1 Supplementary Information for : Metal – organic frameworks as O 2-selective adsorbents for air separations

Oxygen is a critical gas in numerous industries and is produced globally on a gigatonne scale, primarily through energy-intensive cryogenic distillation of air. The realization of large-scale adsorption-based air separations could enable a significant reduction in associated worldwide energy consumption and would constitute an important component of broader efforts to combat climate change. Certain small-scale air separations are carried out using N2-selective adsorbents, although the low capacities, poor selectivities, and high regeneration energies associated with these materials limit the extent of their usage. In contrast, the realization of O2-selective adsorbents may facilitate more widespread adoption of adsorptive air separations, which could enable the decentralization of O2 production and utilization and advance new uses for O2. Here, we present a detailed evaluation of the potential of metal–organic frameworks (MOFs) to serve as O2-selective adsorbents for air separations. Drawing insights from biological and molecular systems that selectively bind O2, we survey the field of O2-selective MOFs, highlighting progress and identifying promising areas for future exploration. As a guide for further research, the importance of moving beyond the traditional evaluation of O2 adsorption enthalpy, ΔH, is emphasized, and the free energy of O2 adsorption, ΔG, is discussed as the key metric for understanding and predicting MOF performance under practical conditions. Based on a proof-of-concept assessment of O2 binding carried out for eight different MOFs using experimentally derived capacities and thermodynamic parameters, we identify two existing materials and one proposed framework with nearly optimal ΔG values for operation under user-defined conditions. While enhancements are still needed in other material properties, the insights from the assessments herein serve as a guide for future materials design and evaluation. Computational approaches based on density functional theory with periodic boundary conditions are also discussed as complementary to experimental efforts, and new predictions enable identification of additional promising MOF systems for investigation.


Table of Contents
Section S1. Minimum work calculation 2 Section S2. Comparison of energy demand between N2-and O2-selective adsorbents 3 Section S3. Estimate of entropic contributions to O2 binding 4 Section S4. Adsorption isotherm fitting 5 Section S5. Differential enthalpies and entropies of adsorption 6 Section S6. Calculation of ∆G for VSA and VTSA model processes 7 Section S7. DFT calculations of O2 binding in MOFs  8  Figures  12  Tables  18  References  29 Electronic Supplementary Material (ESI) for Chemical Science. This journal is © The Royal Society of Chemistry 2022

Section S1. Minimum Work Calculations
By combining the first and second laws of thermodynamics, one can establish a useful framework for assessing the theoretical energy requirement for a separation process. The minimum separation work for a multicomponent stream of ideal gases (e.g., O2 and N2 at near-ambient temperature and pressure) can be written as follows:

Section S2. Comparison of energy demand between N2-and O2-selective adsorbents
As a simple estimate, assume that the energy consumption of a given adsorption process is directly correlated with the energy required to regenerate the adsorbent. 1 We can use the negative of the enthalpy of adsorption as a proxy for the required desorption energy. As such, enthalpies of adsorption enable a crude comparison of energy demands across various adsorption processes.
In numerous examples, it has been shown that ΔH of adsorption represents about half of the total energy required for regeneration. 2 Consider that Li-LSX exhibits an N2 binding enthalpy of −22.5 kJ/mol. 3 For every 1 mole of air that is separated, 0.78 mol N2 × 22.5 kJ/mol = 17.55 kJ are required to regenerate the material. Alternatively, assume an O2-selective material exhibits an O2 binding enthalpy of −45 kJ/mol. For every 1 mole of air that is separated, 0.21 mol O2 × 45 kJ/mol = 9.45 kJ are required to regenerate the material. Thus, in this example, the O2-selective material is about twice as energy efficient in separating O2 from N2.

Section S3. Estimate of entropic contributions to O2 binding
The entropy of O2 binding in an adsorbent, ΔS, is dominated by the loss of the two rotational and three translational degrees of freedom of gaseous O2, which become low-frequency vibrations upon binding (see Figure S1). 4 Smaller contributions arise from changes in the spin state of the metal and bound O2 species. The change in O2 entropy upon binding can be estimated from a sum of terms shown in eq. 1-5.
Eq. 1 is the molar rotational entropy of a rigid diatomic rotor, where R is the ideal gas constant, T is the temperature, s is the symmetry number (2 for a homonuclear diatomic), and Θrot is the rotational temperature (2.08 K for O2).

3+8&9 = ;
: ' 5 ;< ! < + 5 /2 Eq. 2 is the Sacktur-Tetrode equation for molar translational entropy of an ideal gas, where R is the ideal gas constant, T is the temperature, kB is the Boltzmann constant, P is the pressure, and L is the thermal wavelength (1.79 ×10 −11 m for O2 at 298 K).
Eq. 3 is the molar electronic entropy due to spin degeneracy, where S is the total spin of the system, operating under the assumption that the spin sublevels are approximately degenerate (i.e., split by an amount that is small relative to kBT).
Eq. 4 is the molar vibrational entropy of a harmonic oscillator, where Θvib = ℏ / D is the vibrational temperature, with ℏ the vibrational energy.
Lastly, eq. 5 is the molar configurational entropy due to indistinguishable binding modes, where σ ' # is the symmetry number of O2 (2 for a homonuclear diatomic), and σ G is the symmetry number of the metal center. As an example, O2 binding to a D4h symmetric heme corresponds to a symmetry number of σ ' # σ G = 16.
The overall expression for the molar entropy change upon binding is then given as eq. 6, where the sum is taken over the five vibrational modes of the MO2 unit highlighted in Figure S1:

Section S4. Adsorption isotherm fitting
Low-pressure isotherms were fit with a dual-site Langmuir-Freundlich equation (eq. 7), where n is the total amount adsorbed in mmol/g, P is the pressure in bar, nsat,i is the saturation capacity in mmol/g, bi is the Langmuir parameter in bar −1 defined in eq. 2, and vi is the Freundlich parameter for each site. 5 For eq. 8, Si is the site-specific entropy of adsorption in units of J/(mol⋅K), Ei is the enthalpy of adsorption in units of kJ/mol, R is the ideal gas constant in units of J/(mol⋅K), and T is the temperature. In the case of Cu I -MFU-4l and Fe-PCN-224, published isotherm data were newly fit to obtain the fit parameters. For the remaining frameworks (Co2(OH)2(bbta), Fe-BTTri, Co-BTTri, Co-BDTriP, Mn-PCN-224, and Co-PCN-224), the published fit parameters were used directly to determine binding enthalpies and entropies (see Tables S1 to S9). For Li-LSX, the published parameters from Ref. 2 were used to determine a binding enthalpy (Table S10).

Section S5. Differential enthalpies and entropies of adsorption
Using the multi-site Langmuir-Freundlich fits, the isosteric enthalpies of adsorption, ∆H, and entropies of adsorption, ∆S, were calculated using the Clausius-Clapeyron relationship (eq. 9), where R is the ideal gas constant, P is the pressure, and T is the temperature.
The ∆H and ∆S as a function of loading (mmol/g) curves were generated for the frameworks given in Figure 4 and Table 5 in the main text. The ∆H values reported in Table S11 and Figure 4 were obtained by averaging the first several values of ∆H in the ∆H versus loading curves where the curve was flat or relatively flat ("low-loading"). We note that ∆H values reported in the literature may also be found to be the highest value of ∆H from the enthalpy versus loading curve. This approach may suitable in cases where there is little variation in the magnitude of ∆H at low loadings (e.g., as is the case for Fe-BTTri). In cases where there is more variation in ∆H, it is not always straightforward what loading values to select to obtain an average. We recommend at the very least, when reporting ∆H values that the loading range used be explicitly stated. Ultimately, the goal is to estimate ∆H and ∆S values that are associated with only the primary binding site.
Note that you cannot average up to the inflection point to obtain ∆H, because doing so will include secondary site adsorption. Consequently, the value of ∆H will be an average of metal site binding and secondary site binding.
The range of loadings associated with the chosen ∆H range was then used to determine an average value of ∆S for each MOF, and ∆G298 was calculated from these values. All thermodynamic parameters are reported in Table S11.
The reported "estimated O2 capacities" as given in Table 5 of the main text and Tables S12-S14 were in most cases obtained by estimating the inflection point in the ∆H versus loading curves based on the second derivative of the enthalpy versus loading as estimated using the finite difference method. The goal with this value is to estimate the number of metal sites that are accessible to O2 binding. Utilizing the inflection point in the ∆H versus loading curve is a wellestablished approach to determine the number of accessible open sites for a given framework. An alternative approach is to take the capacity data from a single isotherm. However, with the latter approach, one cannot always discern if adsorption is due to metal site binding or if there is substantial secondary site adsorption. It is worth noting the limitations of this approach and the complexity involved in these assumptions. Not all ∆H versus loading curves will have an S-like shape, making it difficult to identify the inflection point. This can occur for frameworks with a low-density of binding sites for which the results can be sensitive to experimental error, for example. This is the case for Co-PCN-224 (see the supporting Excel file, "O2IsothermFits"). For this framework we simply assumed the estimated O2 capacity to be the metal site density. For Fe-PCN-224, the inflection points were different for the HT and LT data sets. For simplicity, we used the inflection point from the LT data set.

Section S6. Calculation of ∆G for VSA and VTSA model processes
The working surface coverage, ∆q , is defined in eq. 10 and 11. 5,7 As shown in eq. 10, ∆q is the difference between the surface coverage under adsorption ( ads) and desorption ( des) conditions. The maximal value of ∆ under a given set of working conditions is 1, corresponding to complete coverage of the primary O2 binding sites upon adsorption ( ads = 1) and zero coverage upon desorption ( ads = 0). In eq. 11, P is the pressure in bar, R is the ideal gas constant in units of J/(mol⋅K), T is the temperature in kelvin, and ∆G is in J/mol. For a given temperature and pressure, there is a value of ∆G that will correspond to maximum ∆q.

Section S7. DFT calculations of O 2 binding in MOFs
As discussed in the main text, when performing DFT calculations to study O 2 binding in metalorganic frameworks, one can choose to treat the full crystalline system with periodic boundary conditions or to focus only on the local O 2 binding environment in a cluster calculation. Periodic calculations enable a more realistic description of the MOF geometry, because all of the atoms in the calculation have the correct coordination environment, but they are typically computationally more expensive and, in many cases, make it infeasible to do hybrid functional calculations, which can be important for open-shell systems. Cluster calculations require choosing how to truncate the crystalline system to treat it as an isolated molecule, but have the advantage of being able to use hybrid calculations and beyond-DFT methods from quantum chemistry. Below, we show that both PBE+U calculations with periodic boundary conditions and cluster calculations with hybrid meta-GGA functionals well capture trends in O 2 binding energetics for MOFs with available experimental binding energies to use as a reference. However, one of the materials, Fe-BTTri, undergoes a spin state transition upon O 2 binding, and PBE+U was not able to yield the correct spin state before and after O 2 binding with the same Hubbard U value. The cluster calculations succeeded in giving the spin transition in Fe-BTTri, highlighting the advantage that hybrid functionals provide in capturing the properties of open-shell systems. Additionally, we use the cluster calculations to compare different hybrid and hybrid-meta-GGA functionals.

Section S7.1 M-benzenetriazolates (M3[(M4X)3(benzenetrisazolate)8]2) periodic calculations.
The M-BTTri and Cr-BTT structures contain disordered pore-dwelling cations in order to charge balance the anionic frameworks. Past computational studies using periodic systems have charge balanced the anionic framework by protonating one nitrogen on the azolate per metal node, rather than including such pore-dwelling cations. 8,9 This approach makes geometry optimization converge faster relative to incorporating pore-dwelling cations. On the other hand, the electronic structure of the coordinatively unsaturated metal sites may differ between structures with neutral and anionic linkers. In order to maintain the formal anionic charge on the linkers while excluding pore dwelling cations, we added three electrons to the unit cell [ ( Our structural relaxations used a G point sampling of the Brillouin zone and a 600-eV plane-wave energy cutoff energy. We used spin-polarized calculations with the initial transition metal spin chosen to match the expected spin state. The unit cell shape, unit cell volume, and the ions were relaxed until the Hellman-Feynman forces were less than 0.01 eV/A. To account for Pulay stress due to a changing cell shape, we looped converged calculations from their last set of lattice vectors and atomic positions until the forces were converged after just a single ionic step. The unit cell contains 231 atoms, and optimized lattice parameters are given in Table 15. We initialized our unit cell geometry with the reported experimental structure of Co-BTTri 22 and replaced the metal, ligand, or halogen accordingly (see Figure 3e in the main text for the structure of the isostructural Fe-BTTri). An experimental structure is also reported for Cr-BTT, 23 and we computed the energy of O 2 binding in Cr-BTT based on an initialization from those experimental atomic positions and also from the coordinates of Co-BTTri, with Co replaced with Cr and BTTri replaced with BTT. We did this because in the experimental structures of Co-BTTri and Cr-BTT with bound O 2 , the O 2 molecules are rotated relative to each other. To study the impact on the binding energy of rotations about the M-O axis, multiple O 2 binding geometries were considered. We performed calculations on Cr-BTT with the O 2 oriented end-on at 0°, end-on at 45°, and end-on at 90°, where the angles are with respect to the plane formed by the metal cluster. Both end-on binding modes at 45° and 90° yielded binding energies of 57 kJ/mol, while the 0° end-on mode was 5 kJ/mol less favorable. These results show that rotation about the M-O bond can affect the binding energy by as much as about 10%.
The results obtained for the O 2 binding energies, metal spin densities, and metal-O 2 bond lengths for [(M4Cl)3(benzenetrisazolate)8] (M = Cr II , Mn II , Co II ) are given in Table S16. The binding energy trends (BTT 3− < BTTri 3− < BTP 3− ) are consistent with the results from the cluster calculations (below). For Fe-BTTri, a spin-state transition is expected upon O 2 binding based on results from Mössbauer spectroscopy, 24 in particular, the initially high-spin iron(II) sites transition to low-spin iron(III) upon O 2 binding. However, we found that U values that resulted in a low-spin configuration for Fe in the O 2 bound system did not yield high-spin Fe in the bare framework, and that U values that resulted in high-spin Fe in the bare framework did not yield low-spin Fe in the O 2 bound system. Because the Hubbard U value penalizes double-occupancy of electron orbitals, a higher U value will generally tend to favor high-spin states while a lower U value will tend to favor low-spin states. In order to do a binding energy calculation, one needs to use the same U value for the reactants and products, so our inability to find a U value that was able to yield a spinstate transition prevented us from getting a O 2 binding energy for Fe-BTTri with the experimentally-reported spin-state transition, a limitation of PBE+U. Calculations were also carried out on [(Co4X)3(benzenetrisazolate)8] (X = F, Cl, Br, I) to examine how changing the bridging halide affects O2 binding. These calculations followed the methods described above. Starting from the DFT relaxed structure for Co-BTTri, Cl was replaced with F, Br, or I, and the appropriate ligand, and then the resulting structure was relaxed. Our results are summarized in Figure 5b of the main text and Table S17. 8 ] − ) cluster calculations. All cluster calculations were performed with Q-Chem 5.3 using a def2-TZVP basis set and with symmetry turned off. The structure of each cluster was developed from the experimentally determined structure when available, with hydrogens used to truncate the organic linker (see Figure S7). Furthermore, the carbons of the azolates were frozen during geometry optimization. When experimental structures were not available, clusters expected to be low-spin were initialized using Co-BTTri with metals and/or linkers substituted accordingly. Clusters expected to be high-spin were initialized with Fe-BTTri, as one may reasonably expect high-spin 3d metals to have similar geometries to each other. Previous benchmark DFT studies on metal-ligand bond energies do not agree on a single functional that best matches coupled-cluster results or experimental data, indicating that the functional that most accurately reproduces metal-ligand bond energies may vary depending on the system being evaluated. Nevertheless, functionals such as M06, MN15, MN15-L, ωB97M-V, TPSSh, and B97M-rV are recommended most often among these studies. [25][26][27][28][29][30][31][32] We included additional functionals PBE0 and B3LYP given their common use. For functionals without nonlocal corrections built in (like ωB97M-V or ωB97X-D 33 ), we included Grimme D3(BJ). For M06, we used -D3(0).

Section S7.2 M-azolates ([M 4 X(azolate)
To decide on a functional to use for all other O 2 binding energy cluster calculations, we tested the functionals listed above against the experimentally determined heat of O 2 adsorption in Co-BTTri (see Table S18). Pure functionals (no exact exchange) like BP86, TPSS, MN15-L, and M06-L dramatically overestimate the binding energy, while functionals with >20% exact exchange tended to underestimate the binding energy. TPSSh, M06, and B3LYP yielded a binding energy within 10 kJ/mol of the experimental heat of adsorption (−34 kJ/mol). We expect vibrational contributions to the energy, should one calculate those, to decrease the magnitude of the binding energy. While M06 gives a heat of adsorption that is numerically closer to the experimental heat of O 2 adsorption in Co-BTTri than TPSSh (−29 versus −43 kJ/mol, respectively), its binding energy is less than the experimentally determined value, and including the above-mentioned vibrational contributions are expected to reduce this value further. For this reason, we moved forward with TPSSh as our functional of choice for the remainder of the calculations (except in the case of Cr, see below).
We used TPSSh to calculate the O 2 binding energy at open metal sites in [M 4 X(azolate) 8 ] 2− (M = Co, Fe, Mn) clusters, constructed as above, using Eq. 12 (see Table 19). Consistent with experimental and computational evidence for Co-BTTri, 22 we assumed all metals were antiferromagnetically coupled across the µ 4 -halide, and that this configuration is unchanged upon O 2 adsorption. Cobalt was assumed to be low-spin for all clusters, while Mn and Cr were assumed to be high-spin for all clusters. Iron was assumed to be high-spin in all clusters with a transition to a low-spin state upon O 2 adsorption, consistent with what was found for Fe-BTTri. 24 However, we note that the ground state spin configuration for Fe-BTTri was highly dependent on the initial geometry. Using the Co-BTTri model cluster and replacing cobalt with iron while keeping other atoms in the same place before relaxing resulted in either a low-or intermediate-spin structure, as the Co-BTTri M-N bond length is shorter than that found in Fe-BTTri. These bond length differences in the initial structures are important because the azolate carbons are fixed during the relaxation process and cannot move as much as would be required to access the correct geometry for high-spin Fe. Due to numerical issues encountered using TPSSh and our Cr clusters within this study, binding energies for the Cr-based clusters were computed with M06, which were within the range of 60-80 kJ/mol. 23 We expect these values to be qualitatively consistent with those obtained with TPSSh. All trends found by these cluster calculations are consistent with the results of periodic DFT calculations, that is the binding energy increases as follows: BTT 3− < BTTri 3− < BTP 3− , and Mn < Co < Fe < Cr.

Section S7.3 M-PCN-224 cluster calculations.
The M-PCN-224 series is among only a few examples of MOFs featuring four-coordinate, planar metal centers found in the literature. [34][35][36] Because DFT calculations on molecular porphyrin compounds are common, 37-39 this series of MOFs is an excellent test system for benchmarking functionals. We used molecular porphyrins as a model system to benchmark a select number of functionals to study entropic contributions to O 2 binding. All clusters were obtained from experimentally determined crystal structures of M-PCN-224 by truncating between the porphyrin ring and the rest of the organic linker (see Figure S7). The Mn-porphyrin was assumed to remain high-spin for both the bare structure and the O 2 -bound structure. The Co-porphyrin was assumed to remain low-spin. The Fe-porphyrin was assumed to transition from high-spin iron(II) to low-spin iron(III) upon O 2 binding.
We focused on Mn-porphyrin for our functional benchmarking study, as many functionals tested did not deliver the correct degree of electron transfer for the O 2 -adsorbed structure, even after being initialized as Mn IV -O 2 2− . As Table 20 indicates, TPSSh, PBE, and B97M-rV are the functionals that best capture a two-electron transfer to yield a peroxide species, and furthermore only TPSSh and B97M-rV provide reasonable estimates for the experimentally determined binding energy. Because no analytical Hessians were implemented for VV10 dispersion corrections in Q-Chem, obtaining vibrational frequency and entropy data would be more time consuming for B97M-rV. Thus, we calculated most of this data with TPSSh (see Tables S20 and S21 for calculated ∆S and O-O vibrational frequencies using TPSSh for Co-, Mn-, and Fe-PCN-224).
The entropy of O 2 binding for each cluster, which needs to account for additional configurations of the bound O 2 molecule, was computed as: 3238=,U = 3+8&9,U + +23,U + ?$@,U where S total,x is the entropy of a given system, x, i and f represent the initial and final state, respectively, and S conf , S trans , S rot , and S vib represent the configurational, translational, rotational, and vibrational contributions to the entropy. The contributions from configurational entropy can be estimated by Rln (N) where R is the gas constant and N is the number of configurations. Note that this assumes all N configurations are degenerate. For side-on O 2 binding geometry like that in Mn-PCN-224, N = 4 due to the fourfold degeneracy that can be intuited from the symmetry of the binding site and verified from the single-crystal x-ray diffraction structure of the O 2 -bound structure. End-on binding geometry results in an 8-fold degeneracy, meaning N = 8 for Co-PCN-224 and Fe-PCN-224. Adding the fourfold configurational entropy to the calculated ∆S ads for O 2 binding in Mn-PCN-224 with TPSSh, we obtain a final calculated binding entropy of −179 J mol −1 K −1 , which is similar to the value calculated in this work using the Clausius-Clapeyron relationship, −174 ± 20 J mol −1 K −1 (see Tables S20 and S11).
To calculate the configurational entropy contribution for end-on O 2 structures, like those observed for Co-and Fe-PCN-224, the rotation of the O 2 molecule needs to be considered. Here, we performed potential energy surface scans by fixing the torsion angle of N-M-O in 15° increments for both the Co-porphyrin and Fe-porphyrin using TPSSh. Note that while our calculated binding energies using TPSSh are within 10 kJ/mol of the experimental ground-state O 2 binding enthalpy, we should not expect quantitatively accurate excited states, though we expect qualitative trends will hold (see Figure S8). If kT >> V max ,where V max is the energy barrier to rotation, we may assume a free rotor approximation and compute the entropy contribution accordingly. If kT << V max we may assume the configurational entropy is roughly RlnΩ, where Ω is the number of energetic minima along the rotation path. For kT ~ V max , we must treat the internal rotation rigorously as a hindered rotor. Interested readers may reference Pitzer and Gwinn's seminal work on this topic, 40 as well as challenges addressed by Pfaendtner et al. 41 The Fe-porphyrin notably has a rotation barrier of approximately 5 kJ/mol with barriers at 90° increments (see Figure S8), meaning we may reasonably approximate the configurational entropy contribution as a 4-fold energetically degenerate contribution. Along with the additional 2-fold contribution of the O 2 binding with equal probability on the two sides of the porphyrin plane, this results in a total of eight degenerate positions. The Co-porphyrin, on the other hand, exhibits a binding energy corresponding to physisorption and accordingly we see a rotational barrier of 2 kJ/mol. The energetic minima, therefore, are accessible at finite temperature and would contribute greater configurational entropy than in the case of the Fe-porphyrin.   Table S14. Figure S3. Calculated volumetric O2 working capacities for Cu I -MFU-4l, Co-BDTriP, and Co-BTP in a VTSA process with adsorption of air at 1 bar (0.21 bar O2) and 298 K and desorption at 0.2 bar and varying temperatures. It is clear that the optimal VTSA conditions differ for each material, as a consequence of their differing free energy values for O2 adsorption and volumetric metal site densities. Figure S4. Calculated usable surface coverages (Δθ) for Cu I -MFU-4l, Co-BDTriP, and Co-BTP in a VTSA process with adsorption of O2 at 0.21 bar and 298 K and desorption at 0.2 bar and varying temperatures. These three frameworks were chosen to illustrate different temperature-dependent behaviors given their relatively high usable surface coverages. The free energy values for O2 adsorption have important consequences for optimal conditions. At 298 K, Co-BDTriP displays the highest useable coverage, at moderate-to-high temperatures, Cu I -MFU-4l instead exhibits the highest values, while above 395 K, Co-BTP has the greatest Δθ.  Table S1. These calculations are based on experimental isotherms collected at low temperatures (203 to 233 K). 42 Figure S6. IAST O2/N2 selectivities for Co-BDTriP at the indicated temperatures for a 1 bar inlet feed of O2/N2 in varying ratios. The multi-site Langmuir-Freundlich parameters used to obtain these values were obtained from a previous report and the O2 isotherm values are contained in Table S5. These calculations are based on experimental isotherms collected at low temperatures (195 to 226 K). 22  Points denote energies obtained via DFT cluster calculations using the methodology explained above. Lines represent curve fits to a single harmonic model of the form + cos( + !"# $%& ), where b is the bias term, a is the amplitude, is the phase shift, f is the frequency, and is the angle in degrees. The barrier to rotation for Co-porphyrin is roughly 1 millihartree (~2.6 kJ/mol) while the barrier to rotation for Feporphyrin is roughly 2 millihartree (~5.2 kJ/mol). Table S1. Parameters obtained from fits to O2 adsorption data for Cu I -MFU-4l at the indicated temperatures, using a dual-site Langmuir-Freundlich model (eq. 7 and 8). Published isotherm data were newly fit in this work to obtain these parameters. 42 Table S2. Parameters obtained from fits to O2 adsorption data for Co2(OH)2(bbta) at the indicated temperatures, using a dual-site Langmuir-Freundlich model (eq. 7 and 8). These parameters are reported directly from a previous publication. 43 Parameter Values  Table S3. Parameters obtained from fits to O2 adsorption data for Fe-BTTri using a dual-site Langmuir-Freundlich model (eq. 7 and 8). These parameters were obtained directly from a previous publication, 24 where isotherms obtained at −78, −61, and −49 °C were simultaneously fit to one dual-site Langmuir-Freundlich equation. Table S4. Parameters obtained from fits to O2 adsorption data for Co-BTTri using a dual-site Langmuir-Freundlich model (eq. 7 and 8). These parameters were obtained directly from a previous publication, 22 where isotherms obtained at 195, 213, and 223 K were simultaneously fit using one dual-site Langmuir-Freundlich equation.  Table S5. Parameters obtained from fits to O2 adsorption data for Co-BDTriP, using a multi-site Langmuir-Freundlich equation, obtained directly from a previous publication. 22 Note that isotherm data obtained at 195, 213, and 223 K were simultaneously fit to derive the given parameters.   Table S12. Data used for calculating gravimetric and volumetric working capacities as reported in Table 5 in the main text and Tables S13 and S14 below. Theoretical O2 capacities reported in mmol/g and g/L assume one O2 bound per framework open metal site. Estimated O2 capacity was determined as described in Section S5 above. In the case of Co-BTP, the same value as determined for Co-BTTri was used. For each framework, the ratio of the estimated to theoretical O2 capacity in mmol/g was used as a multiplicative factor to determine the estimated O2 capacity in g/L. The latter value was then multiplied by the surface coverage for a given set of conditions to determine the volumetric working capacity. a Assumed to be the same as Co-BDTriP. b Estimated in most cases from the inflection point of the experimental isosteric heat of adsorption as a function of loading, which was approximated from the second derivative of the enthalpy versus loading, estimated using the finite difference method (see Section S5). c Assumed to be the same as for Co-BTTri. d Determined by multiplying the ratio of the Estimated and Theoretical Capacities in mmol/g by the Theoretical capacity in g/L, i.e.,

Column 5
Column 4 × Column 6. Table S13. Calculated working capacities of various frameworks in a VSA process assuming desorption at 1 mbar, ordered by decreasing working capacity (mmol/g). In the case of Fe-PCN-224, the capacities at low temperature (LT) and high temperature (HT) were determined separately (see Table S8). The density of exposed metal sites in Co-BTP was is assumed to be equal to that in Co-BTTri.  Table S14. Calculated working capacities of various frameworks in a VSA process assuming desorption at 10 mbar, ordered by decreasing working capacity (mmol/g). In the case of Fe-PCN-224, the capacities at low temperature (LT) and high temperature (HT) were determined separately (see Table S8). The density of exposed metal sites in Co-BTP was is assumed to be equal to that in Co-BTTri.