Experimental and theoretical investigations of the gas adsorption sites in rht-metal–organic frameworks

	Fig. 4 Inelastic neutron scattering (INS) spectra for H2 in (a) rht-MOF-1 at loadings of 1 H2/Cu (red) and 2 H2/Cu (violet), (b) rht-MOF-4a at loadings of 0.9 H2/Cu (red) and 1.5 H2/Cu (violet) with the difference spectrum shown in blue, and (c) rht-MOF-7 at loadings of 0.75 H2 per formula unit (black), 1.5 H2 per formula unit (red), 2.25 H2 per formula unit (green), 3 H2 per formula unit (blue), and 4 H2 per formula unit (magenta). The INS spectra for rht-MOF-1 and rht-MOF-4a were reproduced from ref. 25 within the guidelines provided by Wiley-VCH (Germany). Copyright 2012 Wiley-VCH (Germany). The INS spectra for rht-MOF-7 were reproduced from ref. 48 within the guidelines provided by the American Chemical Society. Copyright 2014 American Chemical Society.

At both loadings, a peak can be observed at approximately 9.0 meV in the INS spectra. This peak most likely corresponds to H₂ sorbing onto the Cu²⁺ ions of the copper paddlewheels on the basis of what was observed through INS measurements on other MOFs containing these MBBs.^25,49–51 Indeed, INS studies on HKUST-1 also revealed a peak near 9.0 meV in the resulting spectra.⁵⁰ Since both rht-MOF-1 and HKUST-1 contain [Cu₂(O₂CR)₄] clusters, this peak at ca. 9.0 meV in the individual spectra can likely be attributed to H₂ sorbing onto such sites. This was actually confirmed through two-dimensional quantum rotation calculations for a H₂ molecule sorbed about the Cu²⁺ ion of the copper paddlewheels in both MOFs, as such calculations produced rotational levels that are near 9.0 meV for the lowest j = 0 to j = 1 transition.^50,52 Note, in the absence of a barrier to rotation, a H₂ molecule rotates freely with energy levels that are representative of a rigid rotor. The lowest j = 0 to j = 1 transition for unhindered H₂ corresponds to a value of 14.7 meV.

At 2 H₂/Cu loading, a well-defined shoulder ranging from 6.5–8.0 meV becomes apparent in the INS spectrum for rht-MOF-1. The authors in ref. 25 attributed this peak to H₂ sorbing onto the Cu²⁺ ions of the [Cu₃O(N₄CR)₃] units in the MOF. A peak within the aforementioned range of energies was not observed in the INS spectra for HKUST-1 since these Cu₃O trimers are not present in this MOF.⁵⁰ Thus, the assignment of the 6.5–8.0 meV peak to H₂ sorbing onto the Cu²⁺ ions of the [Cu₃O(N₄CR)₃] MBBs appears to be valid, especially since this was later confirmed through two-dimensional quantum rotation calculations.⁵² It appears that the Cu₃O trimers become more occupied at higher loadings, which is consistent with what was observed through GCMC simulations of H₂ sorption in this MOF.

The INS spectra for rht-MOF-1 also contain a small, but noticeable peak at approximately 5.0 meV for both loadings. This peak is associated with H₂ sorbing onto the most favorable binding sites in the MOF. Note, in general, peaks that occur at lower neutron transfer energies in the INS spectra correspond to a higher barrier to rotation and therefore, a stronger interaction with the host. Two different GCMC simulations of H₂ sorption in rht-MOF-1 revealed that the most preferential H₂ sorption sites in the MOF are the NO₃⁻ counterions (see section III.A.1).^52,53 Sorption onto these nitrate ions correspond to the initial H₂Q_st in the material as verified through simulations involving explicit many-body polarization.⁵²

INS measurements on In-soc-MOF, another MOF possessing nitrate counterions,⁵⁴ also contain a peak near 5.0 meV in the resulting spectra. The authors in that reference claimed that this peak should correspond to H₂ sorbing onto the NO₃⁻ ions. Two-dimensional quantum rotation calculations for H₂ sorbed onto the nitrate ions in both MOFs yielded a j = 0 to j = 1 transition of 5.63 and 5.78 meV for rht-MOF-1 (ref. 52) and In-soc-MOF (ref. 55), respectively. These calculations therefore suggest that the transition occurring at about 5.0 meV in the INS spectra for both MOFs is associated with sorption onto the nitrate counterions.

A large peak can be observed at about 14.0 meV in the INS spectrum for rht-MOF-1 at both loadings. This peak is associated with H₂ sorbing onto the weaker binding sites in the MOF, most notably, the spacious interior of the cub-O_h cages according to GCMC simulations and attendant quantum dynamics calculations.⁵² The H₂ molecules localized at such sites exhibit rigid rotor-like behavior since they give rise to transitions that are near the free rotor limit of 14.7 meV. As a result, these H₂ molecules have very low barriers to rotation within the material.

As with the INS spectra for rht-MOF-1, a peak at about 9.0 meV can be observed in the spectrum for rht-MOF-4a at both loadings. This neutron transfer energy value is consistent with the lowest energy transition observed in other neutral MOFs containing copper paddlewheels.^49–51 Thus, this peak at ca. 9 meV should correspond to H₂ sorbing onto the Cu²⁺ ions of the copper paddlewheels in the MOF. The INS spectra for rht-MOF-4a also reveal a peak at around 10.5 meV. The authors in ref. 25 attributed this peak to sorption within the vicinity of the isophthalate moieties. A peak with high intensity was also observed at frequencies just below 13.5 meV, which could correspond to sorption near the alkoxy groups on the linkers. Note, unlike rht-MOF-1, quantum dynamics calculations were not performed on the H₂ binding sites in rht-MOF-4a. Thus, the assignments of the peaks at approximately 10.5 and 13.5 meV in the INS spectra for this MOF are tentative and uncorroborated.

With regards to H₂ sorption, Li et al. showed that rht-MOF-7 can sorb 2.65 wt% of H₂ at 77 K/1 atm and has an initial Q_st of 8.29 kJ mol⁻¹.¹⁹ On the other hand, the corresponding values measured by Eddaoudi's group are 2.20 wt% and 6.77 kJ mol⁻¹, respectively.⁴⁸ INS measurements of H₂ sorbed in rht-MOF-7 revealed a number of clearly defined peaks in the spectra, which are associated with different binding sites in the MOF. The INS spectra that were collected at various loadings for this MOF are shown in Fig. 4(c). The assignments of the peaks in this spectra have been confirmed through two-dimensional quantum rotation calculations on H₂ sorbed at the binding sites that were discovered through GCMC simulations.

A relatively low energy peak can be observed in the INS spectra at around 6.8 meV. The low energy of this rotational tunnelling transition is indicative of a high barrier to rotation, and hence a very strong interaction with the host. Indeed, this peak is associated with H₂ sorbed at the most favorable sorption site in rht-MOF-7. The intensity of this peak appears to saturate below a loading of 1.5 H₂ per formula unit, which indicates that there is a limited number of these sites available in the MOF.

GCMC simulations of H₂ sorption in rht-MOF-7 revealed that the most favorable binding site in the MOF is located between two neighboring Cu²⁺ ions that project into the T-T_d and T-O_h cages,⁴⁸ named the CuB ions according to the convention by Yan et al.¹³ An illustration of this site is shown in Fig. 5(a). The angular nature of the L7 linker causes two CuB ions to be in proximity to each other in the structure. Thus, as the H₂ molecule is sorbed in this region, it can interact with the two adjacent CuB ions simultaneously, providing for a very favorable interaction. Two-dimensional quantum rotation calculations for H₂ sorbed at this site produced a rotational level of 6.84 meV for the lowest transition, which is in excellent agreement with the lowest energy peak observed in the INS spectra for the MOF.⁴⁸ Further, there are only 12 of these sites available within a unit cell of the MOF, which explains why the peak at ca. 6.8 meV is saturated below 1.5 H₂ per formula unit loading.

	Fig. 5 Molecular illustration of a H2 molecule (orange) sorbed at various sites in rht-MOF-7 as determined from the GCMC simulations performed in ref. 48: (a) between two CuB ions, (b) onto a single CuA ion, (c) onto the 1,3,5-triazine groups of the linkers, and (d) within the corner of the T-Td cage. These sorption sites correspond to the peaks observed at approximately 6.8, 9.0, 11.0 and 13.5 meV, respectively, in the INS spectra for the MOF (Fig. 4(c)). Atom colors: C = cyan, H = white, N = blue, O = red, Cu = tan. These figures were reproduced from ref. 48 within the guidelines provided by the American Chemical Society. Copyright 2014 American Chemical Society.

The INS spectra show a peak at approximately 9.0 meV that gradually increases in intensity at higher loadings. This peak is typical for H₂ sorbing onto a single Cu²⁺ ion of the copper paddlewheel unit as observed in rht-MOF-1 (Fig. 4(a)),^25,52rht-MOF-4a (Fig. 4(b)),²⁵ HKUST-1,⁵⁰ and PCN-12.⁵¹ In the case of rht-MOF-7, the ca. 9.0 meV peak is associated with sorption onto the CuA ions, the Cu²⁺ ions that project into the cub-O_h cages in the MOF (Fig. 5(b)). This was indeed confirmed through two-dimensional quantum rotation calculations.⁴⁸ Unlike the environment of the CuB ions, the CuA ions are much farther apart from each other. Thus, as the H₂ molecule sorbs onto the CuA ions, it cannot interact with any other components of the MOF structure. This results in a relatively weaker interaction compared to sorption between two neighboring CuB ions. Note, the intensity of the 9.0 meV peak is nearly twice as high as that for the 6.8 meV peak at the highest loading measured (4 H₂ per formula unit). This is consistent with the expected relative saturation amounts about both types of Cu²⁺ ions as there are two CuA sites for every region between two adjacent CuB ions.

Additional peaks can be observed at approximately 11.0 and 13.5 meV in the INS spectra for rht-MOF-7, especially at low loadings. GCMC simulations and two-dimensional quantum rotation calculations provided clarification on the identity of these sites.⁴⁸ The center of the linker in the MOF can sorb up to three H₂ molecules, with each sorbate interacting with a N atom on the 1,3,5-triazine group (Fig. 5(c)). This suggests that the peak at about 11.0 meV could correspond to sorption onto the 1,3,5-triazine moieties since the intensity of this peak at the highest loading is about three times as high as that for the lowest energy peak in the spectra. This was convincingly supported by two-dimensional quantum rotation calculations, as such calculations for H₂ sorbed onto the 1,3,5-triazine groups yielded a j = 0 to j = 1 transition near 11 meV.

GCMC simulations of H₂ sorption in rht-MOF-7 revealed that the H₂ molecules also occupy the corners of the T-T_d cages (Fig. 5(d)),⁴⁸ similar to what was observed for D₂ sorption in NOTT-112 through NPD (see section II.A).¹³ Two-dimensional quantum rotation calculations for H₂ sorbed in this area generated rotational levels that are close to 13.5 meV for the two lowest j = 0 to j = 1 transitions.⁴⁸ Thus, the peak at ca. 13.5 meV in the INS spectra should correspond to H₂ sorbing within the corners of the T-T_d cages. This also makes sense from a loading perspective since up to four H₂ molecules can sorb within this region according to the GCMC simulations and the intensity of the 13.5 meV peak is approximately four times as high as that for the lowest energy peak.

Overall, INS studies of H₂ sorbed in rht-MOF-1, rht-MOF-4a, and rht-MOF-7 revealed that the Cu²⁺ ions of the copper paddlewheels are the principal binding sites for H₂ in these MOFs. This was exemplified by the fact that the spectra for all three MOFs contain a peak occurring at about 9.0 meV for all loadings measured. The presence of different functionalities in these rht-MOFs also gave rise to distinct features in the individual spectra. As demonstrated in the context of rht-MOF-1 (ref. 52) and rht-MOF-7 (ref. 48), the assignments of the peaks in the INS spectra can be verified through GCMC simulations and attendant quantum dynamics calculations.

As stated earlier (in section II.B.1), rht-MOF-1 is a cationic MOF that contains extra-framework nitrate counterions within the material. These NO₃⁻ ions are located within the cub-O_h cages in the solvated structure of the MOF. Molecular dynamics (MD) simulations revealed that these nitrate counterions migrate to the corners of the T-T_d cages in the dehydrated structure; these regions therefore represent the equilibrium locations of the NO₃⁻ ions in the solvent-free material. The authors in ref. 53 carried out GEMC simulations on rht-MOF-1 with the nitrate ions positioned in the corners of the T-T_d cages. Note, the aforementioned finding for the equilibrium locations of the NO₃⁻ ions in the dehydrated rht-MOF-1 was also reproduced from theoretical studies in our group.⁵²

Babarao et al. evaluated the preferred H₂ sorption sites in rht-MOF-1 by plotting the density contours of H₂ sorbed in the MOF at 77 K and different pressures.⁵³ The density contour plots that they generated at 77 K and 10, 100, and 1000 kPa are shown in Fig. 6. At 10 kPa, it can be observed that the H₂ molecules mainly sorb onto the nitrate counterions that are located in the corners of the T-T_d cages. This suggests that the unbound NO₃⁻ ions are the most favorable sorption sites for H₂ in rht-MOF-1 since they are highly occupied at low loading.

	Fig. 6 Density contours of H2 molecules in rht-MOF-1 at 77 K and 10 (left), 100 (middle), and 1000 kPa (right) based on the number of H2 molecules per Å3 according to the GEMC simulations performed in ref. 53. The COM distributions of NO3− counterions are depicted in cyan. Atom colors: C = gray, H = white, N = blue, O = red, Cu = peach. This figure was reproduced from ref. 53 within the guidelines provided by the American Chemical Society. Copyright 2010 American Chemical Society.

At 100 kPa, the density contours reveal that the H₂ molecules occupy the regions intersecting the cub-O_h and T-O_h cages as well as the cub-O_h and T-T_d cages.⁵³ The H₂ molecules further populate these intersecting regions at 1000 kPa. Moreover, occupancy can be observed within the T-T_d cages at this pressure. Interestingly, the COM distributions of NO₃⁻ ions are similar across all three pressures, implying that the positions of these counterions do not change significantly upon H₂ sorption at 77 K and varying pressures.

Simulations of H₂ sorption in rht-MOF-1 were also carried out by our group previously using GCMC methods.⁵² The three-dimensional histogram showing the most frequent sites of H₂ occupancy in the MOF at 77 K and a very low pressure (0.001 atm) is displayed in Fig. 7. It can be observed that the majority of H₂ molecules are sorbed onto the nitrate counterions within the corners of the T-T_d cages at this loading. This is consistent with what was discovered by Babarao et al. from their simulations in rht-MOF-1 at low pressure.⁵³ Indeed, these NO₃⁻ counterions represent the most favorable H₂ sorption sites in the MOF since they are charged particles that increase the electrostatic field within the framework. It appears that they are more preferred than any of the open-metal sites in the MOF. Furthermore, sorption onto these counterions correspond to the initial H₂Q_st of the MOF as supported by our close reproduction of the experimental Q_st plot from GCMC simulations.⁵²

	Fig. 7 Three-dimensional histogram showing the most frequent sites of occupancy (cyan) for H2 molecules in rht-MOF-1 at 77 K and 0.001 atm according to the GCMC simulations performed in ref. 52. Atom colors: C = green, H = white, N = blue, O = red, Cu = black. This figure was reproduced from ref. 52 within the guidelines provided by the Royal Society of Chemistry. Copyright 2014 Royal Society of Chemistry.

Note, in our theoretical study on rht-MOF-1, we also observed sorption onto the Cu²⁺ ions of the [Cu₂(O₂CR)₄] and [Cu₃O(N₄CR)₃] units.⁵² Such metal sites were captured in the simulations due to implementing many-body polarization interactions. After the NO₃⁻ counterions, the Cu²⁺ ions of the copper paddlewheels represent the next most favorable binding site, followed by the Cu²⁺ ions of the Cu₃O trimers. This is consistent with what was discerned through INS studies on the MOF (see section II.B.1).²⁵ These Cu²⁺ ion sites were not reproduced in the work of Babarao et al.,⁵³ presumably due to the lack of explicit polarization effects in their simulations. At higher loadings, sorption was also identified within the cub-O_h cages in the MOF.⁵² The authors in ref. 53 also claimed to observe H₂ sorbing into these cages at higher pressures.

Babarao et al. also examined the CO₂ binding sites in rht-MOF-1 in their work.⁵³ The authors stated that the CO₂ sorption sites are similar to those shown in Fig. 6 for H₂ sorption. However, they observed that the locations of the NO₃⁻ ions are more dispersed due to the greater thermal motion at 298 K. In addition to plotting the density contours and three-dimensional histograms and inspecting the modeled structure for binding sites, the preferential sorption sites in a MOF can be monitored through analysis of the radial distribution function (g(r)). Here, the normalized particle number for a sorbate is plotted at varying distances from a reference atom (usually from the host). This was demonstrated in ref. 53, where the authors evaluated the g(r) of CO₂ about the nitrate ions in rht-MOF-1.

Fig. 8 shows the g(r) of CO₂ carbon atoms about the N atoms of the NO₃⁻ ions in rht-MOF-1 at 298 K and different pressures (10, 100, and 1000 kPa). At 10 kPa, a significant peak can be observed at approximately 3.3 Å. This peak indicates a considerable amount of CO₂ molecules sorbing onto the nitrate ions at low loading. Indeed, as in the case of H₂, a very strong interaction exists between the CO₂ molecules and the NO₃⁻ ions. Hence, these counterions represent favorable sorption sites for CO₂ in rht-MOF-1. It can be observed that the magnitude of the peak at ca. 3.3 Å decreases at higher pressures. This is because, in addition to the nitrate ions, the CO₂ molecules are sorbing onto other regions in the MOF structure at higher loadings, most notably, the regions intersecting the cub-O_h/T-O_h cages and cub-O_h/T-T_d cages; this results in a lower relative occupancy about such counterions. Note, our group also used g(r) analysis to evaluate the favorable binding sites in rht-MOFs.^{36,45,48,52,56,58,59,61}

	Fig. 8 Radial distribution function (g(r)) of CO2 carbon atoms around the COM of the NO3− counterions in rht-MOF-1 at 298 K and 10 (solid), 100 (dashed), and 1000 kPa (solid and dotted) according to the GEMC simulations performed in ref. 53. This figure was reproduced from ref. 53 within the guidelines provided by the American Chemical Society. Copyright 2010 American Chemical Society.

In our work on PCN-61,⁵⁶ we showed that simulations using a polarizable H₂ potential⁶⁴ generated sorption isotherms and Q_st values that are in outstanding agreement with the corresponding experimental measurements for the MOF. On the other hand, simulations utilizing potentials that neglect this interaction^64,65 failed to reproduce experimental observables. Further, the inclusion of explicit many-body polarization effects was necessary to capture the sorption of H₂ onto the open-metal sites in the MOF.⁵⁶

Simulations involving explicit many-body polarization interactions allow for the binding sites to be discerned through the distribution of the induced dipoles on the sorbate molecules. This was first demonstrated in the MC simulation studies carried out by Belof et al. on In-soc-MOF.⁶⁶ The normalized sorbate population is plotted as a function of the induced dipole magnitudes. The resulting dipole distribution for a sorbate in a MOF contain a number of different peaks, with each peak generally correlating to a region of occupancy in the material. In general, a peak that is found at high induced dipole magnitudes corresponds to sorption onto the most favorable binding sites in the MOF. This is because such sites induce high dipoles on the sorbate.

Fig. 9 shows the sorbate induced dipole magnitudes plotted against the normalized H₂ population in PCN-61 at 77 K and various pressures (0.02, 0.15, 0.30, 0.50, and 1.0 atm) as obtained from simulations using a polarizable H₂ potential in the MOF.⁵⁶ A broad peak can be observed from about 0.25–0.50 D, which is most notable at the lowest loading considered (0.02 atm). This peak corresponds to H₂ sorbing onto the exposed Cu²⁺ ions in the MOF as verified through examining the regions of sorbate occupancy for H₂ molecules with these induced dipole magnitudes. Specifically, these H₂ molecules were found to sorb onto the CuA ions as presented in Fig. 10(a). Indeed, the highly charged and polar Cu²⁺ ions of the copper paddlewheels induce rather high dipoles on the H₂ molecules, which have a permanent dipole moment of 0 D in bulk on average.

	Fig. 9 Normalized distribution of the induced dipoles on H2 molecules sorbed in PCN-61 at 77 K and various pressures (0.02 atm = black, 0.15 atm = red, 0.30 atm = green, 0.50 atm = blue, 1.00 atm = orange) according to GCMC simulations involving explicit many-body polarization performed in ref. 56. This figure was reproduced from ref. 56 within the guidelines provided by the American Chemical Society. Copyright 2012 American Chemical Society.

	Fig. 10 Three-dimensional histogram showing the initial H2 sorption sites (blue) in (a) PCN-61 and (b) Cu-TPBTM about the CuA and CuB ions, respectively, as determined from GCMC simulations involving explicit many-body polarization performed in ref. 56 and 58. Atom colors: C = green, H = white, N = blue, O = red, Cu = black. These figures were reproduced from ref. 58 within the guidelines provided by the American Chemical Society. Copyright 2013 American Chemical Society.

A second peak can be observed from approximately 0.05–0.10 D in the H₂ dipole distribution for PCN-61. Correlating this peak to regions of occupancy in the MOF revealed that H₂ molecules with these induced dipoles sorb into the corners of the T-T_d cages.⁵⁶ This area was also discovered as a sorption site in other neutral rht-MOFs, such as NOTT-112 (section II.A)¹³ and rht-MOF-7 (section II.B.3).⁴⁸ Note, such induced dipole magnitudes are comparable to that for the permanent dipole on CO (0.122 D),⁶⁷ which has a normal boiling point of 82 K. An additional peak that increases in intensity at higher pressures can be observed from 0.0–0.05 D. This peak corresponds to H₂ molecules crowding into the more spacious regions of the MOF (e.g., the center of the T-T_d and T-O_h cages).⁵⁶ As H₂ molecules are sorbed into such areas, the sorbates exhibit lower induced dipoles since they are nearly representative of “free” H₂.

Although Cu-TPBTM and PCN-61 are highly isostructural, differing only in the functionality located between the isophthalate groups and the central aromatic ring of the linker (as well as minor differences in the unit cell lengths, pore sizes, etc.), they exhibit distinct gas sorption mechanisms at low loading according to the GCMC simulations performed by our group.⁵⁸ As with PCN-61, we showed that implementing classical polarization was requisite for reproducing experimental observables and capturing the sorption of H₂ onto the open-metal sites in Cu-TPBTM. However, ab initio calculations revealed that Cu-TPBTM exhibits a different charge distribution about the copper paddlewheels compared to PCN-61; this had an effect on the initial binding sites in both MOFs.

Electronic structure calculations on different representational fragments of PCN-61 indicate that the CuA ions, the Cu²⁺ ions projecting into the cub-O_h cages in the MOF, display a greater partial positive charge relative to the CuB ions.⁵⁶ Analogous calculations on Cu-TPBTM revealed the opposite trend, where it was discovered that the CuB ions, the Cu²⁺ ions projecting into the T-T_d and T-O_h cages, exhibit the higher partial positive charge.⁵⁸ The CuA ions have a greater partial positive charge in PCN-61 probably due to the fact that they are located in a more favorable chemical environment in general by projecting into the cub-O_h cages. However, in Cu-TPBTM, it appears that the presence of the negatively charged amide O atom on the linker causes the partial positive charge of the CuB ions to increase through an inductive effect (and thereby decreasing its electron density) since the amide groups are proximal to such Cu²⁺ ions in the structure. This could explain why the partial positive charge is greater on the CuB ions compared to the CuA ions in this MOF.

As explained briefly for NOTT-112 in section II.A., the sorbate molecules are more attracted to the type of Cu²⁺ ion having the higher partial positive charge in rht-MOFs. Indeed, GCMC simulations of H₂ sorption in PCN-61 and Cu-TPBTM with the inclusion of explicit many-body polarization interactions revealed that the H₂ molecules sorbed initially onto the CuA ions in the former (Fig. 10(a)),⁵⁶ and onto the CuB ions in the latter (Fig. 10(b)).⁵⁸ In other words, for the primary sorption site, the H₂ molecules bind onto the Cu²⁺ ions located inside the cub-O_h cages in PCN-61, whereas they sorb onto the Cu²⁺ ions located outside the cub-O_h cages in Cu-TPBTM. We note that sorption of H₂ was also observed within the corners of the T-T_d cages and onto the amide groups in Cu-TPBTM according to GCMC simulations.⁵⁸ Additionally, a similar phenomenon was observed in the case of CO₂ sorption in both of these rht-MOFs.⁶¹

	Fig. 11 Density distribution profiles between CO2 and the COM of rht-MOF-7 at 298 K and 10 (black) and 100 kPa (red) according to the GCMC simulations performed in ref. 57. This figure was reproduced from ref. 57 within the guidelines provided by the American Chemical Society. Copyright 2012 American Chemical Society.

GCMC simulations of gas sorption were also carried out in rht-MOF-7 by our group in 2014, where the CO₂ and H₂ sorption mechanism and binding sites in the MOF were investigated.⁴⁸ It was shown that the simulated CO₂ and H₂ sorption isotherms and Q_st values were in close agreement with the experimental measurements reported by Eddaoudi and co-workers.²⁰ These simulations were executed using polarizable potentials for the respective sorbates.^64,69 The inclusion of explicit many-body polarization interactions in simulation allowed for a significant quantity of CO₂ and H₂ molecules to sorb onto the open-metal sites in the MOF at low loading.⁴⁸

A number of distinct CO₂ binding sites were observed in rht-MOF-7 from the simulations performed by our group.⁴⁸ The most favorable of these corresponds to the sorption of CO₂ between two neighboring CuB ions, where each oxygen atom of the sorbate interacts with a single Cu²⁺ ion of adjacent copper paddlewheels (Fig. 12(a)). This sorption site is actually an example of a single-molecule trap for CO₂, which has been similarly observed in other MOFs.^70,71 The small and angular nature of the L7 linkers permit two neighboring [Cu₂(O₂CR)₄] clusters to be in proximity to each other, thus allowing this sorption site to exist in the material. Further, this binding site corresponds to the initial CO₂Q_st value for the MOF (ca. 45 kJ mol⁻¹)²⁰ as validated through our classical GCMC simulations involving explicit polarization.⁴⁸ Indeed, as demonstrated in the context of rht-MOF-7, the current smallest member of the rht-MOF family, tuning the pore sizes in MOFs can lead to optimal interactions between the sorbate molecules and the framework.

	Fig. 12 Molecular illustration of a CO2 molecule sorbed (a) between two CuB ions and (b) onto a single CuA ion in rht-MOF-7 as determined from the GCMC simulations performed in ref. 48. Atom colors: C = cyan, H = white, N = blue, O = red, Cu = tan. These figures were reproduced from ref. 48 within the guidelines provided by the American Chemical Society. Copyright 2014 American Chemical Society.

The next most preferrential sorption sites for CO₂ in rht-MOF-7 are the CuA ions.⁴⁸ An illustration of a CO₂ molecule sorbing onto this site is shown in Fig. 12(b). Unlike what was observed about the CuB ions, a CO₂ molecule can only sorb onto a single CuA ion since such Cu²⁺ ions are positioned farther apart from each other as a result of being located in the cub-O_h cages. The interaction for sorption onto a CuA ion is weaker than that for binding between two adjacent CuB ions. GCMC simulations revealed that the corners of the T-T_d and T-O_h cages and the 1,3,5-triazine groups are also sites of occupancy for the CO₂ molecules in the MOF, especially at higher loadings. These CO₂ sorption sites were also discovered in the simulation studies performed by Jiang's group in ref. 60, which was the third paper that reported theoretical gas sorption results in rht-MOF-7. Note, the preferred H₂ binding sites in the MOF were also identified from our simulations;⁴⁸ these sites are discussed in section II.B.3 and shown in Fig. 5.

The measured CO₂ uptakes for the MOF by the three groups at 298 K/1 atm are similar to each other (ca. 4.2, 4.6, and 4.0 mmol g⁻¹ in ref. 27–29, respectively). When comparing to other MOFs within the rht-MOF platform, only rht-MOF-7,¹⁹rht-MOF-9,^31,33 and Cu-TPBTM¹⁵ have higher experimental CO₂ uptakes under the same conditions to the best of our knowledge. In addition, according to the empirical fitting by Wang et al.,²⁷ NTU-105 exhibits an initial CO₂Q_st of about 36 kJ mol⁻¹, which is third to only rht-MOF-7 (ref. 19 and 20) and rht-MOF-9 (ref. 31) in the rht-MOF family. The same authors demonstrated that the MOF has a H₂ uptake of 2.75 wt% at 77 K/1 atm and a zero-loading Q_st value of roughly 6.6 kJ mol⁻¹.²⁷ This value for the H₂ uptake is among the highest of reported rht-MOFs at the same state point.^27,34 NTU-105 was also shown to be one of the top sorbents for CH₄ storage.^29,72

The three experimental references for NTU-105 also list the results from GCMC simulations of gas sorption in the MOF.^27–29 All three groups reported simulated gas sorption isotherms in decent agreement with their experimental measurements using nonpolarizable potentials.^68,73 Attempts at elucidating the favorable binding sites for CO₂ in NTU-105 were made by Wang et al.²⁷ and Yan et al.²⁸ The former investigated the interactions between the CO₂ molecules and the MOF by analyzing the g(r) of these sorbates around different framework atoms.²⁷Fig. 13 shows the g(r) of CO₂ carbon atoms about the Cu²⁺ ions of the copper paddlewheels and the various N atoms of the 1,2,3-triazole groups of the linker in NTU-105 at 298 K and three different pressures (1, 10, and 100 kPa). The three distinct N atoms are denoted N1, N2, and N3, where N1 represents the N atom connected to the isophthalate group and N3 is the N atom that is closest to the central aromatic ring. Note, unlike what was implemented in other GCMC simulation studies on rht-MOFs,^{28,33,45,48,52,56,58–61} the simulations in ref. 27 treated all Cu²⁺ ions as chemically equivalent.

	Fig. 13 Radial distribution function (g(r)) of CO2 carbon atoms around the Cu2+ ions (black) and various N atoms on the 1,2,3-triazole group of the linker (N1 = green, N2 = blue, N3 = magenta) in NTU-105 at 298 K and 1 (left), 10 (middle), and 100 kPa (right) according to the GCMC simulations performed in ref. 27. This figure was reproduced from ref. 27 within the guidelines provided by the Nature Publishing Group. Copyright 2013 Nature Publishing Group.

The g(r) of CO₂ carbon atoms about the Cu²⁺ ions at all three pressures reveal a modest nearest-neighbor peak ranging from ca. 3.2–3.6 Å. This suggests that there are some CO₂ molecules sorbing onto the open-metal sites in NTU-105 within the simulations. The aforementioned range for the Cu²⁺–C(CO₂) interaction is comparable to that observed in HKUST-1 through NPD studies.⁷⁴ The significant peak spanning from approximately 5.2–6.8 Å (maximum at 6.0 Å) in the g(r) around the metals probably corresponds to CO₂ localizing in the corners of the T-T_d cages. Additionally, it can be deduced that the CO₂ molecules display strong affinity toward the N1 atoms as exemplified by the large peak ranging from ca. 4.4–6.0 Å in the g(r) about such atoms across all pressures. The CO₂ molecules also exhibit favorability toward the N2 and N3 atoms since the g(r) of sorbates about these N atoms reveal a nearest-neighbor peak occurring at short distances.

Yan et al. discovered a number of different CO₂ sorption sites in NTU-105 from their GCMC simulations by inspecting the modeled structure at 298 K and various pressures.²⁸ At 10 kPa, the authors identified that the CO₂ molecules initially sorb onto the CuA ions in their simulations, which they denoted site I (Fig. 14(a)). This site is analogous to what is depicted in Fig. 12(b) for rht-MOF-7. At the same pressure, two additional CO₂ sorption sites were observed, which the authors referred to as sites II and III (Fig. 14(b)). Site II corresponds to the sorption of CO₂ in the center of the triangular-shaped window formed by three isophthalate moieties and three [Cu₂(O₂CR)₄] clusters in the T-T_d cage. This site is essentially located in the corner of the T-T_d cage, which has been observed as a favorable binding site for the sorbate in other rht-MOFs through MC simulations.^48,53,59,61 Site III is located within the region formed by the peripheral arms from three different L8 linkers in the T-T_d cage, where the CO₂ is proximal to the N1 atom. This site is consistent with what was discerned in the g(r) of CO₂ molecules about the N1 atoms in the GCMC simulation studies executed by Wang et al.²⁷

	Fig. 14 Molecular illustration of the CO2 sorption sites in NTU-105 at 298 K and ((a) and (b)) 10 kPa and ((c) and (d)) 50 kPa as determined from the GCMC simulations performed in ref. 28: (a) onto a single CuA ion (site I), (b) at sites II and III (see text in section III.A.5), (c) within the T-Td cages, and (d) within the small cavity created by four L8 linkers connecting the T-Td and T-Oh cages. Atom colors: C = gray, N = blue, O = red, Cu = cyan. This figure was reproduced from ref. 28 within the guidelines provided by the Royal Society of Chemistry. Copyright 2013 Royal Society of Chemistry.

At a higher pressure (50 kPa), the authors in ref. 28 observed that the CO₂ molecules crowd into the spacious region of the T-T_d cage (Fig. 14(c)) and the small cavity surrounded by four L8 linkers connecting the T-T_d and T-O_h cages (Fig. 14(d)). They also identified a significant amount of CO₂ molecules sorbing in the cub-O_h cages at this pressure. Further, at pressures of 50 and 100 kPa, their simulations revealed a chain of CO₂ molecules forming through the Cu²⁺–CO₂, 1,2,3-triazole–CO₂, and CO₂–CO₂ interactions in the MOF (Fig. 15). Overall, the results from GCMC simulations performed by Wang et al.²⁷ and Yan et al.²⁸ confirmed that the presence of open-metal sites and polar 1,2,3-triazole groups in NTU-105 contributes to high CO₂ uptake in the material.

	Fig. 15 Molecular illustration of the preferrential CO2 sorption sites in NTU-105 at 298 K and (a) 50 kPa and (b) 100 kPa as determined from the GCMC simulations performed in ref. 28. Atom colors: C = gray, H = white, N = blue, O = red, Cu = peach. This figure was reproduced from ref. 28 within the guidelines provided by the Royal Society of Chemistry. Copyright 2013 Royal Society of Chemistry.

The authors in ref. 33 carried out GCMC simulations and DFT calculations in order to gain information on the CO₂ sorption sites in rht-MOF-9. Their GCMC simulations revealed that the CO₂ molecules prefer to sorb onto the Cu²⁺ ions of the copper paddlewheels and the secondary amine groups on the linker. In order to examine the role of the s-heptazine groups toward CO₂ sorption, Liu et al. carried out DFT calculations of a CO₂ molecule interacting with the secondary amine group on a truncated organic linker of the MOF and two other hypothetical variants of the linker in which the N content of the s-heptazine ring decreased sequentially. The calculations were performed at the 6-311++G(d,p)/B3LYP level of theory using the Gaussian09 package.⁷⁵ The optimized distances between the CO₂ oxygen atom and H atom of the secondary amine group as well as the calculated binding energies for the CO₂–HNR₂ interaction for all three model compounds are shown in Fig. 16.

	Fig. 16 Optimized position of a CO2 molecule about the secondary amine groups within the truncated linker in rht-MOF-9 as well as different analogues of the s-heptazine unit as determined from the DFT calculations performed in ref. 33. The distances between the CO2 oxygen atom and the H atom of the secondary amine group are shown along with the calculated binding energies. Atom colors: C = gray, H = white, N = blue, O = red. This figure was reproduced from ref. 33 within the guidelines provided by the Royal Society of Chemistry. Copyright 2014 Royal Society of Chemistry.

Geometry optimizations revealed that the interaction distance between the CO₂ oxygen atom and the secondary amine H atom decreases with increasing number of N atoms on the polycylic aromatic ring. The binding energy associated with the CO₂–HNR₂ interaction for the truncated linker of rht-MOF-9 was calculated to be −10.3 kJ mol⁻¹, while those for the other two linkers are notably lower (both at −4.07 kJ mol⁻¹), indicating weaker guest–host interactions.³³ It is clear from these comparisons that the electronegative O atoms of the CO₂ molecule prefer to bind to the electropositive H atoms of the secondary amine group on the linker. However, the authors in ref. 33 attributed the stronger CO₂ affinity for the truncated linker of rht-MOF-9 to the greater density of N atoms on the polycylic aromatic ring, namely a synergistic effect with the N atoms that are proximal to the CO₂–HNR₂ interaction. Indeed, as the CO₂ molecule sorbs onto a secondary amine group of the L9 linker in the MOF, the positively charged C atom of the sorbate can also interact with the negatively charged N atom of the s-heptazine group that is nearby. We note that the richness of N atoms in rht-MOFs does not always lead to an increase in CO₂ sorption affinity as explained in the next section.

Despite being highly isostructural to rht-MOF-1, rht-MOF-pyr was shown to display a much greater stability in moisture, water, steam, and acid.³⁵ Indeed, this MOF retained its crystallinity after being exposed to ambient air with a relative humidity (RH) of ca. 70% for a week, water for 15 days at room temperature, steam (100% RH at 100 °C) for 6 hours, and aqueous HCl solution with a pH of 2.5 for two weeks at 298 K. The BET surface area of rht-MOF-pyr did not change significantly after being subjected to the aforementioned conditions. Many other rht-MOFs do not display the same type of stability as they lose their crystallinity after prolonged exposure to air.^31,35 According to the electronic structure calculations performed by our group, the improved stability for rht-MOF-pyr relative to rht-MOF-1 can be attributed to the increase in electron density of the N atoms that are coordinated to the Cu²⁺ ions of the Cu₃O trimers, which resulted in stronger bonds with such Cu²⁺ ions.³⁵ This in turn lead to an increase in the stability about the [Cu₂(O₂CR)₄] clusters. Note, an analogue containing 1,2,3-triazole groups was also synthesized in ref. 35 and shown to exhibit water and chemical stability.

rht-MOF-pyr was shown to display higher atmospheric CO₂ uptake than rht-MOF-1 at 273 and 298 K according to experimental measurements.³⁶ The former also exhibited a greater CO₂/CH₄ selectivity at 298 K/1 atm on the basis of ideal adsorbed solution theory (IAST) calculations.⁷⁶ These results seem counterintuitive as it was expected that rht-MOF-1 would display higher CO₂ uptake and selectivity due to possessing more N atoms on the framework. However, as demonstrated from GCMC simulations and DFT calculations carried out by our group, the local electric field of the [Cu₃O(N_4−x(CH)_xCR)₃] (x = 0 or 2) units in the two MOFs played a more dominant role toward CO₂ sorption than the number of exposed N atoms on the linkers.³⁶

GCMC simulations of CO₂ sorption in rht-MOF-1 and rht-MOF-pyr identified the NO₃⁻ counterions, the Cu²⁺ ions of the copper paddlewheels, and the Cu²⁺ ions of the Cu₃O trimers as favorable binding sites for the sorbate in both MOFs.³⁶ This is consistent with what was observed for H₂ sorption in rht-MOF-1 through related studies.⁵² Since the main difference in the CO₂ uptakes among the two MOFs was expected to be due to the interaction between the CO₂ molecules and the Cu₃O trimers, additional calculations about such units were implemented, one of which included DFT calculations for a single CO₂ molecule positioned about the [Cu₃O(N_4−x(CH)_xCR)₃] (x = 0 or 2) clusters for both rht-MOFs.³⁶ Such electronic structure calculations were performed to investigate the significance of substituting tetrazole with pyrazole on CO₂ sorption and to assess the difference in the binding energies about these MBBs.

The DFT calculations executed in ref. 36 utilized a truncated hexatopic building unit for both rht-MOFs, where all carboxylate groups of the L1 and L2 linkers were replaced with optimized H atoms. The CO₂ molecule was optimized to an energetically favorable position within both model compounds using the 6-31G* basis set for all C, H, N, and O atoms, the LANL2DZ effective core potential basis set⁷⁷ for the Cu²⁺ ions, and the B3LYP functional.^78,79 These calculations were performed with the NWChem ab initio software.⁸⁰ The optimized positions for a CO₂ molecule about a Cu²⁺ ion of the truncated hexatopic building unit for rht-MOF-1 and rht-MOF-pyr are shown in Fig. 17. The calculations revealed nearly equivalent distances for the Cu²⁺–O(CO₂) interaction, but notable differences in the orientation of the CO₂ molecule about these units.

	Fig. 17 Optimized position of a CO2 molecule about the Cu3O trimer within the truncated hexatopic building unit in (a) rht-MOF-1 and (b) rht-MOF-pyr as determined from the DFT calculations performed in ref. 36. The distances (in Å) between the Cu2+ ion and the closest O atom of the CO2 molecule are also shown. Atom colors: C = cyan, H = white, N = blue, O = red, Cu = tan. These figures were reproduced from ref. 36 within the guidelines provided by the Royal Society of Chemistry. Copyright 2015 Royal Society of Chemistry.

It was observed that as the oxygen atom of the CO₂ molecule binds onto the Cu²⁺ ion of the Cu₃O trimer in rht-MOF-pyr, it can also interact with the nearby positively charged H atoms of the pyrazole groups simultaneously (Fig. 17(b)).³⁶ This synchronized binding keeps the sorbate molecule in-plane with respect to the [Cu₃O(N₂(CH)₂CR)₃] trimers, resulting in a favorable interaction. In contrast, as the CO₂ oxygen atom sorbs onto the Cu²⁺ ion of the trimer in rht-MOF-1, it is repelled by the negatively charged N atoms of the tetrazole groups. In order to minimize N–O interactions, the CO₂ molecule orients at an angle and tilts out-of-plane with respect to the [Cu₃O(N₄CR)₃] trimers, leading to a less favorable interaction (Fig. 17(a)). The magnitude of the calculated binding energy for the interaction between CO₂ and the Cu²⁺ ion of the truncated hexatopic building unit was indeed greater for rht-MOF-pyr relative to rht-MOF-1 (−22.6 vs. −21.3 kJ mol⁻¹).