Elucidating the Germanium Distribution in ITQ‐13 Zeolites by Density Functional Theory

Abstract ITQ‐13 is a medium‐pore zeolite that can be prepared in all‐silica form and as silicogermanate with Si/Ge ratios as low as 3. Usually synthesised in the presence of fluoride, ITQ‐13 is among the very few systems containing fluoride anions in two distinct cage types, cube‐like d4r units and [4 ⋅ 56] cages. Here, dispersion‐corrected density functional theory (DFT) calculations are used to investigate the energetically most favourable Ge distributions for Si/Ge ratios between 55 and 6. The calculations show Ge atoms are incorporated at both the corners of d4r cages and at the basal plane of the [4 ⋅ 56] cages, in accordance with 19F NMR spectroscopy. Two Ge atoms at adjacent corners of [4 ⋅ 56] cages are stable at the highest Ge content considered (Si/Ge=6). Such a local environment has not yet been considered in the experimental literature. A calculation of the corresponding 19F NMR resonance points to overlap with other resonances, which might preclude its clear identification. Additional calculations investigate the variation of the dynamic behaviour of the fluoride anions as a function of the local environment as well as the selective defluorination of the [4 ⋅ 56] cages.


Introduction
The zeolite ITQ-13 was first reported by Corma's group from the Institute of Chemical Technology (Instituto de Tecnología Química, ITQ) at the Polytechnic University of Valencia in a patent published in 2002. [1] ITQ-13 is a medium-pore zeolite with a three-dimensional pore system consisting of channels formed by nine-and ten-membered rings (9MR/10MR) of TO 4 tetrahedra. [2] In addition to the all-silica form, labelled ITQ-13_ SiO 2 throughout this article, this zeolite can also be synthesised as borosilicate, aluminosilicate, [2,3] and silicogermanate. [1,4] Due to its narrow channel system and high acidity, ITQ-13 is a very interesting material for catalytic applications. In the cracking of vacuum gasoil, Castañeda et al. observed a higher propene/ propane ratio when employing ITQ-13 instead of the widely used zeolite ZSM-5 as catalyst additive. [3] They attributed this difference to a higher shape selectivity towards propene caused by the narrower pore dimensions, a finding that was confirmed in subsequent work. [5] ITQ-13 was also found to give a product spectrum different from other zeolite catalysts  in methanol-to-hydrocarbon (MTH) conversions, potentially enhancing the flexibility of the MTH process in the context of varying demands for different products. [6] ITQ-13 is the type material of the ITH framework, [7] which can be decomposed into four types of discrete cages: doublefour ring (d4r) cages (face symbol [4 6 ], labelled t-cub in the nomenclature of natural tilings [8] ), lau cages (face symbol [4 2 · 6 4 ], t-lau), stf cages (face symbol [4 · 5 6 ], t-nuh) and [4 · 5 2 · 6 2 ] cages (t-mel). It may be noted that the face symbol [4 · 5 2 · 6 2 ] was used for the stf cages in various earlier works. [2,4,[9][10][11][12][13] However, the 6MRs are not strong rings, being the sum of two 5MRs, and therefore this symbol does not conform to the rules outlined in natural tiling theory. [8] The arrangement of 2 d4r cages, 2 stf cages, 4 lau cages, and 6 [4 · 5 2 · 6 2 ] cages in the unit cell (u.c.) results in the formation of 9MR channels running along the crystallographic a direction, and 10MR channels running along b and c (Figure 1). In the as-synthesised form of all-silica ITQ-13, the head groups of the hexamethonium dications that are used as organic structure-directing agents (OSDAs) are located at the intersection of 9MR and 10MR channels, with the alkyl chain oriented parallel to c. The synthesis of ITQ-13_SiO 2 requires both use of an OSDA and the addition of fluoride to the reaction mixture, as the fluoride anions play a structure directing role, particularly in the formation of the d4r cages. The crystal structure determination showed that these anions reside in two different environments: [2] Half of the fluoride anions occupy the centre of the d4r cages, whereas the other 50 % are bonded to an Si atom at the basal 4MR plane of the [4 · 5 6 ] cages, forming an [SiO 4 F] À trigonal bipyramid. The latter fluoride location is disordered over four symmetry-equivalent positions in the cage with an occupancy of 0.25. The coexistence of two different fluoride environments in one zeolite structure is a relatively rare phenomenon, although another example has been reported recently for the case of all-silica MWW. [14] Due to the sensitivity of the 19 F NMR chemical shift to the local environment, solid-state NMR can help to elucidate which T atoms are found at the corners of the cages that host the fluoride anions. This is particularly interesting for silicogermanates, as X-ray diffraction methods cannot provide insights into the local structure due to lack of long-range order in the Ge distribution. In-depth studies of ITQ-13 samples containing different amounts of Ge have been reported by Vidal-Moya et al. [4] and by Liu et al. [11,12] The ITQ-13_SiO 2 19 F resonance at δ = À 38 ppm was ascribed to fluoride anions encapsulated in d4r cages, [15] whereas the peak at δ = À 66 ppm stems from [SiO 4 F] À trigonal bipyramids. [16] It is known from the crystal structure that these bipyramids are part of the basal plane of the [4 · 5 6 ] cages. [2] The incorporation of Ge gives rise to additional resonances at δ = À 8 ppm, À 20 ppm, and À 55 ppm. These peaks vary in intensity depending on the Si/Ge ratio, whereas those at δ = À 38 and À 66 ppm decrease and, ultimately, disappear upon increasing Ge content. The intensity evolution of the five distinct 19 F NMR resonances observed by Vidal-Moya et al. [4] and by Liu et al. [11] is summarised in Table 1.
Although the resonance at δ = À 55 ppm was straightforwardly attributed to fluoride in [4 · 5 6 ] cages having one Ge atom in the basal 4MR, [4] the assignment of the remaining two resonances has been the matter of some debate, and d4r cages with different amounts and/or arrangements of Si and Ge were considered to be responsible for their appearance. [12,[17][18][19] Recent, combined experimental and computational studies of ITQ-13 [12] and STW-type silicogermanates [19] agree that the resonance at δ = À 20 ppm can be assigned to d4r cages with isolated Ge atoms (that is, Ge atoms having only Si atoms at neighbouring corners of the cage), whereas the resonance at δ = À 8 ppm is due to fluoride in d4r cages having at least one GeÀ OÀ Ge link. Configurations with different numbers of isolated Ge atoms or different numbers of GeÀ OÀ Ge links give rise to 19 F NMR resonances with very similar chemical shifts, requiring 2D 19 F- 29 Si NMR correlation experiments to (partially) resolve them; [12] as a consequence, there are only two broad peaks in the 1D NMR spectra, despite a multitude of possible local arrangements. [4,11] The analysis of the 19 F and 29 Si NMR spectra of ITQ-13 samples with different Ge contents resulted in the conclusion that Ge atoms preferentially occupy the T2 and T5 sites, which are associated with the d4r cages, and the T7 sites, which form the basal plane of the [4 · 5 6 ] cages. [4] It is important to note that the d4r cages form the sole connection of layers constituted by the other building units along the a direction ( Figure 1). As an acid treatment causes a selective breaking of Ge À O bonds, the d4r cages in Ge-rich ITQ-13 samples can be removed, resulting in layered solids that could be used as precursors in the synthesis of other mesostructured materials by means of the Assembly-Disassembly-Organisation-Reassembly (ADOR) process. [13] Furthermore, the (partial) degermanation of ITQ-13 samples through acid leaching results in the formation of mesopores, which can improve the accessibility of the active sites and, hence, increase the catalytic activity. [20,21] The presence of Ge atoms in the vicinity of the fluoride anions also influences the fluoride removal behaviour. For the all-silica zeolite ITQ-13_SiO 2 , an alkaline treatment of the assynthesised sample at elevated temperature resulted in a complete removal of fluoride from the [4 · 5 6 ] cages, whereas fluoride anions occupying the d4r cages remained in the structure. [10] The crystallinity of the zeolite was fully retained. In Ge-containing samples, fluoride could also be removed from the d4r cages, but the degree of fluoride removal depended heavily on the Ge content. [11] This indicates that the number of Ge atoms at the corners of the d4r cages, and possibly also their local arrangement with respect to each other, strongly influence the thermodynamics and/or kinetics of defluorination.
Since experimental investigations provide only indirect insights, computational methods are an important alternative pathway to predict the preferred Ge locations and/or respective arrangements of Ge atoms in a given zeolite structure. Both force field methods [18,22,23] and density functional theory (DFT) calculations [24][25][26][27][28] have been used for this purpose, addressing silicogermanate zeolites with topologies of varying complexity. Since the number of possible configurations quickly becomes very large when introducing several Ge atoms per unit cell (an issue that will be discussed in more detail for the specific case of ITQ-13 in the Results section), a comprehensive sampling was usually unfeasible and findings obtained for low Ge contents were typically extrapolated to higher Ge contents to generate a limited set of probable configurations. Altogether, the computational investigations corroborated the preference of Ge to locate in d4r units, as well as an increased stability of arrangements containing GeÀ OÀ Ge links.
In this work, dispersion-corrected DFT calculations are performed to investigate the energetically preferred Ge distributions in ITQ-13 zeolites having Si/Ge ratios between 55 and 6, considering realistic models of as-synthesised zeolites that include fluoride anions and OSDA cations. For Ge contents corresponding to more than one Ge atom per unit cell, a variety of different configurations are sampled, considering, however, only an occupation of the T2, T5, and T7 sites. At low Si/Ge ratios (= high Ge contents), calculations predict the stability of [4 · 5 6 ] cages with two Ge atoms in the 4MR. As such cages have not yet been considered in experimental studies, 19 F chemical shift calculations are performed to identify the resonance of the fluoride anions incorporated in these building units. For selected ITQ-13 models, DFT-based molecular dynamics calculations are carried out to investigate how the dynamic behaviour of the fluoride anions is affected by the local environment. Finally, the thermodynamics of fluoride removal are studied using calculations for partially defluorinated ITQ-13 models.

ITQ-13 models
The crystal structure of as-synthesised ITQ-13_SiO 2 (orthorhombic, space group Amm2) was taken as starting point. [2] The disorder of the hexamethonium OSDAs and of the fluoride anions incorporated in the [4 · 5 6 ] cages was removed, resulting in a fully ordered structure that is depicted in Figure 1(b). The removal of disorder inevitably reduces the symmetry, and only the A-centering is retained in the final structure model of ITQ-13_SiO 2 . This model was optimised using the dispersion-corrected DFT approach described in the following subsection, optimising all atomic coordinates and Table 1. Intensity of distinguishable 19 F NMR resonances of ITQ-13 samples with different Ge contents. [4,11] The assignment to different building units according to more recent studies is given in the column header. Intensities are given on a qualitative scale, based on the NMR spectra shown in the original articles. the unit cell parameters a, b, and c, but fixing the unit cell angles to 90 degrees. Models of ITQ-13 containing 1, 2, 3, 4, 6, or 8 Ge atoms per (conventional) unit cell were constructed on the basis of the DFT-optimised structure of ITQ-13_SiO 2 . Again, the atomic coordinates and a, b, and c were optimised, fixing the angles to 90 degrees. For partially defluorinated models, different approaches were compared (described in detail in the corresponding part of the Results Section).

Periodic DFT calculations and DFT-based molecular dynamics simulations
DFT structure optimisations and DFT-based ab-initio molecular dynamics (AIMD) simulations were carried out using the CP2K code, [29] version 7.1, installed on the HLRN-IV facilities (HLRN -North-German Supercomputing Alliance). The Quickstep DFT module integrated into CP2K is based on a mixed Gaussian and plane wave approach. [30] All calculations used the PBE exchange-correlation functional [31] and the D3 dispersion correction proposed by Grimme et al. [32] A plane wave cutoff energy of 600 Ry was employed, and the first Brillouin zone was sampled at the Γ point, only. The structure optimisations used "molecularly optimised" triple-zeta (TZVP-MOLOPT) basis sets, whereas the AIMD simulations made use of double-zeta (DZVP-MOLOPT-SR) basis sets. [33] The core electrons were represented with Goedeker-Teter-Hutter pseudopotentials devised by Krack. [34] The structure optimisations were considered converged when the maximal residual force was smaller than 10 À 6 Ha bohr À 1 and the maximum geometry change was below 2 × 10 À 5 bohr. The pressure tolerance in the variable-cell optimisations was set to 5 × 10 À 4 GPa. The AIMD simulations were carried out for two temperatures, 298 K and 408 K, in the canonical (NVT) ensemble. Using a time step of 0.5 fs, the simulations were equilibrated for 10,000 steps (5 ps), followed by a production stage of 30,000 steps (15 ps). A Nosé-Hoover thermostat was used with a time constant of 50 ps. [35,36] For each system, three independent trajectories were computed for each temperature. From the AIMD trajectories, root mean square displacements (RMSDs) of fluoride anions were computed using the VMD software. [37] For cases of particular interest, the evolution of the atomic coordinates of individual fluoride anions was evaluated. AIMD average structures, in which the coordinates of the constituent atoms were obtained by averaging over the instantaneous positions during the production phase of the AIMD simulation, were also computed with VMD. All structure visualisations were prepared using VESTA. [38] Cluster DFT calculations of the isotropic 19

F shifts
To obtain 19 F chemical shifts associated with different fluoridecontaining building units, non-periodic cluster models of the relevant building units were extracted from the DFT-optimised structures, and saturated by attaching hydrogen atoms to the "dangling" oxygen atoms. 19 F isotropic chemical shifts were computed using the gauge-independent atomic orbital method [39] as implemented in Gaussian 16 revision C.01. [40] Two hybrid exchange-correlation functionals, PBE0 [41] and B3PW91, [42,43] were tested with Dunning's correlation consistent triple-zeta basis sets (cc-pVTZ). [44,45] The B3PW91 functional has been employed in previous computational predictions of the 19 F chemical shifts in fluoride-containing silicogermanates, [12,18] whereas the PBE0 functional was used with some success for other fluorine-bearing species. [46] In each case, the computed chemical shifts were referenced against the 19 F chemical shift of CCl 3 F (δ = 0 ppm) obtained with the same method.

Results and Discussion Preferred Ge distributions
All-silica ITQ-13: To begin with, the structure of purely siliceous ITQ-13 was optimised after removing the disorder of fluoride anions and hexamethonium OSDAs as described above. The resulting unit cell parameters, a = 12.607 Å, b = 11.467 Å, c = 22.188 Å, are only slightly overestimated when compared to the experimental values (a = 12.525 Å, b = 11.391 Å, c = 22.053 Å). This confirms the previous finding that the PBEÀ D3 functional delivers excellent predictions of the unit cell parameters of allsilica zeolites. [47,48] The F1 atom resides at the centre of the d4r cage, with all eight FÀ Si distances falling between 2.6 and 2.7 Å ( Figure 2). As in the starting structure, the F2 atom is bonded to one of the Si7 atoms, with an F2À Si7 distance of 1.78 Å ( Figure 2). This distance agrees well with previous NMR and DFT results for zeolites containing trigonal-bipyramidal [SiO 4 F] À units. [48][49][50] 1 Ge atom per unit cell (Si/Ge = 55): Although no experimental study reports an ITQ-13 silicogermanate with such a low Ge content, ITQ-13 models with 1 Ge/u.c. were constructed to investigate the site preference of Ge in the absence of any potential Ge À Ge interactions. Upon the removal of disorder, all symmetry elements with the exception of the A-centering are lost. Therefore, 28 of the 56 T sites in the unit cell become non-equivalent, and all of these were considered as Ge sites. Table S1.1 of the Supporting Information contains the relative energies ΔE with respect to the most favourable configuration (for which ΔE = 0 by definition) as well as the unit cell parameters. In the lowest-energy configuration, Ge is located at the T7 site to which F2 is bonded (labelled T7_1 in Table S1.1), forming a [GeO 4 F] À trigonal bipyramid ([4 · 5 6 ] 1Ge , Figure 3e). The F2À Ge distance of 1.90 Å is considerably shorter than typical FÀ Ge bonds in d4r units (discussed below), [27] but exceeds the sums of covalent or ionic radii. [51,52] The other T7 sites are at least~20 kJ mol À 1 higher in energy (relative energies ΔE are always given in kJ mol À 1 per unit cell). In other low-energy configurations that are within 11 to 20 kJ mol À 1 of the Ge@T7_1 configuration, Ge is located at the T2 or T5 sites, that is, either of the T sites that are associated with the d4r units. In these configurations, the F1 atom is always displaced from the cage centre towards the Ge atom, however, the individual F1À Ge distances vary considerably, from 2.12 to 2.57 Å (d4r 1Ge , Figure 3a). The fact that all configurations are nevertheless close in energy indicates a very shallow potential energy surface for displacements of fluoride within the cage, as observed in a previous DFT study of AST-type silicogermanates. [27] Configurations with Ge at any T site other than T7, T2, or T5 are at least 39 kJ mol À 1 higher in energy, agreeing perfectly with the experimental observation that only these three T sites are occupied by Ge at Si/Ge ratios as low as~6 . [4] It is interesting to note that some of the other sites (T1, T4, T8, T9) are high in energy despite being associated with 4MRs. In other words, while all preferred Ge locations are associated with 4MRs, not all T sites associated with 4MRs are preferred Ge locations. The strong energetic preference for these three sites is greatly reduced when considering a bareframework model of ITQ-13 (Table S1.2), where the T6 and T9 sites are very close in energy to the T5 site, and even lower in energy than T2 and T7.
Due to the clear preference of Ge for the T7, T2, and T5 sites, the calculations for higher Ge contents considered only these three sites. For each Ge content, representative configurations were generated to sample different distributions. A sampling of all possible arrangements quickly becomes unfeasible due to the very large number of configurations: For k Ge atoms per unit cell, there are 24!=ð 24 À k ð Þ!k!Þ distinct arrangements, corresponding to 276/2,024/10,626/134,596/735,471 configurations for 2/3/4/6/8 Ge atoms per unit cell. Even after removing symmetry-equivalent configurations, a huge number remains: To illustrate this for the case of 6 Ge/u.c., the number of non-equivalent combinations was calculated using the Supercell code [53] for an ITQ-13 model without fluoride and OSDA (space group Amm2). This resulted in 17,029 distinct configurations, a number that is still much too large to be practically tractable with DFT calculations. Moreover, this is an underestimate of the total number of distinct configurations, as the inclusion of fluoride anions and OSDA molecules greatly reduces the number of symmetry elements, resulting in fewer equivalences.
The results of these calculations are compiled in Tables S2.1 to S6.2, and all optimised structures are supplied in PDB format at https://doi.org/10.6084/m9.figshare.17067752. In these tables and files, labels of the following format are used: ITQ-13_kGe_ Y_ZZZ. Here, k represents the number of Ge atoms per unit cell. Y corresponds to a letter that is used to group configurations with similar Ge distributions together. Y = A always corresponds to models where all Ge atoms occupy T7 sites, and B, C… represent configurations where an increasing number of d4r sites are occupied. Separate letters are assigned to groups of configurations having a different distribution of Ge among the two d4r cages. For example, in the ITQ-13_4Ge case, G is used for a 2 : 2 distribution, H for a 3 : 1 distribution, and I for a 4:0 distribution. Finally, ZZZ is an index number that is assigned to generate a unique label for each configuration. Where different configurations in one group contain different numbers of GeÀ OÀ Ge linkages, the enumeration begins with those having the largest number of such linkages.
2 Ge atoms per unit cell (Si/Ge = 27): A total of 18 configurations with 2 Ge atoms per unit cell were considered (Tables S2.1 and S2.2). In the energetically most favourable model, T7 sites in both [4 · 5 6 ] cages are occupied by Ge, in accordance with the results for 1 Ge/u.c. Configurations in which two adjacent T7 sites in the same cage or one T7 and one d4r site (T2/T5) are occupied are about 10 to 15 kJ mol À 1 less favourable. If the two Ge atoms are both located at d4r sites, "distributed" configurations with two d4r 1Ge cages are similar in energy to some configurations containing a single GeÀ OÀ Ge linkage in one cage (d4r 2Ge,pair , Figure 3b), being about 25 kJ mol À 1 above the lowest-energy scenario. The location of both Ge atoms at non-neighbouring T sites belonging to the same d4r cage sites is distinctly less favourable.
3 Ge atoms per unit cell (Si/Ge = 17.7): The results for the 28 configurations containing 3 Ge/u.c. are compiled in Tables S3.1 and S3.2. A distributed arrangement with two [4 · 5 6 ] 1Ge cages and one d4r 1Ge cage emerges as the most favourable scenario, however, a model with one [4 · 5 6 ] 2Ge,pair cage ( Figure 3 f), where an adjacent T7 site instead of a d4r site is occupied by the third Ge atom, is very close in energy (ΔE = 3.8 kJ mol À 1 ). Configurations where 2 Ge atoms are associated with d4r cages are at least 10 kJ mol À 1 higher in energy, and those in which all 3 Ge atoms are located at d4r sites are at least 28 kJ mol À 1 less favourable. In the latter case, a 2 + 1 distribution over the two cages is generally favoured over a localisation of all Ge atoms at corners of the same cage. Among the set of configurations in which all Ge atoms belong to the same d4r cage, there is a clear tendency to maximise the number of GeÀ OÀ Ge linkages, replicating the findings of previous work on AST-type systems. [27] 4 Ge atoms per unit cell (Si/Ge = 13): For a Ge content of 4 Ge/u.c., 43 configurations were included in the calculations (Tables S4.1 and S4.2). As could be anticipated from the results for lower Ge contents, the most favourable configuration corresponds to a distribution of the Ge atoms over all four available cages, that is, a configuration containing two [4 · 5 6 ] 1Ge cages and two d4r 1Ge cages. A configuration where Ge atoms are exclusively located at T7 sites (two [4 · 5 6 ] 2Ge,pair cages) is, however, only slightly less favourable (ΔE = 5.5 kJ mol À 1 ). Comparatively small ΔE values of less than 10 kJ mol À 1 are also obtained if the Ge atoms are distributed over two [4 · 5 6 ] 1Ge cages and one d4r 2Ge,pair cage. If at least one of the [4 · 5 6 ] cages has no Ge atom in the 4MR, this will incur an energy penalty, with all configurations containing one all-silica [4 · 5 6 ] 0Ge cage being disfavoured by at least 20 kJ mol À 1 compared to the lowest-energy case. When placing all 4 Ge atoms at corners of the d4r cages, configurations that have a 2 : 2 distribution are favoured over those with a 3 : 1 or 4:0 distribution. Within each group, a tendency to favour configurations having the largest possible number of GeÀ OÀ Ge linkages is still present. However, the scatter in the ΔE values obtained for configurations having an identical number of such links is often considerable.
6 Ge atoms per unit cell (Si/Ge = 8.3): A total number of 48 configurations with 6 Ge/u.c. were compared (Tables S5.1 and 5.2). As this constitutes the largest number of distinct models for any Ge content, the results are presented in particular detail.
The ΔE values of all models are visualised in Figure 4, grouped hierarchically according to 1) the overall distribution of Ge atoms between [4 · 5 6 ] and d4r cages, 2) the distribution of the Ge@d4r atoms among the two cages, and 3) the total number of GeÀ OÀ Ge links in the structure. The energetically most favourable configuration, indicated by an orange star, contains two [4 · 5 6 ] 1Ge cages and two d4r 2Ge,pair cages. It is important to note that some other models having the same combination of building units are about 25 kJ mol À 1 higher in energy (Figure 4, orange columns). Apparently, different ways to assemble the same types of cages may lead to rather different total energies, depending on their respective arrangement and orientation. This implies that the total energy is not solely determined by the local environments, but that there are other factors at play that cannot be captured using simple criteria like the number of Ge atoms in the constituent cages or the number of GeÀ OÀ Ge linkages.
All models having two [4 · 5 6 ] 2Ge,pair cages are within 4 to 8 kJ mol À 1 of the most favourable configuration, regardless of the Ge distribution among the two d4r cages (Figure 4, blue columns). Therefore, it seems reasonable to expect that such cages are present in ITQ-13 samples with Si/Ge ratios below 10. Conversely, the occupation of a third T7 site by Ge is energetically very unfavourable (purple column). Returning to the large number of configurations containing two Ge@T7 and four Ge@d4r atoms, the two aforementioned trends to a) distribute Ge evenly over the available cages (2 : 2 distribution favoured over 3 : 1 and 4:0) and to b) maximise the number of GeÀ OÀ Ge linkages are still detectable. However, the two trends counteract each other, as the maximal number of possible GeÀ OÀ Ge links increases with the number of Ge atoms at the corners of a single cage. Therefore, a 4:0 distribution with 4 GeÀ OÀ Ge linkages (1 st bright red column) has a smaller ΔE value smaller than both the least favourable 2 : 2 distribution with 2 GeÀ OÀ Ge linkages and either of the two 2 : 2 distributions with no GeÀ OÀ Ge linkages that were included (brown columns). The same effect is visible for the configurations with six Ge@d4r atoms: While the ΔE values of all these models are large, amounting to at least 69 kJ mol À 1 , they are relatively close together in energy. The most favourable configurations with a 5 : 1/6:0 distribution, with 5/7 GeÀ OÀ Ge links, lie only 1/5 kJ mol À 1 above the lowest-energy 3 : 3 distribution (3 GeÀ OÀ Ge links).
8 Ge atoms per unit cell (Si/Ge = 6): The results for the 28 configurations with 8 Ge/u.c. are compiled in Table S6.2. The lowest-energy configuration contains two [4 · 5 6 ] 2Ge,pair cages and two d4r 2Ge,pair cages, but some models with an uneven distribution of the four Ge@d4r atoms among the two cages are reasonably close in energy, with ΔE in the range of 11 to 16 kJ mol À 1 . Configurations in which either more or less than two Ge atoms are associated with the [4 · 5 6 ] cages are distinctly less favourable (all ΔE values > 38 kJ mol À 1 ), pointing to a strong tendency to favour [4 · 5 6 ] 2Ge,pair cages at relatively high Ge contents. For configurations with six or eight Ge@d4r atoms, the respective ΔE values show rather large variations. Not all of the individual differences can be explained as being due to the distribution of Ge among the two d4r cages and/or the number of GeÀ OÀ Ge links. A particularly interesting case is the ITQ-13_ 8Ge_K_003 configuration: It contains two d4r 4Ge,4GeÀ OÀ Ge cages, with the Ge-containing 4MRs lying perpendicular to the a axis. Among those configurations having all 8 Ge atoms at the corners of d4r units, this model is the lowest in energy, being about 13 kJ mol À 1 more favourable than the second-lowest energy case. The presence of d4r 4Ge,4GeÀ OÀ Ge cages has been linked to the complete disassembly of Ge-rich ITQ-13 samples (Si/Ge < 3) into layered solids upon acid treatment, as a removal of such an all-Ge 4MR would result in a disintegration of the d4r units, disconnecting the layers. [13] Based on the results of the present work, it can be expected that at least 12 Ge/u.c. (4 at T7 sites, 8 at d4r sites) would be required for a successful disassembly. The sample for which a complete disassembly was achieved had an even higher Ge content (Si/Ge = 2.5, corresponding to about 16 Ge/u.c.).
To summarise, the DFT study of ITQ-13 models containing between 1 and 8 Ge atoms per unit cell allows to draw the following conclusions: * Ge atoms preferentially locate at the T sites forming the basal 4MR plane of the [4 · 5 6 ] cages (T7 site) and at the sites forming the d4r cages (T2 + T5 site). As all other possible locations are much higher in energy, it is unlikely that they will be occupied by Ge at all. ITQ-13 samples with Si/Ge ratios below 3 have been synthesised. [13] Even such Ge-rich compositions could be achieved by occupying exclusively the T7 and d4r sites, with an occupation of 1 = 2 of the T7 sites and all d4r sites (= 4 + 16 = 20 Ge/u.c.) corresponding to an Si/Ge ratio of 1.8.
* Agreement with the experimentally observed preference of Ge for the T2, T5, and T7 sites [4] is achieved only with models containing fluoride anions and OSDA cations. This observation confirms the previous notion that calculations for bareframework models are of limited validity to predict the most likely Ge location(s), as they ignore the important role of fluoride anions and OSDA cations in stabilising the preferred Ge sites. [27] Since only hexamethonium cations were considered, it cannot be inferred whether a change of the OSDA would lead to a variation in the site preference, or whether it is governed solely by the local environment and interactions with the fluoride anions.
* With regard to the [4 · 5 6 ] cages, an occupation of one T7 site by Ge is strongly favoured. It can thus be expected that the amount of all-silica [4 · 5 6 ] 0Ge cages will be very limited if there are more than~4 Ge atoms per unit cell (Si/Ge > 13). Indeed, the corresponding 19 F NMR resonance at δ = À 66 ppm, which is strong in ITQ-13_SiO 2 and in samples with an Si/Ge ratio above 20, is much weaker in more Ge-rich samples (Table 1 [4,11] ). The occupation of the T7 site by Ge, predicted by the calculations even for very low Ge contents, is confirmed experimentally through the appearance of a new resonance at δ = À 55 ppm, which is absent in ITQ-13_SiO 2 . This peak is visible even in the least Ge-rich sample  * With regard to the d4r cages, a distribution of Ge among the available cages is energetically favoured over a coexistence of all-silica cages and cages having Ge atoms at several corners, even at low Ge contents. This prediction is in line with the rapid intensity decrease of the 19 F NMR resonance at δ = À 38 ppm, which stems from fluoride incorporated in d4r 0Ge cages, at Si/Ge ratios below 20 (more than~3 Ge/u.c.). At higher Ge contents, different distributions of Ge among the d4r cages, as well as different arrangements within a given cage, are relatively close in energy, pointing to a coexistence of a multitude of local environments. As a consequence, the 19 F NMR resonance at δ = À 20 ppm, indicative of d4r cages having isolated Ge atoms at one or several corners, remains detectable up to an Si/Ge ratio of 4.5 (~10 Ge/u.c.), even though there are, on average, at least 3 Ge atoms per d4r cage at this Ge content. For a given number of Ge atoms per cage, arrangements having a larger number of GeÀ OÀ Ge links tend to be favoured. Some significant approximations had to be made: First, the DFT optimisations deliver only the total energy at 0 K, ignoring thermal effects. Although this approximation may affect the energetic ordering of configurations that are relatively close in energy, it is unlikely that the qualitative trends identified above would be changed. Second, the calculations can only predict the relative stabilities of the periodic zeolite structures. In zeolite synthesis, the actual distribution of Ge in the final product will be determined during the formation of small building units (such as individual d4r cages), which then assemble to form the extended structure. The periodic DFT calculations performed here capture neither the thermodynamic stability of such discrete building units nor their formation kinetics. Despite these inevitable limitations, the good agreement of the calculation results with the available experimental data gives reason to be confident that the chosen approach is suitable to predict probable low-energy configurations.

Prediction of 19 F NMR chemical shifts
As mentioned in the previous section, the occurrence of [4 · 5 6 ] 2Ge,pair cages with two neighbouring Ge atoms in the basal 4MR plane has not yet been proposed in experimental studies. In particular, there is no unassigned 19 F chemical shift that could correspond to fluoride anions in these cages. However, it is possible that the resonance stemming from these cages overlaps with another peak. This might obscure the presence of an additional building unit, especially if the resonance is rather weak. To test this hypothesis, calculations of the 19 F NMR chemical shifts were carried out for a total of six building units. For five of these cages, d4r 0Ge , d4r 1Ge , d4r 2Ge,pair , [4 · 5 6 ] 0Ge , and [4 · 5 6 ] 1Ge , the (approximate) shifts are known, whereas the sixth building unit is the [4 · 5 6 ] 2Ge,pair cage. Non-periodic cluster models were extracted from the DFT-optimised structures, and the isotropic chemical shifts were computed using the PBE0 and B3PW91 functionals with cc-pVTZ basis sets. The results are compiled in Table 2.
Comparing the computed 19 F NMR chemical shifts to the experimental reference values, the mean of absolute errors is similar for both functionals, amounting to 4.2 ppm for PBE0 and 3.8 ppm for B3PW91. In view of the limited number of experimental data points, and the lack of any specific optimisation of the computational approach (for example, in terms of the combination of exchange-correlation functional and basis set), such an agreement appears satisfactory, and sufficiently good to draw semi-quantitative conclusions on the resonance stemming from fluoride anions in [4 · 5 6 ] 2Ge,pair cages. As shown in Table 2, both functionals give very similar shifts in the range of δ = À 16 ppm for these fluoride anions. In other words, the associated resonance should fall between the two peaks at δ = À 8 ppm (d4r cages with at least one GeÀ OÀ Ge link) and δ = À 20 ppm (d4r cages with isolated Ge atoms). Both peaks are rather broad, and in some Ge-rich samples, the intensity between them does not fall to zero. [11] Also, the broad peak at δ = À 8 ppm does not appear to be fully symmetric, with a shoulder in the range of δ = À 11 to À 14 ppm (best visible in Figure 3c and d of Ref. [11]). Given the uncertainty of the DFT-based prediction of the chemical shift, which is on the order of 5 ppm, it is possible that the resonance stemming from fluoride-containing [4 · 5 6 ] 2Ge,pair cages was so far not observed in experimental studies due to its overlap with the peaks at δ = À 8 or À 20 ppm.

Dynamics of fluoride anions
To investigate the dynamics of the fluoride anions, AIMD simulations were performed for temperatures of 298 K and 408 K for a total of 10 different ITQ-13 models with 0 to 8 Ge atoms per unit cell. The latter temperature was chosen because it is typical for the synthesis of ITQ-13. [2] 6 ] cages, T = 298 K: The RMSD of fluoride anions incorporated in all-silica [4 · 5 6 ] 0Ge cages amounts to 0.22 Å at 298 K. A very similar value was previously obtained for a model of STF-type Mu-26, which contains the same type of cage. [48] The plot of all individual values ( Figure S6.1) confirms the absence of any increased RMSDs that would be indicative for a dynamic exchange of fluoride between different Si atoms. [16,48,54,55] The fluoride anions only undergo oscillations about their equilibrium positions at the apex of the [SiO 4 F] À trigonal bipyramids, as illustrated in Figure 5(a). The average RMSD(F) obtained for fluoride anions in [4 · 5 6 ] 1Ge cages is only slightly larger than for the all-silica case, indicating that FÀ Ge bonds are somewhat more flexible than FÀ Si bonds. For fluoride anions incorporated in [4 · 5 6 ] 2Ge,pair cages, the RMSD(F) is significantly larger, amounting to 0.27 Å. An analysis of individual trajectories shows that this is due to a movement of fluoride between the Ge atoms, with similarly short contacts to both atoms occurring over the course of the trajectory. This behaviour is visualised in Figure 5(c). As a consequence of these oscillations, the average position of fluoride computed over an AIMD trajectory lies approximately at equal distance from both Table 3. RMSDs of fluoride anions located in [4 · 5 6 ] cages. All values were calculated as averages over the RMSDs computed for individual F positions in individual AIMD trajectories. The number of RMSD values N is given in brackets. For 408 K, both the overall RMSD(F) values and RMSD(F) computed considering only those fluoride anions that do not undergo dynamic events ("noDE") are reported. For comparison, the 298 K value from previous work on the STF-type all-silica zeolite Mu-26 is included. [48] Zeolite  [48] 0   [27] 0.275 ./. 24 d4r 1Ge ITQ-13 0.217 � 0.019 0.266 � 0.020 21 AST [27] 0.218 ./. 24 d4r 2Ge,pair ITQ-13 0.217 � 0.012 0.266 � 0.012 12 AST [27] 0.232 ./. 24 d4r 3Ge,2GeÀ OÀ Ge ITQ-13 0.226 � 0.009 0.265 � 0.004 3 AST [27] 0.246 ./. 24 d4r 4Ge,4GeÀ OÀ Ge ITQ-13 0.253 � 0.009 0.309 � 0.007 3 AST [27] 0.264 ./. 24 Ge atoms [d(FÀ Ge) � 2.2 Å], whereas one FÀ Ge contact is significantly shorter than the other in the DFT-optimised structures (in the representative cage shown in Figure 3(f), the FÀ Ge bond is 1.96 Å long, while the distance to the other Ge atom amounts to 2.45 Å). Fluoride in [4 · 5 6 ] cages, T = 408 K: Typical RMSD(F) values computed for fluoride in all-silica [4 · 5 6 ] 0Ge cages fall in the range of 0.25 to 0.30 Å (Figure S6.1). The growth with respect to the 298 K values is attributed to the increased thermal motion at 408 K [for a harmonic oscillator, an increase of (408/298) 0.5 � 1.17 would be expected [56] ]. It is, however, noteworthy that the RMSDs of some individual fluoride anions are significantly larger, typically exceeding 0.5 Å, and resulting in an average RMSD(F) all of 0.36 Å ( Table 3). As established in previous work, such a drastic enhancement of the RMSD can be explained with dynamic "events" that correspond to a movement of the fluoride anion between different Si sites. [48,55] Solid-state NMR measurements provide evidence for the room-temperature dynamic disorder of the fluoride anions in some all-silica zeolites like Silicalite-1 and ITQ-4. [16,54] Although such measurements have not yet been reported for elevated temperatures, a previous AIMD study showed that the increased thermal motion may lead to the occurrence of dynamic events in zeolites that do not exhibit dynamic behaviour at room temperature, one example being STF-type Mu-26. [48] It is hence not surprising that the same kind of behaviour is found in [4 · 5 6 ] 0Ge cages of ITQ-13. An evaluation of the atomic coordinates shows that ca. 1 Å "jumps" may occur along the a and b directions. In one case, a single fluoride anion visits three Si atoms during the 15 ps trajectory (Figure 6a). If fluoride anions undergoing dynamic events are excluded from the calculation of the average value, the resulting RMSD(F) noDE (noDE = no dynamic events) amounts to 0.265 Å, which is 18 % larger than the 298 K value.
Concerning fluoride anions incorporated in [4 · 5 6 ] 1Ge cages, some RMSD values fall outside the typical 0.26 to 0.30 Å range. However, the individual increases are much less pronounced than for [4 · 5 6 ] 0Ge , and excluding these cases from the average RMSD(F) calculation results only in a modest change (Table 3). An evaluation of the individual trajectories of these fluoride anions reveals that such increases are due to short-lived jumps towards one of the surrounding Si atoms. Unlike observed above for the all-silica cages, the fluoride anions quickly return to the Ge atom, typically after a picosecond or less, and do not remain bonded to a Si atom for longer time intervals. A representative example of this behaviour is shown in  range is observed. As illustrated in Figure 6(c), the fluoride anions rapidly move back and forth between the two Ge atoms, with no extended residence times at either site.
Fluoride in d4r cages, T = 298 K: The RMSD values computed for fluoride anions in different types of d4r cages are compiled in Table 4. As a fairly comprehensive study of the dynamics of fluoride-containing d4r cages has been reported previously for AST-type silicogermanates, [27] encompassing a larger range of compositions up to d4r 8Ge cages, the results for the relevant types of cages are also included. Due to the absence of localised FÀ Si bonds, fluoride anions in all-silica d4r 0Ge cages possess a considerable freedom of motion, reflected by a fairly large RMSD(F) of 0.29 Å. The formation of FÀ Ge bonds in d4r cages containing 1 or 2 Ge atoms results in drastically reduced RMSD(F) values. Because the fluoride anions in d4r 2Ge,pair cages do not approach the Ge atoms as closely as in [4 · 5 6 ] 2Ge,pair cages, they remain confined to a narrower region between the two Ge atoms, and the corresponding RMSD is considerably smaller (compare Figures 6c and 7c). When more than two Ge atoms occupy corners of the d4r cage, the RMSD(F) rises again because fluoride anions form short contacts to different Ge atoms over the course of the AIMD simulations. This trend was even clearer in the previous work on AST-type systems, especially when moving towards more Ge-rich d4r cages (the RMSD(F) for a d4r 8Ge cage amounts to 0.36 Å). [27] Altogether, the quantitative deviations in the RMSDs between this and the previous study do not exceed 0.02 Å, which is plausible given the primary influence of the local environment on the freedom of motion.
Fluoride in d4r cages, T = 408 K: The RMSD(F) values obtained for a temperature of 408 K are 15 % to 22 % larger than those computed for 298 K, as expected. By and large, the same trends are found as for 298 K. When comparing the results for d4r 2Ge,pair to d4r 3Ge,2GeÀ OÀ Ge cages, the slight increase of the RMSD observed for 298 K does not occur for 408 K. However, this may be an artefact arising from the very limited sampling of the latter type of environment.

Partial defluorination of ITQ-13
Liu et al. subjected ITQ-13_SiO 2 to an alkaline treatment. [10] After 24 h at pH = 13.5 and elevated temperature (448 K), the disappearance of the 19 F NMR resonance at δ = À 66 ppm showed that the fluoride anions were completely removed from the [4 · 5 6 ] cages, whereas those in the d4r cages remained unaffected. In a subsequent work on Ge-containing ITQ-13 samples, the same group demonstrated that the alkaline treatment is also effective in removing fluoride from [4 · 5 6 ] 1Ge cages (disappearance of the resonance at δ = À 55 ppm), whereas only partial, if any, removal from d4r cages took place for samples with low and intermediate Ge contents (Si/Ge = 21 and 9). [11] Only for the most Ge-rich samples, with Si/Ge ratios of 4.5 and 3.2, a near-complete removal from the d4r cages occurred. These observations could be explained using different arguments. On the one hand, the different defluorination behaviour may be caused by differences in the thermodynamic stability of the fluoride environments. On the other hand, it could be related primarily to kinetic effects, such as a more facile release of fluoride from [4 · 5 6 ] cages through the larger 5MR windows. While the latter point would require a different computational approach, the relative stability of different environments can be assessed using DFT optimisations of partially defluorinated models.
Three different possibilities to generate partially defluorinated models were compared for ITQ-13_SiO 2 , in each case generating two models in which either of the two types of fluoride anions was removed. In the first approach, the remainder of the structure was left unchanged. Due to the uncompensated positive charge of the OSDA cations, a charge of + 2/u.c. was assigned in the DFT calculations. In the second approach, 50 % of the OSDA nitrogen atoms were replaced by carbon to achieve neutrality. In the third approach, one of the two hexamethonium cations was removed, again resulting in a charge-neutral model. For each approach, the two models were optimised separately, with or without an optimisation of the unit cell parameters. The difference in stability of the two models was then expressed as ΔE(F@d4r-F@ [4 · 5 6 ]), where the label in brackets designates the type of fluoride anions still present in the structure. In other words, a negative value corresponds to a higher stability of the model containing fluoride only in the d4r cages. The full results for all approaches tested on ITQ-13_SiO 2 are compiled in  6 ]) are fairly similar, ranging from À 47 to À 59 kJ mol À 1 per fluoride anion. Regardless of the chosen approach, the removal from [4 · 5 6 ] cages is significantly more favourable than the removal from d4r cages, in qualitative agreement with the experimental observations. This result indicates that the high thermodynamic stability of fluoride-containing d4r cages does indeed contribute to the observed selective removal from [4 · 5 6 ] cages upon alkaline treatment.
Since the main aim of the following calculations was a qualitative prediction of the relative stability, calculations on partially defluorinated models of Ge-containing ITQ-13 employed only the third approach (removal of one OSDA per u.c.). While the results from the calculations with and without an optimisation of the cell parameters are compiled in Table S8.2, the present discussion focusses on calculations using a fixed cell, for which the resulting ΔE(F@d4r-F@ [4 · 5 6 ]) values are given in Table 5. Progressive incorporation of Ge atoms at the corners of the [4 · 5 6 ] cages while retaining all-silica d4r 0Ge cages reduces the energy difference between the partially defluorinated models, with ΔE(F@d4r-F@[4 · 5 6 ]) having only a slightly negative value for the [4 · 5 6 ] 1Ge case. This does not agree with the experimental observation of a selective defluorination of [4 · 5 6 ] 1Ge cages evidenced by the disappearance of the 19 F NMR resonance at δ = À 55 ppm. For a model with 2 Ge atoms per [4 · 5 6 ] cage, an incorporation of fluoride in [4 · 5 6 ] 2Ge,pair cages is actually even favoured over the d4r 0Ge cages. Moving towards models with d4r 1Ge and d4r 2Ge,pair cages, it is always more favourable to retain fluoride in the d4r cages than in the [4 · 5 6 ] cages, and the evolution of the ΔE(F@d4r-F@ [4 · 5 6 ]) values shows that an increase in the number of Ge atoms per cage tends to further stabilise the d4r building units. The high stability of these fluoride environments agrees with the negligible removal from d4r units in Ge-containing ITQ-13 samples with high and intermediate Si/Ge ratios. [11] Conclusions DFT calculations considering one Ge atom per ITQ-13 unit cell reproduce the experimentally observed preference for the T2, T5, and T7 sites only if the OSDA cations and fluoride anions are included. Upon increasing the number of Ge atoms per cell, purely siliceous d4r cages and [4 · 5 6 ] cages disappear quickly. This is ascribed to a strong energetic preference for a distribution of Ge among the available building units, as opposed to a coexistence of purely siliceous cages and cages with several Ge atoms at the corners. At higher Ge contents, a range of local environments are expected to coexist. These results are in accord with both the large width of the 19 F NMR resonances observed at low Si/Ge ratios, and with the presence of the δ = À 8, À 20, and À 55 ppm resonances at Si/Ge ratios as low as 3. It is not unusual to observe a considerable scatter in the total energies obtained with different models containing the same type of building units, indicating that factors other than the local environment play a role.
Whereas experimental evidence for [4 · 5 6 ] 1Ge cages with one Ge atom in the basal 4MR plane had already been presented, the calculations predict [4 · 5 6 ] 2Ge,pair cages to be stable at intermediate and low Si/Ge ratios. As the calculated 19 F chemical shift falls between the strong and broad δ = À 8 and À 20 ppm peaks, the contribution of these cages may have been overlooked. Further experimental work using advanced NMR methods is thus needed to clarify this point. We note that an occupation of not more than two T sites per 4MR means that the [4 · 5 6 ] and [4 · 5 2 · 6 2 ] cages would stay connected via two shared T sites if the Ge atoms were removed. Hence, the computational prediction of [4 · 5 6 ] 2Ge,pair cages does not disagree with the observation that the layers oriented perpendicular to the a axis remain intact upon degermanation of Ge-rich ITQ-13 samples. [13] The AIMD simulations do not indicate that the fluoride anions in the [4 · 5 6 ] cages are dynamically disordered at room temperature. Thus, the experimentally observed disorder in the crystal structure is of a static nature, in accordance with the presence of a (weak) resonance at δ = À 146 ppm in the 19 F to 29 Si cross-polarisation NMR spectrum. [4] At 408 K, a typical zeolite synthesis temperature, the dynamic behaviour of fluoride anions strongly depends on the local environment: Whereas dynamic "jumps" between different Si atoms occur in purely siliceous cages, displacements away from the Ge atom are short-lived in [4 · 5 6 ] 1Ge cages. If there are two Ge atoms at adjacent corners, the fluoride anions move rapidly back and forth between them. It is of interest to assess whether NMR is able to probe these distinct scenarios, potentially leading to further structural insights regarding the occurrence of different types of [4 · 5 6 ] cages. For fluoride in d4r cages, the observed trends agree with those of a previous AIMD study of AST-type silicogermanates, [27] indicating that the local structure is the main factor determining the freedom of motion.
Regarding partially defluorinated models, the calculations provide clear evidence for the exceptional stability of fluoride in d4r cages, both for all-silica and Ge-containing ITQ-13. This observation agrees with the experimental finding of a selective  6 ] 0Ge and [4 · 5 6 ] 1Ge cages upon alkaline treatment, and indicates that the higher thermodynamic stability of fluoride anions in d4r cages is a key factor preventing their removal, despite the rather harsh treatment conditions (however, it cannot be ruled out that kinetic effects may also play a role in the more facile removal of fluoride from [4 · 5 6 ] cages). Although the calculations indicate that [4 · 5 6 ] 2Ge,pair cages provide an even more stable fluoride environment than d4r 0Ge cages, it is likely that these building units do not coexist in real ITQ-13 samples because [4 · 5 6 ] cages with more than one Ge atom will appear only at relatively high Ge contents. Admittedly, the DFT results do not explain the near-complete defluorination of Ge-rich samples. This behaviour may be due to a temporary breaking of GeÀ OÀ Ge linkages forming several adjacent edges of the d4r units, especially when there are four Ge atoms forming an entire 4MR (d4r 4Ge,4GeÀ OÀ Ge , Figure 3d). An approach based solely on DFT optimisations of partially defluorinated models cannot capture the possibility of a temporary bond breaking. Therefore, future work will employ AIMD simulations to investigate the interaction of ITQ-13 with alkaline or acid media.

Supporting Information
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