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. 2023 Jul 22;3(5):274–282. doi: 10.1021/acsorginorgau.3c00014

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

Daniel Malcolm †, Laia Vilà-Nadal †,*
PMCID: PMC10557121  PMID: 37810411

Abstract

graphic file with name gg3c00014_0009.jpg

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.

Keywords: cluster chemistry, molecular structure, electronic structure, computational chemistry, polyoxometalate benchmarking

Introduction

Molecular metal oxides, commonly referred to as polyoxometalates (POMs), are ordered, inorganic metal-oxide clusters,1,2 with the general formula [MOx]n (where M = Mo, W, V, Nb, x = 3–7, n = 6–368).3 These clusters spontaneously self-assemble from oxometalate monomers under appropriate, usually acidic, reaction conditions.4 The range of potential applications for POMs spans many different fields and disciplines including use within biological systems,5,6 as components within supramolecular assemblies,7,8 as catalysts,9,10 as electron storage molecules,11,12 and for increasing the storage capabilities of portable memory devices.13

One particularly promising area of application is porosity/adsorption, where the wheel-shaped POM [P8W48O184]40–, shortened to {P8W48},14 is an especially good candidate owing to its relatively large central pore (1 Å/0.1 nm diameter), exceptional electrochemical properties, unusually high anionic charge, and robust synthetic route (Figure 1).14−16 The central pore can be utilized for several different purposes, including encapsulating countercations17 and providing a scaffold for a multimetal construction, where the metal is Fe,18 or Cu,19,20 that confers magnetic properties to the POM as a whole. A {P8W48} wheel is formed from 4 [P2W12O48]14– hexa-vacant lacunary units, shortened to {P2W12}, each of which originates from a Wells-Dawson (WD) type framework (P2W18O62]6–), abbreviated as {P2W18},16,17 after it has been exposed to mildly basic conditions. WD species are frequently utilized in POM chemistry due to their relative stability, which extends across 6 isomers and a large combination of heteroatoms and lacunary sites.21,22 Other than the {P2W18} WD already outlined, 2 other WDs capable of forming stable hexalacunaries after basic degradation have been identified: [Se2W18O60]4–23 and [As2W18O62]6–.24 Creation of these lacunary sites under basic conditions allows for the insertion of new transition metal elements not currently present in the POM, enabling the capability for fine-tuning of the redox properties, catalytic localization and activation of the framework,22 and assembly of the POM into a building block suitable for POMzite construction.23,25,26

Figure 1.

Figure 1

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Synthesis of (A) [P8W48O184]40– via [P2W18O62]6– WD and [P2W12O48]14– lacunary intermediates16,17 and (B) [Se8W48O176]32– via [Se2W18O60]4– WD and [Se2W12O46]12– lacunary intermediates.23 Basic conditions exist only during step 2, during which the framework loses roughly one-fourth of its structure.

In 2017, Boyd et al. demonstrated how {P8W48} POMs can additionally be used to construct a species of porous nanomaterial commonly referred to as a POMzite.26 In these POMzites, individual POMs are linked together by transition metal (TM) oxide anions of the form [MOx]q–27 (where M = Mn,28,29 Co,27 V,27 Ni,26 Ag,30x = 4–6). The pairing of a rigid structure with a high degree of customizability grants POMzites the capacity to rival similar porous materials, such as zeolites and metal organic frameworks (MOFs);31 displaying the benefits of both while suffering from the disadvantages of neither.32

One particularly promising study by Zhan et al. illustrates this point perfectly, where the POMzite synthesized was capable of existing as one of 8 distinct states and of transforming from one state to another when exposed to changes in NH3 or CH3OH concentration or in temperature/hydration.33 Each conformation has different absorption properties and stabilities, allowing for precise tuning and enhancement of functionality for a particular application. This inherent ability of a material to repeatedly alter its crystallinity and properties based on controllable stimuli has the potential to revolutionize the materials industry.

Compared with zeolites, the elements that compose POMzites are rarer,34 which, combined with the lack of a comprehensive understanding of their self-assembly processes, acts to drive up the costs associated with researching these materials. Tackling this problem in a brute force manner in the lab promises to therefore be a costly endeavor,35 with no guarantee of yielding an optimal POMzite capable of recuperating financial losses. Consequently, an alternate method is required that reduces the fiscal burden either by limiting synthetic costs36 or by employing a computational approach which reduces lab time.

Inverse design37,38 is a method that has the potential to provide a workaround; designing a molecule or material in this manner requires a theoretical model of the product, one that is expected to fulfill a specific role, followed by working backward along the synthetic route until the reagents and reaction conditions necessary to yield the desired product are elucidated. It also allows for easy experimentation with novel ideas, testing the waters to determine if an approach is feasible before expensive lab work is undertaken.17,39 This approach, however, requires a greater understanding of the self-assembly process in order to accurately simulate both real and hypothetical structures.40 If we are to properly apply the tenets of inverse design, we must have the capabilities to build and analyze complex computational models of POMs and have a deep knowledge of their self-assembly processes.41

Herein we present our {X8W48} wheel, {X2W18} WD and {X2W12} hexalacunary calculation-based data, complete with HOMO–LUMO gap energy values, molecular electrostatic potential maps (MEPs), and standard deviation (STD) calculations. This is intended to deepen our fundamental understanding of these molecules so as to simulate them and currently theoretical but chemically promising derivatives more accurately.

Computational Details

All calculations were performed using the Amsterdam Modeling Suite (AMS 2023.1).42,43 In this work, we have been comparing the results from using several different functionals: the nonempirical Perdew–Burke–Ernzerhof (PBE), the generalized gradient approximation (GGA) exchange-correlation functional,44 the empirical exchange-correlation functionals of Becke and Perdew,45,46 the B3LYP hybrid functionals,47 the PBE0 functional of Adamo and Barone,48,49 a dispersion correction in the form of DFT-D2,50 which was applied to PBE (PBE-D) and B3LYP (B3LYP-D), the range separated functional wB97X,51 and the Minnesota 2006 local functional (M06-L).52 Relativistic corrections were included by means of the ZORA formalism.53 Triple-ζ polarization (def2- TZP),54 triple-ζ plus polarization (def2-TZ2P), and (def2-QZ4P) basis sets were employed to describe the valence electrons of all atoms, all of which were from the ADF basis set library.55 Structures were optimized in the presence of a continuous model solvent by means of the conductor-like screening model (COSMO), with water as a solvent.56,57

The solvation radii values used were the standard van der Waals values for ADF,58 determined by Alvarez.59 Computational results were obtained using the ARCHIE-WeSt High Performance Computer (see www.archie-west.ac.uk) based at the University of Strathclyde.

Results and Discussion

Initially, we tested the accuracy and time effectiveness of the computational methods available in SCM-ADF.41 We chose our functionals and basis sets from a broad range of methods, some of which had been previously used in other computational POM studies. The most used functional in the literature was PBE,41,60−62 as established by Swart and co-workers in their 2021 review;63 in terms of basis sets, the literature indicated that def2-TZVP is the best choice, although TZP acts as a substitute due to def2-TZVP not being included in the ADF package.23,64,65 We also compared the effects of using either no, small, or large frozen cores and of single point vs optimization tasks.

To this end, we utilized GGA (PBE, BP8641), GGA-D (PBE-D), hybrid (B3LYP,41 B3LYP-D, PBE041,66), and range separated functional(s) (wB97x), and a few basis sets (TZP,62,66 TZ2P,66 QZ4P66) to obtain a broad distribution of results and to aid in selecting the appropriate level of theory for our purposes.

The functionals which most closely corresponded to the empirical data out of the range tested were PBE and BP86 (Figure 2). Going forward, we chose to use a GGA (PBE) functional and TZP basis set, paired with a small frozen core and a COSMO solvation model67 as part of an optimization task (see SI-1 for full results, as well as for details on fragments and results of benchmarking).

Figure 2.

Figure 2

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HOMO–LUMO gap energy values for a range of functionals and basis sets. The data presented here are for {P2W18}. Functional calculations were run with a TZP basis set, small frozen cores, and the COSMO model with water as a solvent; these conditions were maintained for the basis set calculations, with the only difference being PBE as the functional.

To complete our benchmarking, we also compared the accuracy of our results against work done by Cameron et al.,23 Zhang et al.,68 and Vilà-Nadal and co-workers.69,70 Our results were very close in value to those of Vilà-Nadal and Zhang, and, despite a larger difference in values caused by different computational software, were in good agreement with the Cameron work as well. Our optimization calculations of {P8W48} and {P2W12} yielded the nature of the HOMO and LUMO orbitals (Figure 3), as well the energy gap between them,71,72 and the molecular electrostatic potentials (MEPs) (Figure 4). The HOMOs for both POMs receive their greatest collective atomic contribution from the framework oxygens, specifically the PY orbitals, located “behind” the heteroatoms in the center of the POM. This is a typical distribution observed in POMs, as described in an RSC paper by Poblet et al.73 In addition to {P8W48}, we also ran calculations on [Se8W48O176]32– and [As8W48O184]40–, both of which have been previously reported in the literature (see SI-3 for {As8W48} and {Se8W48} HOMO and LUMO visualizations, and SI-4 and -7 for the electronic values for all hexalacunary and {P8W48} POMs featured in this work).23,74,75

Figure 3.

Figure 3

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Visualization of HOMO and LUMO orbitals for {P2W12} (A) and {P8W48} (B), with labeling of the 4 atoms that contribute most to their respective orbital band.

Figure 4.

Figure 4

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MEPs for [P8W48O184]40– (A), K8[P8W48O184]32– (B), [Se8W48O176]32– (C), and K8[Se8W48O176]24– (D) and LUMO visualizations for [P8W48O184]40– (E), K8[P8W48O184]32– (F), [Se8W48O176]32– (G), and K8[Se8W48O176]24– (H). Geometries were optimized and MEP generated with DFT/PBE/SFC/TZP. More nucleophilic (negative) regions are visualized in red, and more electrophilic (positive) regions are visualized in blue. The color ranges for the MEPs are −2.40 to −1.50 (A), −1.90 to −1.20 (B), −1.80 to −1.20 (C), and −1.40 to −0.73 (D). Basis sets, TZ2P and QZ4P, were observed to alter the HOMO–LUMO gap value only negligibly and took at least 9 times longer to converge.

In contrast, the position of the LUMO orbitals differs between the {P2W12} and {P8W48} structures; in the lacunary (Figure 3B), they are localized on the tungsten atoms, the DYZ orbital specifically, connected to the main HOMO oxygens, forming a complete square at the back of the lacunary. With the full {P8W48} wheel, however, the LUMO shifts onto the tungsten atoms which link each lacunary quarter of the wheel together (Figure 4E). The fact that successive reductions will increase electron density in these areas is key to understanding how injection of electrons affects regional stability, as it may influence the tendency of the ring to disintegrate back into its lacunary substituents if reduced to a high enough degree. The threshold at which this disintegration will occur is currently unknown but appears to be high, allowing for at least 18 or 27 successive reductions of {P2W18} or {P8W48} respectively.76

The MEPs revealed that the interior of the ring is more nucleophilic than the exterior, which explains why this POM is exceptionally good at trapping cations within its central pore (Figure 4A and C). This polarization of electrons is likely due to the phosphorus atom, which is in the closest proximity to terminal oxygen atoms along the interior face.

Countercations, such as those present in K8[P8W48O184]32–, are introduced during synthesis to stabilize the highly anionic charge of the framework; they achieve this by situating themselves near the highly nucleophilic oxygen atoms, thereby reducing the high degree of polarization and increasing the overall electrophilicity of the POM. This is clearly visible in Figure 4B and D, where the “red hot” nucleophilic region in the center diffuses over more of the POM, visible as an orange section. A small reduction in nucleophilicity is visible for {Se8W48} around the “hinge” areas where the lacunaries link up compared to {P8W48}; this is due to {Se8W48} lacking 2 oxygens per hinge region in these areas. With K8{P8W48}, the presence of the countercations within the highly nucleophilic in the interior face is reduced in intensity, closer to that of the surrounding areas.

The MEPs we obtained were in good agreement with the literature, where cations/cationic scaffolds assemble within the pore specifically; the works of Ulrich Kortz,20,77 and Thomas Boyd,17 spring to mind. Thus, we can prove that we can produce an accurate DFT-level model of {P8W48}. LUMO visualizations in Figure 4E and F are almost identical, indicating that inclusion of countercations has a minimal effect on the position and intensity of the LUMO orbitals. There is, however, an observable, if slight, difference in LUMO localization between Figure 4E and F, implying that the choice of heteroatom can help tune reduction, specifically where it occurs (see SI-5, -6, and -8 for the full range of MEPs obtained during this work).

We initially utilized only 8 K countercations in our geometry, yet the full formula for {P8W48} is K28Li5H7[P8W48O184]; the models we have constructed thus far may be less than accurate at describing the true structure, especially given that our benchmarking for {P8W48} has not been conducted against empirical data. To rectify this, we built several Kn{P8W48} frameworks, progressively adding K countercations every time. We based the positions of each potassium cation on available POMzite xyz files,26,78 which can include up to 18 K cations per {P8W48} wheel, and added in the rest based on the principle of maintaining/improving symmetry of the overall structure (see Figures 5, S19, and S20). Symmetry is a key factor to keep in mind when designing a molecular model, as a more symmetrical system will take less effort to converge due to there being fewer unique interactions throughout the molecule to consider.

Figure 5.

Figure 5

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Measurement of angles and diameters within the [P8W48O184]40– (A) wheel, with angles (blue), the smaller, “inner”, pore diameter (yellow), and the larger, “outer”, pore diameter (green). (B) The pore diameter increases as more cations are included in the {P8W48} structure. A subplot is included that shows the experimentally obtained values in relation to those measured from calculations.

Determining the mean diameter of the {P8W48} from several points of experimental data, we compared this value against that from our optimized geometries (see SI-9 for the full list of structures used and the data extracted from them); we discovered that the structure with 8 countercations was the closest in diameter to the experimental mean. Inclusion or exclusion of more cations increased the diameter value. When also compared against the computational effort required to converge each geometry (Figure S20), it becomes clear that 8 K countercations yields the best reflection of reality while still being computationally efficient; an efficient calculation is able to reach the convergence point for a structure within a reasonable amount of time given the number of cores used. For molecules of a size akin to {P8W48}, a total calculation time of less than a week when 30 cores are used is considered efficient. Additionally, we compared our converged geometries for {As8W48} and {Se8W48} against the available empirical data, and both were in good agreement (see SI-10 and -11 for the full {As8W48} and {Se8W48} benchmarking data).

We theorize that the ideal model only contains 8 K cations due to the implicit limitations imposed by this computational modeling. Cations such as K are surrounded by a score of solvent molecules in solution, which prevents tight bonding occurring between the cation and POM; when using an effective solvation model such as COSMO, however, where the solvent is simulated via a medium, this aspect of solvent interaction is lost. The significance of this is that each cation in a theoretical model now exerts a much greater influence on the overall electron distribution and stability of the molecule than would be observed in solution.

When the difference in diameter values between our theoretical models and the available empirical data is arranged into a boxplot (see Figure 6), we can observe several points of interest. First, there is little change in the proportions of the differences between calculated and empirical diameters as more cations are included in the structure; inner diameter 2 and outer diameters 1 and 2 barely change across the four boxplots. The exception is inner diameter 1, which experiences an increase in diameter between the addition of 8 and 14 potassium cations (see SI-12 for the full list of potassium countercation data, including the error values).

Figure 6.

Figure 6

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Boxplots showing difference between calculated and empirical diameters across a range of 4 distinct diameters for a [P8W48O184]40– (A), K8[P8W48O184]32– (B), K14[P8W48O184]26– (C), and K18[P8W48O184]22– (D) framework.

We theorize that this increase in the value of inner diameter 1 is caused by the uneven addition of cations to the exterior of the POM; two hexalacunary sections receive 2 K cations, while the other two only benefit from one. This configuration results in a pinched geometry, with the two sections featuring 2 cations repelling more strongly from the similarly cationic pore than the other two.

This increase in the value of inner diameter 1 actually increases symmetry throughout the POM; the “default” structure without any cations is slightly oval, with one inner diameter longer than the other. The addition of cations aids in decreasing the difference between these two diameter values, with a crossover point occurring between the inclusion of 8 and 14 potassium cations and the inner diameter values only coming within 5 pm of each other between the addition of 14 and 18 cations (Figure 7). The inclusion of cations is therefore essential for maintaining symmetry throughout the POM.

Figure 7.

Figure 7

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Comparison of values for the two inner diameter measurements in various Kn[P8W48O184](40–n)– POM structures. There is a large uptick in the pore diameter between the addition of 8 and 18 Potassium cations.

It is worth noting that cations 9–14 are added to the exterior of the POM, instead of within the pore. This arrangement of cations outside the pore as well as within is key for enforcing symmetry in a computational model, as all areas of the POM are now stabilized and prevented from being too electron dense.

This enforcement of symmetry, however, comes at the cost of increasing divergence from the empirical data. As can be seen in Figure 5, there is a difference of roughly 5 Å for the inner diameter and 8 Å for the outer equivalent.

While this difference is relatively small, it will likely continue to increase if one wanted to completely charge neutralize the POM or if TM oxides were bound to the framework to simulate a portion of a wider POMzite network.

Coupled with the standard increase in computational nodes and time required when one adds more atoms to a molecular system, there most likely exists a crossover point where, in most instances, the accuracy of results obtained from the model is of a suitable quality to not necessitate a more complex molecular model be utilized.

From our results, we have determined K8[P8W48O184]32– to be the best all-around representation of the full K28H7Li5[P8W48O184] POM framework. It is relatively easy to converge the structure with DFT, with the computational effort rising sharply upon inclusion of additional cations, and the POM exhibits pore dimensions that are more closely in line with the empirical data than the other models we tested.

Finally, we decided to run a small experiment looking at whether countercations other than K could increase the HOMO–LUMO gap for, or otherwise via a difference in size or charge aid in stabilizing, the {P2W12} and {P8W48} POMs (see SI-13 for full results). Based on trends outlined in the literature,1 we expect tungsten-based POMs to be less polarized and reactive when exposed to smaller cations, thereby exhibiting a larger HOMO–LUMO gap.

Based on our models, we found that more cationic ions, such as Mg2+ or Ca2+, tended to stabilize the HOMO and LUMO orbitals relative to their monocationic counterparts, though the HOMO–LUMO gap was reduced in magnitude. We also observed that the size of the HOMO–LUMO gap decreased slightly overall as the size of the monocation increased (see SI-13, specifically Table S22 and Figure S30, for more details).

Standard deviation (STD) and mean atomic charge (MAC) calculations conducted for each POM species proved more enlightening with respect to the effect of different cation elements; the alkali metal and earth cations with the smallest ionic radius displayed the lowest SD value for the molecule as a whole and relatively low values when the constituent elements were examined individually. A small STD value in this context signifies a less polarized POM, which will, in turn, be less reactive and therefore more stable overall. MAC data similarly placed smaller cations as promoting delocalization of the framework electrons, moving the mean elemental charge toward neutral zero more than their larger counterparts. (see Figures 8 and SI-13, specifically Tables S23 and 24).

Figure 8.

Figure 8

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Variation in range of atomic charges within a X8[P8W48O184]n− POM, where X = Li+, Na+, K+, Rb+, Be2+, Mg2+, Ca2+.

Conclusions

In this work, we have conducted DFT-level computational research into {X8W48}-type POMs and their precursor species, WD and WD-hexalacunaries, and used the data collected to identify the structural characteristics in the molecule responsible for key chemical and electronic properties. We have also determined K8[P8W48O184]32– to be the simplest representation of the full K28Li5H7[P8W48O184] molecule, while still being accurate to the empirical data present. Unless one wishes to model a POMzite subsection, for instance, or another molecular system that uses the {P8W48} POM as a building block that sees the overall anionic charge far exceed the original, already high value of −40, K8{P8W48} is a very suitable model. Finally, we conducted some preliminary theoretical work into the effect of using countercations other than potassium for {P8W48} POMs, with an indication that there are subtle trends down an elemental group or across a row, but overall, the presence of any countercation plays a bigger role in altering molecular properties than the species deployed. In the future, we hope to gain a better understanding of the dynamics of cation–POM interactions by studying the cation mobility on the POM surface.

Acknowledgments

The authors acknowledge Jake Thompson and Michael Nicolaou from the LVN-group for helping converge particularly troublesome calculations and for aiding with coding our Python-based graphs. We also thank Maria Aliaga for proofreading the manuscript. Financial support for this work was provided by University of Glasgow and the Engineering and Physical Sciences Research Council Grants (EP/S030603/1; EP/V048341/1; EP/S031170/1), Royal Society of Chemistry RSC Hardship Grant (Covid-19). We thank the EPSRC Doctoral Training Parntertship (DTP) funding received by the University of Glasgow for Daniel Malcolm PhD studentship “Metal oxides by design” project 2443457 (EP/R513222/; EP/T517896/1). We also thank the University of Glasgow (UofGla) Early Career Development Programme (ECDP) 2021, the UofGla Reinvigorating Research Scheme 2022, and the School of Chemistry for long-lasting support. Results were obtained using the ARCHIE-WeSt High-Performance Computer (www.archie-west.ac.uk) based at the University of Strathclyde.

Glossary

Abbreviations

{P2W18}

the parent Wells-Dawson phosphotungstate polyoxometalate anion, with the formula [P2W18O62]6–

{P2W12}

the main [P2W12O48]14– lacunary synthesized from the parent WD

{P8W48}

the wheel-like POM [P8W48O184]40–

K8{P8W48}

the full wheel with Potassium countercations present, full formula K8[P8W48O184]32–

{Se8W48}

[Se8W48O176]32–

{P4W24}

a half-section of {P8W48}, [P4W24O96]28–

Data Availability Statement

The data underlying this study is freely available in the ioChem-BD database at https://www.iochem-bd.org/handle/10/344938.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsorginorgau.3c00014.

  • Additional experimental and computational information, including empirical data obtained from the literature and full explanations behind calculations of structural errors (PDF)

Author Contributions

L.V.-N. conceived the idea, designed the project and together with D.M. designed the modeling strategy. D.M. did all the theoretical calculations and analyzed the data together with L.V.-N. D.M. wrote the paper with input from L.V.-N. CRediT: Daniel Malcolm formal analysis (equal), investigation (equal), methodology (equal), writing-original draft (equal), writing-review & editing (equal); Laia Vilà-Nadal conceptualization (lead), data curation (lead), formal analysis (equal), funding acquisition (equal), investigation (equal), methodology (equal), project administration (lead), resources (lead), software (lead), supervision (lead), validation (lead), visualization (equal), writing-original draft (equal), writing-review & editing (equal).

The authors declare no competing financial interest.

Supplementary Material

gg3c00014_si_001.pdf (1.3MB, pdf)

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

gg3c00014_si_001.pdf (1.3MB, pdf)

Data Availability Statement

The data underlying this study is freely available in the ioChem-BD database at https://www.iochem-bd.org/handle/10/344938.

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