Computational Study into the Effects of Countercations on the [P8W48O184]40– Polyoxometalate Wheel

Porous metal oxide materials have been obtained from a ring-shaped macrocyclic polyoxometalate (POM) structural building unit, [P8W48O184]40–. This is a tungsten oxide building block with an integrated “pore” of 1 nm in diameter, which, when connected with transition metal linkers, can assemble frameworks across a range of dimensions and which are generally referred to as POMzites. Our investigation proposes to gain a better understanding into the basic chemistry of this POM, specifically local electron densities and locations of countercations within and without the aforementioned pore. Through a rigorous benchmarking process, we discovered that 8 potassium cations, located within the pore, provided us with the most accurate model in terms of mimicking empirical properties to a sufficient degree of accuracy while also requiring a relatively small number of computer cores and hours to successfully complete a calculation. Additionally, we analyzed two other similar POMs from the literature, [As8W48O184]40– and [Se8W48O176]32–, in the hopes of determining whether they could be similarly incorporated into a POMzite network; given their close semblance in terms of local electron densities and interaction with potassium cations, we judge these POMs to be theoretically suitable as POMzite building blocks. Finally, we experimented with substituting different cations into the [P8W48O184]40– pore to observe the effect on pore dimensions and overall reactivity; we observed that the monocationic structures, particularly the Li8[P8W48O184]32– framework, yielded the least polarized structures. This correlates with the literature, validating our methodology for determining general POM characteristics and properties moving forward.


SI−1: Benchmarking Results
Based on the results displayed in Table S2.-S4., we can conclude that ADF at the PBE level accurately describes the HOMO-LUMO energy gap and reduction energy values for POMs.Table S2.simply gave us a baseline to compare our ADF calculations with, whereas Table S3.allowed for comparison with the TURBOMOLE software; the benchmarking against TURBOMOLE is poor but this is attributed to the differences between software packages, as well as the use of B3LYP which we have found to be overestimate POM properties relative to PBE.For Table S4.α-isomers were in very good agreement with the experimental data but less so for the other isomers; this is attributed to the non-α-isomers being built within the ADF programme and not originating from an experimentally obtained xyz file.Manipulating structures to the extent of rotating sections tends to yield results further from the literature than those which are not.Finally, we come to Table S5., where bond lengths and angles for the classical WD framework are benchmarked.Though our calculations are slightly out of the expected range for a couple of properties, namely P-P, and tend to be at the greater extreme of the accepted range, they are generally within the boundaries for the sake of accuracy and provide a solid end to our benchmarking.
By comparing our calculated results against reported empirical and theoretical data, we have demonstrated that PBE and TZP are the most desirable functional and basis set respectively.

SI−2: Alternative Se Quarters
Towards the beginning of this investigation we used a xyz file from a paper by Cameron J.M. et al for our {Se8W48} wheel. 2 It was noticed that the oxygen atom missing from the structure due to the heteroatom anion being SeO3 (the oxygen is not missing when the anion is XO4 or XO6) was in a different position from that usually described for WD cages that contain a XO3 anion (see Fig. S1.) 6,7,8 ; unsure as to whether this was a special case or if a mistake had been made by this paper we made a geometry for the {Se2W12} where the vacant oxygen site was in the position typically assumed to be correct, and a second WD structure where the site was in the more unusual location described by the paper.The aim was to identify if one configuration of site location yielded a more stable structure and thereby elucidate which was more suitable for modelling.
Our calculations found the 'normal' configuration to be the more stable of the two, but it's worth mentioning that there is not a large difference in either the electronic energy or the size of the HOMO−LUMO gap, thus we continued to use the standard configuration for the sake of consistency.
As more hexalacunaries are synthesized and characterized, it would be prudent to determine which structure is correct when these oxo vacancies arise; it may be that the standard configuration is indeed correct and that a previously unknown rearrangement process occurs in an effort to stabilise the lacunary.The TM atoms for all of the relevant structures are within the ring, facing in, leading to the increased degree of distortion in both angle and ring diameter relative to the base {P8W48} wheel (see Fig. S14., where the structure of Co8[P8W48O196] 48-is given as an example of this).K7As10[P8W48O200] 15-is a particularly strong example of this due to not only containing the greatest number of countercations out of the structures considered here, but also due to said cations forming a rigid 'core' which the POM is forced to stretch around.Table S11.Collection of empirical angle dimensions for {As8W48} structures, with a set of angles from a DFT structure for comparison.Included also is the crystal R-factor, which parameterizes the quality of the crystal.

Formula
Crystal Rfactor (%)    As more cations are added, the model gets further away from the experimental data (larger MAE).This is associated with a decrease in the mean STD, which on paper seems to indicate better clustering around the mean; this is misleading, however.The STD trend actually relates to the calculated dimensions growing steadily away from the experimental ones, thus they become more clustered around each other relative to a further calculated value.Standard deviation (SD) decreases throughout the entire tungsten-48 molecules as more potassium cations are added to the structure; this indicates a reduction in molecular reactivity and, therefore, an increase in stability.Examining SD by element doesn't provide much additional insight; oxygen and tungsten, the main constituent elements, become less polarised in an overall uniform manner as more cations are added.Phosphorus increases slightly, but this is due to potassium inclusion not being perfectly symmetrical with regard to these elements.It is worth noting that SD for potassium increases sharply after addition of 4 cations; this is due to a reduction in symmetry from the K4 structure, with more potassium cations being added in increasingly individual locations in order to balance the charge.A lot of the difference in STD within the framework is tied to variation in the element used as cation.The dicationic species in particular have relatively high variance between individual atoms, which may explain why the HOMO-LUMO gaps for these POMs are smaller than their monocationic counterparts.
It is worth mentioning that Be8[P8W48O184] 24-has a strained structure, lacking the ordered symmetry of the other POM frameworks.This may be due to Be being the smallest cation experimented with but regardless, it displays relatively anomalous results, such as a STD value for the phosphorus heteroatom that is two orders of magnitude bigger than the same property from the other POMs.The data for mean atomic charge highlights how the smaller cation has a more stabilizing effect on the POM; Li8[P8W48O184] 32-is the best example of this, with all the mean atomic charge values for the various elements being collectively closer to zero than the other examples.

Figure S1 .Figure S2 .
Figure S1.Comparison between 'standard' and 'alternative' {Se2W12} quarter structures.A green sphere is used to illustrate where the vacant oxygen site is in each framework.(B3LYP/TZP/SFC/COSMO)

Figure S17 .
Figure S17.Geometry of K28[P8W48O184]12-with K cations coloured in order of their addition to the initial [P8W48O184] 40-structure.The orange K atoms were added first, followed by the green, and so on; in this way K8[P8W48O184] 32-contains the atoms coloured orange and green in the above image.

Figure S20 .
Figure S20.Trend of computational time required to converge the structure to increase as more potassium cations are included in the structure.

Figure S21 .
Figure S21.Difference in atomic charge throughout the whole POM species as the number of potassium cation increases.

Table S1 .
List of functionals tested in this study, H-L values for the [P2W18O62] 6-Wells-Dawson.Frozen core options can be: Small (SFC), Large (LFC), or Not present (NFC)

Table S2 .
1omparison between HOMO and LUMO energy values reported by Vilà-Nadal et al.1and those benchmarked by ourselves.

Table S3 .
2omparison between HOMO and LUMO energy values reported by Cameron et al.2(TURBOMOLE) and those benchmarked by ourselves (ADF).

Table S4 .
3omparison between experimentally obtained HOMO and LUMO, and reduction energy values reported by Vilà-Nadal et al.3and those benchmarked by ourselves.

Table S5 .
Comparison 4f bond lengths and other properties for [P2W18O62] 6-between values reported by a paper by Zhang et al.4and those benchmarked during the course of this work.OPT/

Table S6 .
Electronic values for different species of [XmW12On] p− lacunaries obtained with PBE functional.

Table S7 .
Electronic values for different species of [X8W48On] p− obtained with PBE functional PBE/TZP/COSMO/Small Frozen Cores

Table S8 .
Electronic values for different species of Wells−Dawsons obtained with PBE functional.
Calculations with the ALT designation refer to structures described in SI−2

Table S9 .
Collection of empirical angle dimensions for {P8W48} structures, with a set of angles from a DFT structure for comparison.Included also is the crystal R-factor, which parameterizes the quality of the crystal.

Table S10 .
Collection of empirical diameter dimensions for {P8W48} structures, with a set of angles from a DFT structure for comparison.Included also is the crystal R-factor, which parameterizes the quality of the crystal.FigureS13displays where the inner and outer ring diameters measure to and from within the pore.

Table S12 .
Collection of empirical diameter dimensions for {As8W48} structures, with a set of angles from a DFT structure for comparison.Included also is the crystal R-factor, which parameterizes the quality of the crystal.

11: Benchmarking {Se8W48} Pore Diameter Fig
S16. Structure for [Se8W48O176] 32-, showing measurements for angles (blue), inner diameters (yellow), and outer diameters (green).TableS13.Collection of empirical angle dimensions for {Se8W48} structures, with a set of angles from a DFT structure for comparison.Included also is the crystal R-factor, which parameterizes the quality of the crystal.

Table S14 .
Collection of empirical diameter dimensions for {Se8W48} structures, with a set of angles from a DFT structure for comparison.Included also is the crystal R-factor, which parameterizes the quality of the crystal.

Table S15 .
Electronic values for different species of Kn[P8W48O184] (40-n)− Figure S19.Visualization of HOMO and LUMO stabilization as the number of K cations in the geometry increase

Table S16 .
Collection of calculated angle dimensions for Kn{P8W48} structures, with a set of empirical angles for comparison.

Table S17 .
Collection of calculated inner diameter dimensions for Kn{P8W48} structures, with a set of empirical angles for comparison.

Table S18 .
Collection of calculated outer diameter dimensions for Kn{P8W48} structures, with a set of empirical angles for comparison.

Table S19 .
Calculated errors between simulated and experimental data for Kn{P8W48} structures

Table S20 .
Standard Deviation data for Kn[P8W48O184] (40-n)-POMs.The full formula is abbreviated to the appropriate Kn value for the structure.

Table S21 .
Mean Atomic Charge data for Kn[P8W48O184] (40-n)-POMs.The full formula is abbreviated to the appropriate Kn value for the structure.Compared with SD, mean atomic charge gives us a more detailed image of what occurs when the tungsten-48 POM approaches a more charge neutral state; it tells us that electron distribution becomes more evenly distributed throughout the molecule.Traditionally, anionic oxygens become less negatively charged, whilst tungsten and phosphorus become less cationic as they accept more of the negative contribution from surrounding oxygen atoms.Potassium becomes more cationic as more countercations are added to the structure; as more cations are included, not only is the electron distribution less polarised where potassium ions are positioned throughout the structure, but each potassium also bears a smaller individual load with regards to charge balancing.

Table S22 .
Electronic values for different species of X8[P8W48O184] n−

PBE/TZP/COSMO/Small Frozen Cores Figure
S30. Visualization of variations in HOMO and LUMO stabilization as the identity of countercation in a {P8W48}-type POM changes.

Table S23 .
Standard Deviation (STD) values for X8[P8W48O184] n--type POMs.Each POM is abbreviated to only show the Xn countercation for that specific framework.The STD values for tungsten-48 POMs containing a range of different elemental countercations correlate well with the literature in 2 key points; cations are required to stabilise the highly anionic POM wheel, see that the greatest STD value for the whole framework is for the POM with no cations present, and smaller cations are the most effective at stabilizing the structure as they exhibit the largest charge density.This last point is represented by the tendency of smaller cations to trigger precipitation of the POM out of solution.

Table S24 .
Mean atomic charge values for X8[P8W48O184] n--type POMs.Each POM is abbreviated to only show the X countercation, which varies between POMs, for that specific framework.

Table S25 .
Collection of calculated angle dimensions for Kn{P8W48} structures, with a set of empirical angles for comparison.

Table S26 .
Collection of calculated inner diameter dimensions for Kn{P8W48} structures, with a set of empirical angles for comparison.

Table S27 .
Collection of calculated outer diameter dimensions for Kn{P8W48} structures, with a set of empirical angles for comparison.