋯O–C angle is about 120°.

Fig. 9 The radial distribution functions obtained from MD simulations between the formate hydrogen atom and CO₂ are shown, at temperatures ranging from 173 to 393 K. In (a), the calculated H(formate)–O(CO₂) distance is illustrated, while (b) depicts the predicted H(formate)–C(CO₂) distance. According to these radial distributions, the most probable H⋯O–C interaction angle is ca. 120°.

MD simulations have yielded the distributions of carbon and oxygen atoms, oriented adsorbed CO₂ in the channel, confirmed the existence of an attractive interaction between formate hydrogen atoms and CO₂ oxygen atoms, and strongly suggested that CO₂ is participating in both localized and non-localized motion within α-Mg formate. With this knowledge, ¹³C SSNMR spectra can now be motionally simulated to obtain the specific types of guest motions present, along with their respective motional rates and angles.

Additional information regarding CO₂ motion in α-Mg formate

¹³C SSNMR spectra of CO₂ are dominated by the CS interaction, which gives rise to a broad powder pattern when the CO₂ molecule is static. When the CO₂ molecule is undergoing well-defined motion, the ¹³C CS interaction is modulated by the specific motion(s) in a predictable manner. Using the EXPRESS software package,⁹⁵ with reliable knowledge of the static⁹⁶ and experimental motionally influenced CO₂¹³C NMR parameters (Table 1), and joined with MD simulation data regarding the CO₂ adsorption location and motion, the effects of well-defined dynamic motion on SSNMR spectra can be simulated in order to extract motional information. The ¹³C powder pattern of CO₂ adsorbed in α-Mg formate is shown in Fig. S5(a) (ESI†), along with corresponding motional simulations in Fig. S5(b) (ESI†). The experimental ¹³C spectra could only be simulated by incorporating a combination of two motions: a C₆ sixfold rotation through an angle α, as well as a C₂ twofold jumping through an angle β. As seen from Fig. S5(c and d) (ESI†), motional simulations based only on a C₆ rotation as well as simulations considering only a C₂ hopping fail to match experimental spectra, proving unambiguously that both the C₆ and C₂ dynamic motions must be present. The spectral simulations also reveal that both motions occur at a rate ≥10⁷ Hz, which is classified as the fast motion on the NMR timescale and consistent with previous reports of CO₂ dynamics in MOFs at similar experimental temperatures.^81–83,85

In CO₂-loaded α-Mg formate, it is quite likely that the C₆ rotation is a model for localized wobbling of CO₂ upon the adsorption site through a continuum of orientations traced out by α, while the C₂ jumping represents a non-localized “hopping” of CO₂ molecules between two proximate adsorption sites. In this context, α corresponds to the angle between the time-averaged CO₂ orientation (i.e. the localized rotational axis) and the edge of the rotational cone of motion, while β denotes the angle between the localized rotational axis and the non-localized hopping axis. The proposed motions of CO₂ in α-Mg formate along with depictions of α and β are shown in Fig. S6 (ESI†), while the values of α and β are shown in Table S1 (ESI†). These findings are in good agreement with previous studies on CO₂ adsorption in MOFs. CO₂ in MIL-53 also participates in a localized wobbling modeled by a C₆ rotation upon the adsorption site and a twofold hopping between symmetry-equivalent adsorption sites,⁸³ while CO₂ in CPO-27-Mg or Mg–MOF-74 undergoes a localized C₆ rotational wobbling upon a single adsorption site as well as a simultaneous non-localized sixfold hopping between symmetry-equivalent adsorption sites.^81,82 In addition, CO₂ in two SDB-based MOFs has exhibited similar wobbling and hopping behavior.⁸⁵

The motional angles derived from dynamic simulations, α and β, also encode valuable dynamic information (Table S1, ESI†). As the temperature is increased from 173 to 293 K, the wobbling angle α also increases from 45 to ca. 49°; additional thermal energy competes with the adsorptive interaction between CO₂ and the MOF, and the result is that CO₂ locally samples a larger volume of space. Above 293 K, α is generally invariant, although this is somewhat unexpected because α should logically keep on increasing with temperature. In comparison, the twofold hopping angle β increases steadily from 23° at 173 K to 45° at 313 K, but then decreases from 45° at 333 and 353 K to 41° at 393 K. The trends in α, β, Ω, and κ suggest that some subtle structural change occurs in the α-Mg formate MOF at around 313 K. The noticeable drop in β at high temperatures hints that there is less spatial area available for adsorbed CO₂; this likely corresponds to a smaller MOF channel and again hints that negative thermal expansion may be occurring in α-Mg formate.

With the CO₂ motions established from SSNMR experiments and CO₂ adsorption locations revealed from MD simulations, it is now possible to illustrate a motional model for CO₂ in α-Mg formate based on both sets of information. The CO₂ guests participate in an adsorptive interaction with the formate linker hydrogen atoms that are accessible from the pore interior. CO₂ locally wobbles at each adsorption site (Fig. S7(a), ESI†), and should undergo a non-localized twofold hopping to the next adjacent adsorption site (Fig. S7(b), ESI†). The complementary nature and good agreement between the localized and non-localized motions predicted by MD simulations and confirmed by ¹³C SSNMR experiments validate the motional model based on SSNMR experiments.

Conclusions

Comprehensive knowledge regarding CO₂ adsorbed within α-Mg formate, a prototypical small-pore MOF with important applications in carbon capture, has been unraveled using complementary VT ¹³C SSNMR experiments and MD simulations. This work has unlocked exciting and detailed new physical insights in this system, including the number and the location of CO₂ adsorption sites, interatomic distances and angles between the moieties involved in CO₂ adsorption, the specific adsorptive interaction responsible for CO₂ capture, and intimate details of CO₂ motion; this work also reveals the unexpected phenomenon of restricted CO₂ motion in α-Mg formate at elevated temperatures.

In this MOF, there is one crystallographically unique CO₂ adsorption site or two CO₂ adsorption sites located in very similar local environments. ¹³C SSNMR experiments indicate that adsorbed CO₂ molecules exhibit two types of simultaneous motions at rates ≥10⁷ Hz across all temperatures between 173 and 393 K: a localized rotation upon the adsorption site, as well as a twofold hopping between adsorption sites. The geometry, location, and interactions of adsorbed CO₂ molecules within the MOF have been uncovered; CO₂ is located ca. 3.2 Å from the hydrogen atom of the formate linker, the H(formate)⋯O–C(CO₂) angle is 120°, and the C–H(formate)⋯O(CO₂) angle is 180°, indicating that the main adsorptive interaction in this system is a distant interaction between the formate MOF linkers and CO₂. Above 313 K, anomalies in the observed ¹³C NMR parameters and CO₂ motional angles suggest that motion is restricted due to some subtle change in the structure of α-Mg formate, which may result from negative thermal expansion or another process that decreases the channel volume.

Undoubtedly, the final step to unravel the mystery of restricted CO₂ motion at elevated temperatures in α-Mg formate will be a series of detailed powder and single crystal X-ray diffraction experiments in the future, in conjunction with VT SSNMR, MD simulations, IR spectroscopy, and additional complementary characterization routes; any additional knowledge gained regarding this phenomenon will be invaluable for the investigation and rational design of small-pore MOFs for applications in carbon capture and guest adsorption. Pursuing such a strategy, which will result in the accumulation of comprehensive knowledge of CO₂ dynamics and their connection to CO₂ adsorption in a variety of MOFs, offers a very promising avenue to realizing practical applications for MOFs as CO₂ adsorbents.

Acknowledgements

Y. H. thanks the Natural Science and Engineering Research Council (NSERC) of Canada for a Discovery grant and a Discovery Accelerator Supplements Award. A. Z. acknowledges financial support from the National Natural Science Foundation of China (grants 21522310 and 21473244) as well as the Natural Science Foundation of Hubei Province of China (2014CFA043).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp00199a

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