Interaction of water with (silico)aluminophosphate zeotypes: A comparative investigation using dispersion-corrected DFT

Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. Accepted Manuscript

Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal's standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains.
Accepted Manuscript www.rsc.org/pccp PCCP Sparked by the potential use of AlPOs and SAPOs in heat transformation applications, a number of researchers have investigated the adsorption of water in these systems. For example, water adsorption experiments using powder samples were performed for AlPO-5 (AFI topology), 12,13 AlPO-17 (ERI), 13 AlPO-18 (AEI), [12][13][14][15][16] 6,[12][13][14]16 , and a triclinically distorted CHA-type system termed AlPOtric. 16 These materials typically exhibit S-shaped water adsorption isotherms and isobars, a feature that is attractive because a large loading spread can be reached upon a moderate change in pressure and/or temperature (the loading spread corresponds to the difference in water uptake between adsorption and desorption conditions; a larger loading spread leads to a higher attainable energy density). The most promising systems, for example AlPO-18 and SAPO-34, exhibit a loading spread in the range of 300 g kg -1 when assuming H 2 O adsorption at 40 °C and desorption in the range of 100 °C, conditions that are relevant for the temporary storage of solar thermal energy. 16 It is worth noting that, in cases where several systems were compared, fairly similar heats of adsorption were measured for different AlPOs and SAPOs, despite the topological (and, in some instances, compositional) differences among the systems studied. For example, Ristic et al. reported heats of adsorption in the range of 55 kJ mol -1 for AlPO-18, AlPO-tric, and SAPO-34. 16 Typically, the heat of adsorption decreases considerably with increasing water loading in SAPO materials, since the first adsorbed water molecules can interact directly with the framework protons, whereas weaker interactions with the framework and other water molecules dominate at higher loadings. 13 For AlPOs, where such strong interaction sites are absent, it can be expected that the heat of adsorption changes only moderately as a function of the water loading. In addition to the investigation of powder samples, composites of AlPOs or SAPOs and support materials, primarily aluminium sheets or foams, 5,17-20 have been successfully prepared and characterised. The development of stable composites is pivotal for the actual application of these materials in adsorptive heat transformations. This is exemplified by a SAPO-34-coated heat exchanger, which was successfully integrated into a lab-scale adsorption chiller. 20 Computational chemistry methods at different levels of theory have been employed to predict and understand the interaction of AlPOs/SAPOs with water at a microscopic level. Henninger and co-workers used grandcanonical Monte Carlo (GCMC) simulations with an empirical force field to predict water adsorption isobars of AlPO-18. 15 Despite rather promising results, this method has not been widely employed for water in AlPOs or SAPOs, whereas there are numerous studies of water adsorption in aluminosilicate zeolites. 21 A

Page 4 of 33 Physical Chemistry Chemical Physics
Physical Chemistry Chemical Physics Accepted Manuscript larger number of computational investigations relied on electronic structure methods, especially densityfunctional theory (DFT). Early periodic DFT studies addressed the interaction of water with the acid sites of 23 It was shown that the adsorption of a single water molecule does not lead to framework deprotonation, but that the interaction with several water molecules can induce the formation of H 3 O + (H 2 O) n clusters. A later study of the chabazite-type aluminosilicate SSZ-13 showed that the likelihood of framework deprotonation decreases with temperature. 24 A number of DFT-based studies addressed the structure and, in some instances, dynamics of water in the pores of several aluminophosphates. [25][26][27][28] These studies delivered insights into the interatomic interactions governing water adsorption: For example, the rapid filling of the unit cell of AlPO-34 could be explained with the formation of a collective network of hydrogen bonds, 26 and the presence of octahedrally coordinated framework aluminium atoms in water-loaded AlPO-18 was found to be the energetically favoured scenario, in agreement with experimental observations. 27 Furthermore, abinitio Molecular Dynamics (MD) calculations corroborated that the adsorbed molecules have a considerable freedom of motion at room temperature. [25][26][27] Recent DFT-based studies of water in SAPO-34 have addressed various aspects: A series of investigations by Fjermestad et al. elucidated the role of water during framework desilication and silicon island formation. [29][30][31] Van Speybroeck and co-workers used ab-initio MD calculations to study the proton mobility and framework flexibility in water-and methanol-loaded SAPO-34, as well as the effect of water on methanol-to-olefin conversion reactions. 32,33 Particular attention was paid to the changes in lattice parameters in guest-loaded structures, with the most pronounced change being a contraction of the structure along the c-axis upon water adsorption, in agreement with previous experimental observations. 34 Finally, we studied the influence of local heterogeneities (silicon islands, SiAl domains) and defects on the interaction of SAPO-34 with water. 35 While a significant effect was observed at low water loadings, the impact on the total interaction strength at high loadings was only modest.
The present work aims at a more systematic computational exploration of the influence of various structural factors (pore size, pore topology, environment of framework protons) on the interaction of AlPOs and SAPOs with water, covering both energetic and structural aspects. Dispersion-corrected density-functional theory (DFT-D) calculations are employed to study the adsorption in six structurally different AlPOs and their SAPO analogues. In addition to AlPO-34/SAPO-34, 36,37 AlPO-17/SAPO-17, [37][38][39][40] and AlPO-18/SAPO-18, 38,41,42 pairs where either the AlPO or the SAPO system has already been proposed as adsorbent for heat transformation applications, 5,6,[12][13][14][15][16]20 three other systems are evaluated: AlPO-GIS/SAPO-43, 40,43,44 , AlPO-AFX/SAPO-56, 45 and AlPO-RHO/SAPO-RHO. 9,46,47 With the exception of the last two systems, which so   far have only been reported as SAPO materials, not as pure aluminophosphates, all other materials have been successfully synthesised in both AlPO and SAPO form. In all six structures considered, the pores are connected through eight-ring windows. The different structure types were chosen in order to study the influence of pore size and pore geometry: While the main pore systems of AlPO-34, AlPO-17, and AlPO-AFX are formed by elongated cages, AlPO-GIS, AlPO-18, and AlPO-RHO contain more or less isometric pores of different size. The building unit constituting the six structures are visualised in Fig. 1, with one of the main cages being highlighted for each system.
The remainder of this article is organised as follows: After a description of the model systems and the computational methodology, the results of the DFT-D optimisations of guest-free AlPO and SAPO systems are presented. These are followed by a detailed discussion of the DFT-D results for water-containing systems: AlPOs typically exhibit a steep rise of the water adsorption isotherm at a certain relative pressure (corresponding to pore filling). Below this pressure, only very little water is adsorbed due to the absence of preferred adsorption sites. Therefore, only the interaction with large amounts of water (near saturation) is studied for these systems. For SAPOs, initial adsorption at low water pressures will occur at the framework protons, prior to a pore filling at higher relative pressures. Consequently, both the adsorption of small amounts of water (one H 2 O per framework proton) and large amounts (near saturation) are considered in the calculations for these materials. Besides reporting the DFT-D interaction energies (averaged over 5 snapshots for high water loadings), the structural changes upon water adsorption are also assessed.

Preparation of model systems
DFT-D optimisations were performed for all guest-free systems. These optimisations included a relaxation of the lattice parameters and all atomic coordinates (for some of the SAPOs, constraints were applied to avoid a distortion of the unit cell, see Electronic Supplementary Information [ESI] for more details). Initial models of the AlPO structures were constructed either from published crystallographic data, or by starting from an allsilica model of the framework type and replacing the silicon atoms by Al and P in an alternating fashion. For the SAPO systems, the optimised AlPO models were taken as starting point. As it has been established that 8 Si substitution occurs at phosphorus sites of the AlPO matrix, 48,49 isolated phosphorus atoms were replaced by silicon in an ordered fashion, and a hydrogen atom was placed at one of the oxygen atoms surrounding the Si site. This led to a reduction of the symmetry, which is summarised for each system in the Results section (a more detailed description is given in the ESI). Where applicable, different possible substitution sites, and different available locations of the framework proton were considered in the initial DFT-D optimisations (with the exception of SAPO-34, which has been studied previously). For every possible Si site, only the model with the energetically most favourable proton location was included in the subsequent computations including adsorbed water. It has to be pointed out that, in contrast to our previous work, 35 the present study considers only isolated Si atoms, where each Si site requires one proton to balance the charge (N(H) = N(Si)). The possibility of silicon island formation, which may occur at higher Si contents (where N(H) < N(Si)), was not considered.
In order to study the interaction with water, different strategies were pursued for AlPOs and SAPOs: While only high water loadings (near saturation) were considered for AlPOs, both low loadings (one H 2 O per framework proton) and near-saturation conditions were included for SAPOs. In the DFT-D calculations for water-loaded systems, all atomic coordinates and the lattice parameters were relaxed. The same constraints as for the guest-free models were applied for systems containing one water molecule per proton, whereas no constraints were invoked at high water loadings.
Starting structures for SAPOs with one molecule of H 2 O per proton were prepared by placing the guest molecule in the vicinity of the proton. To investigate AlPOs and SAPOs at high water loadings, preliminary grand-canonical Monte Carlo simulations were performed to determine the approximate saturation uptake of each system. These calculations used the Sorption module of the Accelrys "Materials Studio" suite, with each run comprising five million equilibration steps and five million production steps. The GCMC simulations employed parameters from the Consistent Valence Force Field (cvff). 50 These parameters were also used in a GCMC study of water adsorption in AlPO-18 by Henninger and co-workers, where reasonable agreement with experimental adsorption isobars was observed. 15 It is worth noting that several of the AlPOs/SAPOs contain smaller cavities bordered by six-rings in addition to the main pore system that is connected by eightring windows. As these cavities (d6r and can units shown in Fig. 1) are in principle large enough to accommodate a water molecule, it will depend on the ability of the molecules to pass through the six-ring windows whether the cavities contribute to the total water uptake. In a previous combined MD and experimental study of water in AlPO-34, a water molecule was observed at the centre of the d6r unit. 26 On the other hand, these units seem to be inaccessible to water in AlPO-18. 27 In any case, the largest part of the adsorbed water will be located in the larger pores, which is why the present study ignores the possibility of adsorption in these small cavities. These areas were blocked by non-interacting spheres in the preliminary GCMC simulations.
The input structures for the DFT-D calculations were generated from fixed-loading Monte Carlo simulations that also used the cvff parameters. The amount of water molecules used in these calculations was always somewhat lower than the saturation uptake predicted from the GCMC simulations (typically ~15% below the saturation loading). For each system, the fixed-loading MC simulation consisted of at least one million equilibration steps and five million production steps. A total of 200 snapshots were stored throughout the production stage, and the five snapshots were randomly selected from the whole production stage. These snapshots were then used as initial configurations in the DFT-D calculations.
One has to bear in mind that the present approach involves one key approximation: For the systems containing large amounts of adsorbed water, the actual interaction energy would correspond to a weighted average over a practically infinite number of possible arrangement of water molecules in the pores. In the approach used here, this is approximated by averaging the interaction energies calculated for a small number of optimised configurations. Admittedly, this is a rather simplistic procedure; however, the findings of our previous work, 35 and the fact that the standard deviations arising from the averaging over five snapshots are fairly small (never exceeding +/-2.0 kJ mol -1 and being smaller than +/-1.0 kJ mol -1 in half of the cases, see below), indicate that one arrives at a reasonable estimate of the interaction energy, especially if the main aim is an identification of trends, rather than a highly accurate quantitative prediction. A more thorough sampling of configuration space (including temperature effects) could be obtained by running a series of ab-initio MD calculations starting from different snapshots. However, in the view of the rather large estimated error bars of 10 kJ mol -1 reported in a recent ab-initio MD study of water and methanol adsorbed in SAPO-34, 33 it can be anticipated that a computational setup that reduces the error to an acceptable level would be prohibitively expensive, in particular since some of the systems studied have rather large unit cells.

Details of DFT-D calculations
The DFT-D calculations were performed using the CASTEP code, which employs a combination of plane waves (for valence electrons) and pseudopotentials (for "core" electrons). 51 The calculations used on-the-flygenerated ultrasoft pseudopotentials and an energy cutoff of 700 eV. For all structures, only the gamma-point was used to sample the Brillouin zone. The calculations employed the PBE exchange-correlation functional 52 in conjunction with the dispersion correction scheme proposed by Tkatchenko and Scheffler, 53 termed PBE-TS in the following. In a previous study of water adsorption in SAPO-34 and AlPO-34, good agreement of the PBE-TS interaction energies with experimental heats of water adsorption was observed. 35 Furthermore, the PBE-TS functional was employed successfully to predict the structures of sheet silicates, 54 of molecular crystals and various layered materials, 55 and of water-containing zeolites. 56 The PBE-TS interaction energies reported in this study were calculated as follows: The first term corresponds to the PBE-TS energy obtained for the adsorbent (AlPO or SAPO) with n water molecules adsorbed, the second term corresponds to the PBE-TS energy of the guest-free adsorbent, and the last term represents an isolated H 2 O molecule placed in a large box (edge length 20 Å). Throughout this work, all interaction energies are reported as negative values.
In order to directly compare the calculation results to experimental heats of water adsorption, it would be necessary to explicitly calculate vibrational contributions (zero-point vibrational energy ZPVE and temperature contributions). Since the water-containing AlPO and SAPO models studied in this work contain a large number of non-equivalent atoms in the unit cell, a full vibrational calculation would be computationally very expensive. However, we performed preliminary (PBE) calculations for SAPO-34 with one adsorbed water molecule, obtaining a correction term of ~+7 kJ mol -1 for temperatures near room temperature. We observed previously that the PBE-TS interaction energies are typically 8 to 10 kJ mol -1 higher than experimental heats of adsorption (in absolute values -interaction energies are negative, whereas heats of adsorption are positive by definition). 35 This magnitude is in good accordance with the PBE-based temperature correction. With few exceptions that are mentioned explicitly, only the uncorrected interaction energies are discussed throughout this work. As there is reason to assume that the contribution of vibrations will be similar for all AlPOs/SAPOs studied, the trends identified herein should not be affected by the neglect of vibrational effects.

Optimisation of guest-free systems
AlPOs: Table 1 reports the lattice parameters of the DFT-D optimised structures of all AlPOs considered in the present work, together with experimental data for calcined AlPOs. These are available for AlPO-34, AlPO-17, and AlPO-18, whereas no experimental structure data have been reported in the publication reporting a gismondine-type pure aluminophosphate AlPO-GIS. 43 Finally, as mentioned previously, AlPO-AFX and AlPO-RHO are hypothetical systems, since only SAPOs with this topology have been synthesised so far. [45][46][47] For AlPO-34, AlPO-17, AlPO-GIS, and AlPO-AFX the conventional setting of the unit cell was used in the calculations. For AlPO-18 and AlPO-RHO, the optimisation was performed in the primitive cell of space groups C2/c and I23, respectively, and the structures were transformed back into the conventional cell for the comparison reported in Table 1.
For those three systems for which experimental data for calcined, pure AlPO systems are available, the DFT-D optimised unit cell dimensions agree very well with the experimental cell parameters. There is a consistent tendency to overestimate the lattice parameters slightly, with relative deviations of not more than 0.5%. After the DFT-D optimisations, geometric calculations using the PoreBlazer code were performed to determine the accessible volume fraction, the diameter of the largest sphere that can be included without overlapping with the framework (d LS ), and the pore limiting diameter (d PLD ). 59 For the systems with elongated cages, the largest sphere diameter does not fully describe the pore dimensions, as its value depends only on the shortest axis of the cage. To account for this, the length of the longest axis of the cages of AlPO-34, AlPO-17, and AlPO-AFX was estimated from the distance between the centres of the six-rings at the top and the bottom of the cages, subtracting 2 Å to account for the van der Waals radii of the surrounding framework atoms. This quantity, termed d c because the direction of cage elongation is parallel to the crystallographic caxis in these systems, is also given in Table 2.
The accessible volume fractions in the six structures fall in a reasonably narrow range, which leads us to expect that the maximal water uptake should also be similar. In the systems with elongated cages, the largest sphere diameter is fairly similar, which is not surprising given the structural similarities (Fig. 1). water molecules will be able to diffuse through the windows of all these structures; however, it can be anticipated that an even more drastic elliptical distortion than in AlPO-GIS might impede the diffusion of water through eight-ring windows. SAPOs: For the SAPO systems, different locations of the Si atoms and the associated protons were considered. These calculations employed models that had a lower symmetry than the parent AlPO structures, without removing the symmetry completely. It has to be conceded that the use of SAPO models retaining an inherent symmetry might introduce a degree of artificial ordering, since Si atoms and associated protons could be distributed over several low-energy sites in real systems. However, the present approach, in which all framework Si atoms are equivalent by symmetry, has the advantage that different possible Si and H locations can be studied in a systematic fashion, permitting the identification of energetically preferred scenarios.
The SAPO models employed for each system are presented in detail in the ESI, where the silicon and proton locations are also visualised. To distinguish the different models, labels of the form "SAPO-N_SiX_OY" are used, where X designates the location of the silicon atom, and the Y the oxygen atom to which the framework proton is attached (OY is bonded to SiX). The label SiX is left out if there is only one Si site.
Tables S2 to S7 of the Supporting Information report the lattice parameters and relative energies for all models considered. It is apparent that there are many cases where several possible proton locations are very close in energy. To keep the total number of systems tractable, only the lowest-energy proton location for each silicon site was considered in the DFT-D calculations including adsorbed water molecules. Table 3 gives an overview over the number of different models considered for each structure type, and reports the energetically most favourable scenarios. Due to a lack of available crystallographic data for calcined SAPOs, and the dependence of the DFT-optimised lattice parameters on the distribution of Si and H atoms in the framework, a detailed comparison to experimental data was not attempted for these systems.  Fig. S2). In SAPO-43 and SAPO-RHO, the energetically preferred proton locations are associated with eight-ring windows (ESI, Fig.s S4, S6). For these systems, a comparison of the most favourable systems to other possible arrangements shows a tendency to maximise the distance between the framework protons. Scenarios in which two protons point into the same eight-ring window are particularly unfavourable, which seems plausible from simple electrostatic considerations.

Preliminary GCMC simulations
The preliminary GCMC simulations of water adsorption were performed for AlPO and SAPO systems. The approximate saturation uptakes determined from these calculations are listed in Table 4 (while the saturation uptakes of AlPOs and SAPOs with the same topology are not identical, they are sufficiently similar to approximate them by the same value). Unsurprisingly, the four systems with relatively large accessible volumes of more than 0.37 cm 3 g -1 also exhibit similar saturation uptakes in the range of 360 g of water per kg of adsorbent. The saturation uptake of AlPO-GIS/SAPO-43 is only slightly lower, despite the fact that its accessible pore volume is considerably smaller (0.32 cm 3 g -1 ). This could point to a rather large difference between the accessible pore volume calculated by PoreBlazer using the kinetic diameter of nitrogen, and the pore volume that is actually accessible to the (smaller) water molecule.
While the present study does not aim at an accurate quantitative prediction of the saturation uptake, it is nevertheless insightful to compare the results to available experimental data: Jänchen at co-workers reported a water uptake of 283 g kg -1 for AlPO-17 and 388 g kg -1 for AlPO-18 at room temperature and a relative pressure p/p 0 of 0.3, in good agreement with the values predicted from the GCMC simulations. 13 On the other hand, they obtained a lower uptake for SAPO-34 than the calculations (279 g kg -1 ). At a higher relative pressure (p/p 0 = 0.7) and 40 °C, an uptake of ~320 g kg -1 was reported in a subsequent study of SAPO-34, approaching the value predicted in the present work. 16 Altogether, the reasonable correspondence with experimentally determined uptakes gives confidence that the GCMC simulations provide a sufficiently reliable estimate of the saturation uptake.  Table 5 lists the average DFT-D interaction energies obtained of AlPOs at high water loadings, with the number of water molecules per unit cell being given in the last column of Table 4 for each system. Since the energies were obtained by averaging over five snapshots, the standard deviations are also given. It is quite apparent that the interaction energies are virtually identical for all six systems, falling between -64

Aluminophosphates: Interaction with large amounts of water (near saturation)
and -66 kJ mol -1 with standard deviations in the range of 1 kJ mol -1 . The small differences among the interaction energies obtained for different AlPO structures are hardly significant when the magnitude of the standard deviations is considered, therefore, the calculations deliver no indications for an influence of the pore size on the interaction strength. An assessment of the relative contributions of dispersion interactions shows that these are largest for the systems with the smallest pores, as it would be expected based on geometric considerations. In total, however, this contribution appears to be offset by a slightly stronger nondispersive contribution in the systems with larger pores. It is worth noting that the experimentally determined heats of water adsorption for different aluminophosphates are also very similar, typically amounting to ~55 kJ mol -1 13,16 (as discussed above, the systematic difference between DFT results and experimental results can -at least to a large part -be explained with the neglect of vibrational contributions). With regard to the potential application of aluminophosphates in thermal energy storage, there appears to be no possibility to "tune" the interaction strength by judiciously choosing a system with a particular pore size or topology. This finding implies that the energy density will depend virtually exclusively on the amount of water that can be adsorbed in the system. Nevertheless, the pore size will play a crucial role in determining the pressure at which pore filling occurs at a given temperature (with smaller pores leading to filling at lower pressures), an aspect that is of considerable relevance to applications. While the present DFT-based approach is not suitable In AlPO-GIS, the volume remains practically constant. However, an evaluation of the changes in individual lattice parameters reveals a significant deformation of the unit cell, despite the negligible change in volume: An expansion by ~1.8% along a and b is almost exactly compensated by a contraction of ~-3.5% along the caxis. As discussed above, the eight-ring windows in guest-free AlPO-GIS are elliptically distorted, with the elongated axis being approximately parallel to the c-axis. Upon water adsorption, this elliptical distortion is considerably reduced. The pronounced change in framework structure coincides with the frequent formation of five-coordinated Al atoms: Between two and four of these atoms per unit cell are found in the different snapshots, and there is also one case of six-coordinated Al (Fig. 2).
For the case of AlPO-RHO, a pronounced volume reduction of ~-2.6% is observed, with the volume changes of the snapshots varying between -1.9% and -3.6%. A closer inspection of the lattice parameters after transformation to the pseudo-cubic setting of the cell reveals that this contraction is not isotropic, but that the unit cell shrinks anisotropically along one or two directions (Table S13). The contraction is associated with a distortion of the lta cages. Since a considerable degree of flexibility of the RHO structure has been observed and rationalised for the aluminosilicate form, 60

Silicoaluminophosphates: Interaction with small amounts of water (1 H 2 O per framework proton)
The results obtained for SAPO materials with one water molecule per framework proton are summarised in Table 6, which reports interaction energies as well as selected interatomic distances. The following discussion groups the systems according to the position of the framework proton at which the water molecule is adsorbed (eight-ring vs. six-ring protons, last column of Table 6).  Fig. 3 (top). In SAPO-43_O12, the water molecule is also located inside an eight-ring window. Here, the interaction is even stronger (-101 kJ mol -1 ) because the distortion of the eightring window permits two short secondary contacts (Fig. 3 middle). Of all systems where the water molecule is associated with an eight-ring window, the weakest interaction is observed in SAPO-RHO_O11 (-89 kJ mol -1 ). The decomposition of the total interaction energy shows that this is primarily due to a reduced non-dispersive contribution. A closer inspection of the local environment reveals that the water molecule is not located inside the eight-ring window, but above it (Fig. 3 bottom). This leads to fairly long secondary contacts, and thus weaker electrostatic interactions between the guest molecule and the framework.
In those cases where the proton is located at the top of a d6r unit (SAPO-56_Si1_O5, SAPO-18_Si3_O31), the water molecule assumes a tripod-like configuration above the d6r unit, with three relatively short hydrogen-oxygen contacts (Fig. 4, top illustrates this for SAPO-56_Si1_O5). Despite these short contacts, the total interaction is comparatively weak, in the range of -89 kJ mol -1 , with both the non-dispersive term and the dispersion contribution being smaller than for systems where the water molecule is located inside an eight-ring window. In SAPO-17, the interaction with adsorbed water is weakest among all systems, with interaction energies in the range of -75 kJ mol -1 . In both SAPO-17_Si1_O3 and SAPO-17_Si2_O5, the protons point across six-ring windows, with relatively short contacts to the oxygen atoms at the opposite side of the ring. Upon water adsorption, the proton is displaced considerably from its previous equilibrium position in both cases, and the weak overall interaction can be explained with the energetic "penalty" associated with this displacement (Fig. 4 middle and bottom).
In addition to the interatomic distances between the atoms of the water molecule and the closest framework atoms, the length of the intra-framework O-H bond d(O-H) before and after H 2 O adsorption is also given in   Fig. S7). Within each group, an increased elongation corresponds to a stronger interaction, however, the elongation corresponding to a certain interaction energy is much larger if the water molecule is adsorbed at a proton that is associated with a six-ring. These observations provide a possible means for the spectroscopic distinction of different framework protons, as the frequency shift upon water adsorption should be more pronounced in systems where the proton is associated with a six-ring.
For completeness, we also summarise the changes in the unit cell dimensions upon adsorption of small amounts of water in SAPOs: The overall changes in volume are very modest, ranging between virtually no change and a slight volume contraction of up to -0.8%. The typical changes in individual lattice parameters are even smaller (Table S14). For the case of SAPO-34, this observation is in accordance with the findings of the previous computational (ab-initio MD) study of Van Speybroeck and co-workers, who observed only minimal changes in the lattice dimensions upon addition of small amounts of water. 32

Silicoaluminophosphates: Interaction with large amounts of water (near saturation)
The DFT-D interaction energies obtained for SAPOs at high water loadings are included in Table 5. A direct comparison with the corresponding AlPOs shows that the interaction in the SAPO materials is 4 to 7 kJ mol -1 stronger, in the range of -69.5 kJ mol -1 (SAPO-56) to -73 kJ mol -1 (SAPO-34, . For all structure types, the differences in interaction energy between AlPO and SAPO analogues are significantly larger than the calculated standard deviations, which do not exceed 2 kJ mol -1 . A closer inspection of the individual results shows that the difference is primarily due to an increased contribution of non-dispersive interactions in the SAPO materials (Table S15 to S24 of ESI). It is obvious that the electrostatic interaction of water with charged-framework SAPOs will be stronger than for neutral-framework AlPOs by virtue of the direct interaction of some water molecules with framework protons on the one hand, and due to the increased polarity of the pore wall on the other hand. Conversely, the contribution of dispersive interactions (in absolute terms) should be virtually identical for AlPOs and SAPOs with the same topology, and this is indeed observed. As for the AlPOs, there is no apparent correlation of the interaction energy with the pore size. However, while the differences among the interaction energies obtained for different SAPOs are only slightly larger than the typical standard deviation, a correlation of the interaction energy with the Si content For those systems where different Si distributions were considered, particularly SAPO-56 and SAPO-18, the variations among the interaction energies obtained for different models are minimal, so it can be concluded that, in contrast to the pronounced differences at low water loadings, the actual location of silicon atoms and framework protons hardly affects the interaction with water at near-saturation conditions. The same observation was made in our earlier study of SAPO-34, where the interaction energies obtained for a model with eight-ring protons (SAPO-34_O1) was practically the same as for a model with six-ring protons (SAPO-34_O3). 35 For this particular SAPO, the DFT-D interaction energy after applying an approximate correction for vibrational effects of +7 kJ mol -1 compares very favourably with experimentally measured heats of adsorption at high water loadings, which are in the range of 65 kJ mol -1 . 6 An analysis of the changes in volume (and in individual lattice parameters) upon water adsorption shows that the SAPOs behave very similarly to their AlPO counterparts, with the deformations being on average somewhat larger: SAPO-34, -56, and -18 exhibit a slight shrinkage upon water adsorption without preferential orientation, whereas a shortening of the longest axis of the eri cage is observed in SAPO-17. In SAPO-43, an expansion along a and b is offset by a contraction along c, and for the case of SAPO-RHO, a pronounced volume shrinkage in the range of ~-3% is observed, which is often (though not always) fairly anisotropic.
An inspection of the individual snapshots of water-loaded SAPOs shows that the most of the framework protons have left their initial position after the DFT-D optimisation, forming H 3 O + ions or, less frequently, (Fig. 5 top). The charged species in the final configurations are often, but not always, in the vicinity of the original location of the framework proton. It has been established in previous computational work that framework deprotonation does not occur when only one or a few water molecules are adsorbed per proton, while it becomes energetically favourable when larger water clusters (e.g. tetramers) interact with one proton. [22][23][24] A recent ab-initio MD study of water-loaded SAPO-34 emphasised the high mobility of the protons in this system at a temperature of 350 K. 32 While the present work, which is based on static DFT optimisations, cannot quantify the effect of temperature on the mobility, the observation that framework deprotonation occurs in the large majority of cases is in accordance with these previous findings.
The removal of framework protons from their initial positions is observed frequently in all SAPOs studied, regardless of the topology (or silicon content).  (SAPO-34_O1, SAPO-18_Si3_O31), however, this does not necessarily reflect a reduced tendency of these systems to form five-coordinated Al due to the limited number of configurations sampled (in this context, it is worth noting that Al V atoms were found in several snapshots of water-loaded SAPO-34_O1 in our previous study). 35 As discussed previously, ab-initio MD simulations would be very helpful to study the formation of five-coordinated Al in a more quantitative fashion, especially with regard to the influence of temperature. Another interesting observation from the present investigation is the preferential occurrence of five-coordinated aluminium in the direct vicinity of the silicon atoms, which is most pronounced in SAPO-43_O12 (Fig. 5 bottom).

Conclusions
The dispersion-corrected DFT calculations employed in this study have delivered detailed insights into the energetic and structural aspects of water adsorption in AlPOs and SAPOs with different topologies, which can be summarised as follows: (1) Due to the absence of strongly preferred adsorption sites in AlPOs, the interaction with small amounts of water was investigated only for SAPOs. The interaction is markedly stronger when the framework proton points into an eight-ring than in situations where the proton is located above a six-ring. If it was possible to fully control the proton locations in a real material, the interaction energy could be "tuned" in a certain range, with eight-ring protons leading to higher energy densities, and six-ring protons allowing for lower desorption temperatures. However, since the different proton sites are often extremely close in energy (e.g. in , such a control is unlikely to be possible in real materials. Moreover, the considerable mobility of the protons would lead to a rearrangement during water adsorption/desorption cycles. Nevertheless, further insights could be expected from a comparative study of zeotypes that contain eight-rings, but no six-rings on the one hand (e.g. , and systems with six-rings and larger rings, but no eight-rings, on the other hand (e.g. SAPO-5 [AFI topology, twelve-rings + six-rings] or SAPO-11 [AEL topology, ten-rings + sixrings]). 40 It would be interesting to see whether the conclusions of the present study also hold for a wider range of structure types.
(2) At high water loadings, there is no evidence for a significant effect of the topology on the material's affinity towards water. When accounting for the contribution of thermal motion in an approximate fashion, heats of adsorption in the range of 55 to 60 kJ mol -1 can be expected for AlPOs, whereas somewhat higher values between 60 and 65 kJ mol -1 will be attained in SAPOs due to stronger electrostatic interactions. In SAPOs, the interaction with water can be enhanced by increasing the silicon content, which is directly correlated with the amount of framework protons as long as no silicon islands are formed. While no effect of the pore size on the interaction strength is observed, it has to be noted that a smaller pore diameter will lead to a pore filling at lower relative pressures. Therefore, the pore size may still determine the suitability of a certain adsorbent for given operating conditions.
(3) Unlike the adsorption energetics, the structural response of the adsorbents to water shows a considerable variation among the different topologies: While the systems that contain d6r units undergo only a moderate contraction, a much stronger deformation of the framework is observed in the zeotypes with GIS and RHO topologies (regardless of the composition). Moreover, the coordination of water molecules to framework aluminium atoms is observed more frequently in these materials. In this context, it is worth noting that a correlation between the strong binding of water to framework Al atoms and irreversible loss of crystallinity upon hydration of SAPOs has been found in a comparative MAS-NMR study of SAPO-34 (stable) and SAPO-37 (decomposes upon dehydration). 62 Due to the severe structural changes observed for water-loaded GIS-and RHO-type AlPOs and SAPOs, it can be hypothesised that irreversible transformations might occur during water adsorption/desorption cycles. Such changes are likely to have a detrimental effect on the longterm performance of an adsorbent, rendering them unsuitable for heat transformation applications.
Altogether, the DFT-D computations permit us to conclude that the adsorption energetics in AlPOs and SAPOs are hardly influenced by the topology. There is thus little scope to "tune" the interaction strengthwhich is directly related to the amount of thermal energy that can be stored -by a judicious choice of a certain framework type. More promising strategies that can be envisaged are the variation of the silicon content in SAPOs and the incorporation of other elements in the framework (metal-containing aluminophosphates [MeAPOs]). 40 On the other hand, the topology determines the structural response of the material to water, which is why rather large variations in long-term stability have to be expected for AlPOs and SAPOs having different framework types. In this context, the present results, and possible future studies using ab-initio MD simulations, may provide useful information that will facilitate the identification of suitably stable adsorbents.