Computational NMR investigation of mixed-metal (Al,Sc)-MIL-53 and its phase transitions

Compositionally complex metal–organic frameworks (MOFs) have properties that depend on local structure that is often difficult to characterise. In this paper a density functional theory (DFT) computational study of mixed-metal (Al,Sc)-MIL-53, a flexible MOF with several different forms, was used to calculate the relative energetics of these forms and to predict NMR parameters that can be used to evaluate whether solid-state NMR spectroscopy can be used to differentiate, identify and characterise the forms adopted by mixed-metal MOFs of different composition. The NMR parameters can also be correlated with structural features in the different forms, giving fundamental insight into the nature and origin of the interactions that affect nuclear spins. Given the complexity of advanced NMR experiments required, and the potential need for expensive and difficult isotopic enrichment, the computational work is invaluable in predicting which experiments and approaches are likely to give the most information on the disorder, local structure and pore forms of these mixed-metal MOFs.


S1. Structure generation
Structural models for (Al1−xScx)-MIL-53 in the OP, NP, HT and LT forms were generated from crystal structure data reported in literature.S1,S2 Hydrogen atoms were added to the OP, HT and LT structures to produce aryl and hydroxyl groups where appropriate.The NP model was based on the theoretical structure produced in work of Bignami et al., S3 where an experimentally derived hydrated structure of Al-MIL-53 was optimised before removal of water modules and subsequent re-optimisation.
Supercells (1 × 1 × 2) were generated for the OP and HT forms, such that eight metal sites were present in the unit cell, matching the number present in the NP and LT forms.For NP, HT and LT structures, the unit cells were translated to enable direct comparison with the OP structures using the transformation matrices TNP, THT and TLT where T NP = " T HT = " 0 0 1 $ 1 $ 0 0 0 1 0 # , (S1.2) .3)These transformations ensured that the definition of unit cell axes were comparable between the four model systems.Figure S1.1 shows the resulting unit cell structures and numbering scheme used for the eight metal sites.Numbering of the cation sites is consistent between all four of the unit cells (but note that this does not indicate crystallographic inequivalence in the end member).As described in the main text, the SOD program S4 was used to generate all possible symmetry inequivalent cation arrangements for each pore form based on their space groups: OP (Imma), NP (P21/c), HT (C2/c) and LT (P21/c).These space groups result in one, three, one and two crystallographically unique cation sites within the OP, NP, HT and LT unit cells, respectively, and 34, 88, 76 and 32 unique cation arrangements for the set of compositions explored (including the Al-and Sc-MIL-53 end members).
Table S1.1 gives the complete set of (Al1−xScx)-MIL-53 structural models studied computationally, and information on the cation arrangement, composition, and configurational degeneracies.With the exception of the end members, the substitution pattern for a given structure is contained within the structure name.The prefix denotes which type of cation is located at the given numbered positions.For example, Sc-18 contains Sc 3+ on sites 1 and 8, and the remaining sites contain Al 3+ , etc. Table S1.1 also describes the "type" or ordering, i.e., whether the cations are best described as being situated in layers (L) or chains (C), are found in structures that are end members or have very low levels of substitution (E) or are found in structures that have overall less ordering (O).

S2. Calculation of the reference shielding
Reference shieldings (sref) were determined for all nuclei present (i.e., 1 H, 13 C, 17 O, 27 Al and 45 Sc) by comparing calculated values of siso to experimental values of diso for a model system, with where m is the gradient, sometimes referred to as a scaling factor, and sref is determined from the y intercept.δ iso (ppm)

S3. Comparison of results from different versions of CASTEP
As described in the methods section of the main text, calculations have been carried out using CASTEP S5-S8  This indicates that calculated parameters obtained using the two versions of the code are consistent and can be considered together.Emix is slightly more favourable (though still enthalpically unfavourable overall) for higher values of x.This suggests it is (relatively) more favourable to substitute the smaller Al 3+ cation into a Sc-containing framework, rather than vice versa.The degeneracies for each structural model are provided in Table S1.1.The position of the centre-of-gravity (d1, d2) can be calculated (for a specified magnetic field) for a 3QMAS NMR spectrum for a spin I = 5/2, using the referencing convention specific in Ref.where dQ is .3)n0 is the Larmor frequency at the specific field and PQ is defined as .4)where hQ is the asymmetry of the quadrupolar tensor.S11

Figure S1 . 1
Figure S1.1 Schematic showing unit cell structures used for generating models for DFT calculations of (a) OP, (b) NP, (c) HT and (d) LT MIL-53 structures, with metal site numbering used to generate mixedmetal composition and substitution patterns.
For 1 H, 13 C, 17 O and 27 Al, these values were obtained by comparison of the calculated and experimental NMR parameters for OP Al-MIL-53.Plots of calculated siso against experimental diso for 1 H, 13 C and 17 O are shown in FigureS2.1.Using EquationS2.1, values for the gradient, m, and the reference shielding, sref, were calculated to be: −1.117 and 30.873, respectively, for 1 H; −0.958 and 163.59, respectively, for 13 C; and −1.105 and 272.16, respectively, for 17 O.For 27 Al, a single peak is observed in the spectrum with diso = 3 ppm, and therefore the average of the eight 27 Al calculated siso values was taken (for the eight metal sites in the unit cell of Al-MIL-53), giving sref = 556.42ppm.For 45 Sc, sref = 772.85ppm was used based on experimental 45 Sc diso values (54.7 ppm and 56.5 ppm) for LT Sc-MIL-53.S2  Note that while differences in absolute values (and small differences in relative values) may be expected if calculations are referenced differently (e.g., using different model materials or a wider set of materials) these will not affect the overall trends and conclusions outlined in the main text.

Figure S2 . 1
Figure S2.1 Plots of calculated siso against experimental diso for OP Al-MIL-53 and corresponding lines of best fit for (a) 1 H, (b) 13 C and (c) 17 O.

Figure S3 . 4
Figure S3.4 Plots showing calculated 27 Al siso values determined using CASTEP versions 18.1 and 19.11 for (a) HT and (b) LT Al-MIL-53.The grey lines indicate y = x.Note the very small scales on both axes.

Figure S3 . 5
Figure S3.5 Plots showing calculated 17 O CQ values determined using CASTEP versions 18.1 and 19.11 for (a) HT and (b) LT Al-MIL-53.The grey lines indicate y = x.

Figure S4 .
FigureS4.1 shows the calculated unit cell volume for the four different pore forms of (Al1−xScx)-MIL-53 as a function of the cation composition.In general, the unit cell volume increases with increasing x, likely because of the increased size of Sc 3+ (0.745 Å) over Al 3+ (0.535 Å).S9  This volume increase is the largest for the OP form.

Figure S4 . 1 Figure S5 .
Figure S4.1 Plots showing the calculated unit cell volume as a function of the composition of the (a) OP, (b) NP (c) HT and (d) LT forms of (Al1−xScx)-MIL-53.

Figure S6 . 1
Figure S6.1 Schematic showing the two unique C1 environments in the LT form of (Al1−xScx)-MIL-53, shown here for x = 1.These two environments arise due to tilting of the MO6 octahedra which affects the O-C1-O bond angle and results in different 13 C C1 diso values.

Figure S6 .
Figure S6.4 shows the correlation between the calculated 17 O diso value and the Sc-O-Sc angle for Sc-O(H)-Sc groups in OP (Al1−xScx)-MIL-53.

Figure S6 . 4
Figure S6.4 Plot showing calculated 17 O diso values for Sc-O(H)-Sc groups in OP (Al1−xScx)-MIL-53 plotted as a function of the Sc-O-Sc angle, coloured by the composition of the overall framework.

Figure S6 .
Figure S6.5 shows a plot of calculated 17 O CQ against diso for oxygens in all four pore forms of (Al1−xScx)-MIL-53, in which distinct carboxylate groups can be seen for the NP, HT and LT forms.

Figure S6 .
Figure S6.6 plots the calculated 17 O CQ against diso for carboxylate groups bonded to Sc 3+ in LT (Al1−xScx)-MIL-53, showing variation with both the Sc-O bond length and Sc-O=C angle.No direct dependence is seen on the type of cation arrangement or composition.

Figure S6 . 6
Figure S6.6 Plots of calculated 17 O CQ values for Sc-O=C groups in LT (Al1−xScx)-MIL-53 plotted as a function of (a, b) the Sc-O=C angle and (c, d) the O-Sc bond length, coloured by (a, c) type of cation arrangement and (b, d) composition.

Figures S6 .
Figures S6.7 and 6.8 plot the calculated 17 O diso and CQ as a function of the distance between the carboxylate O and the hydrogen atom of the OH group across the pore for LT Sc-MIL-53 (Figure S6.7) and LT (Al1−xScx)-MIL-53 (Figure S6.8).

Figure S6 . 7
Figure S6.7 Plots of calculated 17 O (a) diso and (b) CQ values for Sc-O=C groups in LT Sc-MIL-53 plotted as a function of the distance between the carboxylate oxygen and the hydrogen atom of the OH group across the pore.

Figure S6 . 8
Figure S6.8 Plots of calculated 17 O (a) diso and (b) CQ values for Sc-O=C groups in LT (Al1−xScx)-MIL-53 (for all x) plotted as a function of the distance between the carboxylate oxygen and the hydrogen atom of the OH group across the pore.

Figures S6 .
Figures S6.9 and S6.10 plot the calculated diso values for 27 Al and 45 Sc, respectively, for different compositions of (Al1−xScx)-MIL-53 for each of the four pore forms.For each nucleus two different types of cations site are seen, depending on the nature of the next nearest cations.(Note owing to the imposed ordering discussed in the main text these can only both be Al 3+ or both be Sc 3+ ).

Figure S6 .Figure 6 . 13
Figure S6.13 plots 45 Sc diso as a function of the difference in the average Sc-OH and Sc-OC bond lengths (<Sc-OC> -<Sc-OH>) for a given ScO6 octahedra for (Al1−xScx)-MIL-53 in the LT form coloured by the overall framework composition.These plots show a linear relationship between the two for both types of Sc 3+ .Figure S6.14 shows the change in average Sc-OH bond length is greatest for Sc 3+ in the Al-O(H)-Sc-O(H)-Al environment compared to that of Sc-O(H)-Sc-O(H)-Sc indicating greater structural variation around Sc 3+ due to the presence of Al 3+ , likely driven by differences in cation size distorting the framework structure.S9

Figure 6 .
Figure 6.14 Plot of the average Sc-OC bond length against the average Sc-OH bond length for the ScO6 octahedra in LT (Al1−xScx)-MIL-53, coloured by the type of next nearest neighbouring metals.

Table S1
The equivalent OP and HT cation arrangement after removing symmetry restraints from the given NP or LT unit cell. b versions 18.1 and 19.11.Comparisons of siso and, where applicable, CQ values for the calculated 1 H, 13 C, 17 O and 27 Al NMR parameters in the HT and LT forms of Al-MIL-53 determined using CASTEP 18.1 and CASTEP 19.11 are shown in Figures S3.1-S3.6.These plots show the calculated siso and CQ values for the two codes typically agree well with one another (as expected), and where deviations do occur these are typically small, such as for the calculated 27 Al CQ values.
Plots showing calculated 27 Al CQ values determined using CASTEP versions 18.1 and 19.11 for (a) HT and (b) LT Al-MIL-53.The grey lines indicate y = x.Note the very small scales on both axes.