Size and charge effect of guest cations in the formation of polyoxopalladates: a theoretical and experimental study

The close interplay of theoretical and experimental techniques can facilitate the understanding and rational synthesis of novel inorganic clusters, and here an impressive example is shown for the class of cuboid-shaped polyoxo-12-palladates(ii) with a central metal ion guest.


Introduction
In recent years signicant advances have been made in the control of different variables involved in the formation mechanism of polyoxometalates (POMs). However, there is a lack of systematic studies that aim at identifying unambiguously the driving forces related to the self-assembly or aggregation processes. The "template-directed" method is one popular and extremely important synthetic strategy for obtaining novel POMs. The nuclearity and topology of the products are strongly dependent on the size, shape, and charge of the template ions. For example, anions such as Cl À and SO 4 2À could be encapsu- Besides classical POMs, 3 in the last decade or so an "unconventional" POM family based exclusively on Pd II , Pt III , or Au III addenda has been developed. 4 Since noble metals are wellknown active ingredients of many catalysts, the study of noble metal-containing POMs is a particularly interesting topic. In 2004, Wickleder's group synthesized the rst polyoxoplatinate exclusively based on d 7 addenda ions, [Pt III 12 O 8 (S VI O 4 ) 12 ] 4À . 5 Since then the Kortz group has pioneered the class of polyoxopalladates(II) in 2008, 6 and the class of polyoxoaurates(III) in 2010. 7a The rst polyoxopalladate was the [H 6 6À , Pd 13 AsPh). 8 Interestingly, substitution of the capping groups is accompanied by an increase of the coordination number of the central Pd 2+ ion from 4 (Pd 13 ) to 6 (Pd 13 Se) and even 8 (Pd 13 AsPh).
In addition to the capping groups the central palladium(II) ion in the nanocube {MPd 12 L 8 } (Fig. 1a) can also be replaced by other metal ion guests, including trivalent lanthanide ions (Ln 3+ ¼ Y, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) and 3d transition metal ions (Sc 3+ , Mn 2+ , Fe 3+ , Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ ). 9 Interestingly, the nanostar {MPd 15 L 10 } (Fig. 1b) can be formed only in the presence of Na + , K + , Ag + , or Ba 2+ , 10 whereas in the presence of Sr 2+ ions the "open" nanocube {SrPd 12 L 6 L 0 3 } (L ¼ phenylarsonate, L 0 ¼ acetate) is formed. 10e Such observations bear similarities with the important template role of alkali and alkaline earth ions in the formation of various organic macrocycle-based structures (crown ethers etc.). 11 In addition to the above-mentioned nanocube, nanostar and open-nanocube structural types, some additional polyoxopalladates with unexpected geometries have been obtained, such as the bowl-shaped palladovanadate {Pd 7 V 6 }, 12a the double cuboid-shaped 22-palladates {Cu 2 Pd 22 } 12b and {Na 2 Pd 22 }, 12c as well as palladate macrocycles {Pd n } (n ¼ 60, 72,84,96,108). 13 It is evident that the central metal ion guest as well as the capping groups play a key role in the formation mechanism of polyoxopalladates, but details remain unknown. Hence the rational synthesis of novel polyoxopalladate structural types of desired shape, size and composition is virtually impossible. On the other hand, density functional theory (DFT) methods have been applied to POMs signicantly in the last two decades, in particular with respect to (i) electronic structure, (ii) rationalization of physicochemical properties, and (iii) reactivity as a function of shape and composition. 14 In order to obtain more insight into polyoxopalladate chemistry, in particular with respect to factors that govern guest metal ion encapsulation and to perhaps shed more light on selectivity issues, we have decided to perform systematic theoretical analysis for a series of 35 metal ion guests M involved in the formation of the {MPd 12 L 8 } nanocube and {MPd 15 L 10 } nanostar polyoxopalladate structural types.
The encapsulated cations were selected by considering both their charge and size, which range from alkali and alkaline earth ions to transition metal ions, as well as trivalent and tetravalent main group cations. We have discovered a remarkable competition between Pd 2+ ions and other cations, which is key for the formation of a specic polyoxopalladate structural type. With a focus on eventually being able to computationally predict experimental results, we have carefully studied experimentally (i) the capture of the largest trivalent cation La 3+ inside a polyoxopalladate, and (ii) the selective incorporation of In 3+ vs. Ga 3+ in a polyoxopalladate.

Computational method
All calculations were performed with the Gaussian 09 package. 15 The computational scheme consists of two steps. Geometry optimizations of all nanocube {MPd 12 L 8 } and nanostar {MPd 15 L 10 } polyoxopalladates were carried out at the B3LYP level without symmetry restrictions. 16 The SDD effective core pseudopotential (ECP) basis set was used for La, Yb, Lu, Eu, Ce, Th, and U, 17 the small core potential (CRENBL ECP) was used for Ra, 18 whereas the LANL2DZ basis set was employed for the main group metals (Rb, Cs, Sr, Ba, Ga, In, Tl, Sn) and transition metals (Sc, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Pd, Ag, Cd, Hf) with Los Alamos relativistic core potentials (ECPs). 19 In addition, the 6-31G** basis set was used for O, C, As, Se, H, and the encapsulated small metal ions (Li, Na, K, Be, Mg, Ca). 20 From these calculations, we obtained the energies at the B3LYP level. In order to include the long-range interaction and dispersion effects, single point calculations were performed for all optimized polyanions with two additional functionals, M06 and uB97XD. 21,22 For all steps, the continuum SMD implicit solvation model was used to simulate the effect of the aqueous solution. 23 As shown in Fig. 1, the nanocube {MPd 12 L 8 } and nanostar {MPd 15 L 10 } were selected, in which the central metal ion usually has an oxo-coordination number of 8 and 10, respectively. In order to evaluate the selective encapsulation of different guest metal ions, the reaction mechanism is simulated by scheme (1), and the complexation energy (E com ) was calculated by eqn (2) and (3): (1) where M n+ (H 2 O) 6 is the solvated cation model. Since dehydration is one fundamental factor for an accurate determination of the complexation energy, all cations were solvated by six explicit water molecules and also surrounding by the implicit model. This compound was prepared by exactly the same procedure as Na-LaPd 12 -closed. The initially formed Na-LaPd 12 -closed was removed by ltration. The ltrate was le for further evaporation, which resulted in another portion of dark red, needle-like crystals of Na-LaPd 12 -open within a few days, which were ltered off and air dried. Yield: 0.006 g (19% based on Pd This compound was prepared by exactly the same procedure as Na-GaPd 12 , but with InCl 3 (0.005 g, 0.025 mmol) instead of Ga(NO 3 ) 3 . Red, block-shaped crystals of Na-InPd 12 were obtained aer three days, which were ltered off and air dried. Yield: 0.014 g (44% based on Pd We found that guest cations with a radius smaller than 1.12Å could induce a contraction of the {O 8 } cavity (e.g. Co 2+ , Ni 2+ , Cu 2+ , Zn 2+ , Mn 2+ , Sc 3+ , Fe 3+ , Lu 3+ ) and also guest ions that have not yet been incorporated in the Pd 12 cage experimentally, such as Li + , Be 2+ , Mg 2+ , Ga 3+ , In 3+ , Sn 4+ , Zr 4+ , and Hf 4+ . In particular, Be 2+ , Fe 3+ , Ga 3+ , and Sn 4+ seem too small to be hosted efficiently, and consequently a large contraction occurs to maximize the M-O c interactions. When the ion size is between 1.13 and 1.26Å, a small expansion with Dd less than 0.1Å is needed, except for Th 4+ . However, a signicant distortion of {O 8 } was detected for ions larger than 1.28Å, such as Ce 3+ , La 3+ Sr 2+ , Ag + , K + , Rb + , Cs + , Ba 2+ , and Ra 2+ , where for some cases elongations larger than 0.4Å were observed.
It is remarkable that for most of the experimentally observed palladate nanocubes, the distortion induced by guest metal ion encapsulation is no larger than 0.1Å, and therefore the size matching between the cation guests and the cavity of the Pd 12 cage is an important factor that must be considered. Fig. 2 also suggests that guest cations with a size ranging from 0.97-1.26Å t well within the {O 8 } cavity in Pd 12 regardless of the charge (except Th 4+ ). In contrast, smaller (r # 0.95Å) and larger (r $ 1.28Å) cations are probably poor candidates for constructing {MPd 12 L 8 } palladate nanocubes from a size-matching point of view, with the optimal cation size being in the 0.97-1.26Å range.
Large guest cations are more likely to accommodate themselves in larger polyoxopalladate assemblies with larger cavities. In order to compare with our computational results on the Pd 12 nanocube, we inserted some selected cations (Li + , Na + , K + , Rb + , Cs + , Ag + , Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ , Zn 2+ , Pd 2+ ) also in the Pd 15 nanostar cage. The Pd 15 host provides a pentagonal-prismatic {O 10 } inner coordination sphere, which appears too large for encapsulation of small guest cations, such as Li + , Be 2+ , Mg 2+ , and Zn 2+ (r < 1.2Å). In this case the cations move away from the C 5 symmetry axis of the Pd 15 cage and coordinate to less than 10 oxo-ligands. Two types of such off-center coordination modes were observed from our DFT calculations, C 4 and C 5 as depicted  Although the former conguration includes ve coordinated oxygen atoms, the shorter bonds in the latter situation indicate stronger interactions. As expected, the energy differences illustrate that the C 4 mode is more stable than C 5 by 6.1 kcal mol À1 (Table S2 ‡). On the other hand, encapsulation of Na + , K + , Rb + , Cs + , Ag + Ca 2+ , Sr 2+ , Ba 2+ , and Ra 2+ (r > 1.2Å) is expected to work well for the Pd 15 nanostar cage. Some of them are strongly supported by experiments, which show that NaPd 15 , KPd 15 , BaPd 15 , and AgPd 15 can be easily observed in the presence of Na + , K + , Ba 2+ , and Ag + . 10 It is worth mentioning that Na + prefers to coordinate to a Pd 5 O 5 face (C 5 ) rather than sitting at the body centre of Pd 15 , as suggested by experiment. 10a Interestingly, Pd 2+ prefers a C 4 mode, binding to only four O c of the Pd 5 O 5 face, as shown by XRD. 10a,c The good reproducibility of the experimental results by DFT reemphasizes that the size of the cation guest indeed plays an important role in the formation mechanism of the resulting palladate structure.

Complexation energy and competition between Pd 2+ and other metal cations
Although size-matching has been established as an essential factor during palladate formation, we have to be aware that (i) the cation-cavity interaction and (ii) the dehydration ability of the cation is not included in the analysis. Thus, we next analyse why the reported cations can be encapsulated by the Pd 12/15 cages and predict some potential candidates from an energetic point of view. To rationalize this point, the complexation energy (E com ) of Pd 12 and Pd 15 for the different guest cations was computed as described in the Computational section, and the results at B3LYP level (black points) are shown in Fig. 4, as well as the energy corrections with M06 (red points) and uB97XD (green points) functionals. The results for M06 give virtually identical values as those of B3LYP functional, whereas adding the dispersion correction in uB97XD increases the values of the complexation energies, without changing the overall trends. Therefore, the results at B3LYP level can reasonably identify the trend analysis. Generally, the E com becomes more negative (exothermic) as the formal charge of the guest cation increases from +1 to +4. For alkali and alkaline earth ions the E com is   8 } nanocube cage as a function of the cation guest from monovalent to tetravalent at B3LYP (black), M06 (red), and uB97XD (green) functional level, respectively. The cations are organized by considering both their charge and size. Note that the more negative values indicate a higher affinity of Pd 12 for the respective metal ion. The E com for Ra, U, and Th at uB97XD level is not included (square) due to the unavailable van der Waals radius for these elements.
affected signicantly by the size of the cations. All encapsulations seem to be thermodynamically favourable, except for Cs + , which shows a positive E com of 18.3 kcal mol À1 . It is illustrative that the rst reported polyoxopalladate was Pd 13 with a Pd 2+ ion located at the center, 6 and that the synthesis occurred in the presence of both Na + and Pd 2+ ions. Encapsulation of Pd 2+ in the {Pd 12 (AsPh) 8 } nanocube cage is predicted to be very exothermic with a complexation energy of À54.6 kcal mol À1 , whereas Na + is much less competitive with À42.2 kcal mol À1 . Thus, it is not surprising that the Na + ions are not incorporated in the palladate structure, but rather act just as counter cations.
Following such strategy, all cations were divided into two domains with E com of Pd 2+ as a reference (dashed grey line). The E com values below the reference line indicate that from a thermodynamic point of view, the respective ions are more favourable to stabilize the Pd 12 host cage than the reference ion Pd 2+ . Thus, polyanion nanocubes of the type {MPd 12 (AsPh) 8 } are preferentially formed as compared to {Pd 13 (AsPh) 8 } (Pd 13 AsPh). For instance, encapsulation of Fe 3+ and Sc 3+ ions inside the Pd 12 shell has associated complexation energies of À124.1 ({FePd 12 (AsPh) 8 }) and À116.2 kcal mol À1 ({ScPd 12 (AsPh) 8 }), respectively, both being signicantly more exothermic than Pd 2+ (À54.6 kcal mol À1 , Pd 13 AsPh). Indeed, the nanocube family {MPd 12 (AsPh) 8 } with M ¼ Ca 2+ , Co 2+ , Cu 2+ , Ni 2+ , Zn 2+ , Mn 2+ , Sc 3+ , Fe 3+ , Y 3+ , Yb 3+ , Lu 3+ , and Eu 3+ has already been synthesized by using similar synthetic procedures. 9 In contrast, encapsulation of M ¼ alkali metal ions, Ag + , Be 2+ , Sr 2+ , Ba 2+ , and Ra 2+ in {MPd 12 (AsPh) 8 } is expected to be difficult due to the less favourable complexation energy with respect to Pd 2+ , in spite of some of them (Li + ) having a suitable size. In fact, these hypothetical polyoxopalladates have not been synthesized yet in the laboratory. Such conclusions are also valid for nanocube derivatives with other capping groups, such as arsenate (AsO 4 3À ) and selenite (SeO 3 2À ), see Fig. S3. ‡ The absolute values of E com seem to be inuenced by the charge of the capping group. Interestingly, almost identical complexation energies were obtained when replacing PhAsO 3 2À by SeO 3 2À , which have the same charge and the As V -O and Se IV -O distances are similar. As based on size only, Ag + , K + , Rb + , Cs + , and Ba 2+ can be excluded as guests for the nanocube cage Pd 12 .
We also decided to consider computationally the encapsulation of large guest cations by the 15-palladate nanostar cage {MPd 15 (AsPh) 10 } (Fig. S4 ‡), and then compare to Pd 12 . As expected, the larger guest ions Na + , Ag + , K + , Rb + , Ba 2+ , and Ra 2+ ions were calculated to be both geometrically and energetically suitable for the Pd 15 nanostar rather than the Pd 12 nanocube, and these results are in full agreement with the experimental facts. 10 Most of the smaller cations such as Mg 2+ and Zn 2+ do not t geometrically and are also energetically unfavourable in Pd 15 . On the other hand, Pd 2+ shows a similar ability to be encapsulated by the Pd 12 nanocube and the Pd 15 nanostar, which is consistent with the experimentally observed nanocube Pd 13 -AsPh, 8 8 ] 6À (SrPd 12 -closed) it was slightly less exothermic, À45.4 kcal mol À1 . Therefore, computationally it is predicted that the open form SrPd 12 -open is preferentially formed compared to SrPd 12 -closed. Amongst the unfavourable guest ions for the closed nanocube shell Pd 12 -closed, Sr 2+ shows the smallest E com difference compared to Pd 2+ with only 9.2 kcal mol À1 (and only 4.6 kcal mol À1 for Pd 12 -open) at the B3LYP level, and even smaller differences at the M06 and uB97XD levels. Thus, a competition between Pd 2+ and Sr 2+ guest ions is predicated computationally for such reactions. Experiments showed that only 2% of SrPd 12 -closed is formed, and that the Sr 2+ ion can be substituted by Pd 2+ to form Pd 13 AsPh by simply increasing the pH of the solution. 10e On the other hand, SrPd 12 -open can indeed be isolated in clean form, but to date the Pd 13 -open structural type has not been prepared yet.
It is interesting to note that E com for La 3+ is very close to that calculated for Pd 2+ , which may lead to mixed products LaPd 12closed and Pd 13 AsPh. In contrast to Sr 2+ , calculations suggest that for La 3+ the closed nanocube (LaPd 12 -closed) is slightly more favourable than the open one (LaPd 12 -open), see Table 1. Accordingly, the nature and size of the guest cation directly inuences the shape of the resulting poly-oxopalladate and this in turn strongly suggests a template effect of the cation in polypalladate synthesis.

Potential new candidates for the 12-palladate family
The systematic study of the complexation energies for different cation guests has revealed that competition with Pd 2+ plays a critical role when trying to determine the structure-type of the respective product. Although the energy trend should not be taken quantitatively, it appears to be qualitatively useful in the design of synthetic parameters for discovering new polyoxopalladates.
To date there is a dominance of 3d transition metal and lanthanide elements as central guests of the polyoxo-12palladate nanocube family {MPd 12 L 8 }. Much less attention has been paid on p-block elements. We calculated the encapsulation of Ga 3+ , In 3+ , and Tl 3+ as very exothermic with energies of À115.8, À137.1 and À155.1 kcal mol À1 , respectively. For all three cations, the encapsulation is predicted to be more On the other hand, to date no cation with a charge larger than 3+ has been encapsulated in the Pd 12 nanocube shell. Therefore, we analysed computationally the encapsulation of several tetravalent cations, such as Sn 4+ , Zr 4+ , Th 4+ , U 4+ , and Hf 4+ . As expected, all tetravalent cations exhibit much favourable complexation energies due to the large anion-cation electrostatic interactions. The small Sn 4+ ion has the lowest energy of all computed tetravalent ions and is hence the most promising candidate for encapsulation.
In order to verify the various theoretical predictions experimentally, we designed several key experiments, which concern mainly (i) encapsulation of p-block elements in the Pd 12 nanocube shell, (ii) synthesis of open-and closed-nanocube isomers for La 3+ , and (iii) competition of three guest cations for Pd 12 nanocube shell. Single-crystal X-ray analysis revealed that all three polyoxopalladates are isostructural (Fig. 5a, Tables S3 and S4 ‡). The main differences between LaPd 12 -closed, GaPd 12 , and InPd 12 are the central M-O bond distances with La-O ¼ 2.459(5)Å, Ga-O ¼ 2.211(4)Å, and In-O ¼ 2.293(4)Å, respectively. Notably, La 3+ is the largest trivalent cation ever encapsulated inside a Pd 12 nanocuboid cage and together with the relatively low complexation energy (Table S4 ‡). LaPd 12 -closed presents a good test case for the present study. Interestingly, we are also able to synthesize the open nanocube [LaPd 12 O 6 (OH) 3 (PhAsO 3 ) 6 (OAc) 3 ] 3À (LaPd 12 -open, see Fig. 5b). This structure had so far only been observed for strontium(II) in the center, [SrPd 12 O 6 (OH) 3 -(PhAsO 3 ) 6 (OAc) 3 ] 4À . 10e This result perfectly supports the above mentioned calculations (Fig. 4 and Table 1), as the energetically lower closed structure LaPd 12 -closed is indeed isolated in higher yields compared to the open structure LaPd 12 -open. However, our efforts to prepare additional analogues of MPd 12 -open (M ¼ La 3+ , Sr 2+ ) with other large lanthanide ions have not been successful, suggesting that La 3+ is a unique template amongst all lanthanide ions.

Synthesis and structural characterization of nanocubes
The 13 C and 1 H NMR spectra indicate good aqueous stability of all four polyanions (Fig. S5 and S6 ‡). Moreover, we also performed 71 Ga and 115 In NMR studies on solutions of Na-GaPd 12 and Na-InPd 12 , respectively. The observed singlets in 71 Ga NMR centred at 48.9 ppm (GaPd 12 , Fig. S7 ‡) and the singlet in 115 In NMR centred at 247.7 ppm (InPd 12 , Fig. S8 ‡) are in full agreement with the solid-state structures. The spectra are clean, indicating that no impurities are present, and the signals are rather narrow, in spite of the quadrupolar nature of both isotopes ( 71 Ga, S ¼ 3/2; 115 In, S ¼ 9/2), which is a result of the cubic coordination environment around the metal ions combined with the highly symmetrical (cuboctahedral) structure of the overall polyanion, rendering the electric eld gradient virtually zero.
We also performed ESI-MS studies in order to study the solution and gas phase properties of GaPd 12 and InPd 12 . All peaks shown in the spectra can be assigned to species related to GaPd 12 and InPd 12 , with different numbers of protons or sodium ions attached. For instance, the major envelopes centred at m/z ¼ 1025.45 (Fig. S9a ‡) and m/z ¼ 1041.45 (Fig. S9b ‡) can be attributed to the triply negatively charged [H 2 GaPd 12 ] 3À and [H 2 InPd 12 ] 3À . Additional MS assignments are summarized in Table S5. ‡ 3.5 Selective encapsulation of Ga 3+ or In 3+ in {MPd 12 (AsPh) 8

} nanocube
To date around 60-70 polyoxopalladates are known, and by far most of them belong to the {MPd 12 L 8 } class of nanocubes with being usually d or f block metal ions. 9 However, a competitive study using two or more potential guest cations has never been reported before. Considering that both GaPd 12 and InPd 12 can be followed by NMR in solution, we decided to perform competition studies for this system on fresh reaction solutions. Interestingly, we observed that if equimolar amounts of Ga 3+ and In 3+ ions were present, then only InPd 12 was formed, as conrmed by 71 Ga (no signal) and 115 In NMR (singlet at 254.1 ppm, Fig. 6a). This result indicates that a strong preference exists for InPd 12 compared to GaPd 12 . The free Ga 3+ ions were detectable by 71 Ga NMR at 0 ppm aer the solution had been acidied to pH 1 by 1 M HNO 3 (Fig. 6b).
For the same mixed, equimolar Ga/In system, the ltrated mother solution was allowed to evaporate until the maximum amount of crystals had formed, which were isolated when still covered by mother liquor. These crystals were analysed by ESI-MS and the spectrum obtained showed peaks corresponding exclusively to InPd 12 -related species (Fig. 6c)  We also performed additional competition experiments, for example for the template pairs Ga 3+ /Sc 3+ and In 3+ /Sc 3+ , respectively. Both 71 Ga and 45 Sc NMR signals could be detected for the Ga 3+ /Sc 3+ system aer the reaction, indicating that GaPd 12 and ScPd 12 are both formed and coexist in solution ( Fig. S10 and S11 ‡). For the In 3+ /Sc 3+ system, the 115 In NMR signal for InPd 12 could be detected aer a few seconds; whereas the 45 Sc signal for ScPd 12 could only be obtained overnight. These results indicate that selective encapsulation features exist for the central cation guest M of the Pd 12 nanocube, which t well with the trends of the computed complexation energies shown in Fig. 4. Combining the theoretical and experimental results, we obtain a selectivity order of In 3+ > Ga 3+ z Sc 3+ . The apparent E com difference between In 3+ (À137.1 kcal mol À1 ) and Ga 3+ /Sc 3+ (À116.2/À115.8 kcal mol À1 ) leads indeed to a pronounced encapsulation selectivity for In 3+ , whereas Sc 3+ and Ga 3+ are more difficult to be separated by polyoxopalladate formation, due to similar complexation energies.

Factors governing encapsulation of metal ion templates in different polyoxopalladate shells
In the above mentioned theoretical and experimental studies, we have mainly addressed the two main factors that control incorporation of metal ion guests in the polyoxopalladate nanocube shell Pd 12 : (i) the energy associated with the complexation of a given cation by the empty Pd 12 cage (E com ) and (ii) how the guest ts inside the host cage. In order to gain a deeper understanding of the intrinsic factors governing formation of {MPd 12 L 8 }, we decided to perform an energy decomposition analysis for E com . From an energetic point of view, we can subdivide the encapsulation process of the cation guest in three steps: (i) dehydration of the cation, (ii) deformation of the Pd 12 host shell, and (iii) binding between the cation and the Pd 12 host. Thus, E com can be expressed as the sum of DE def + DE dehyd + DE bind . In Fig. 7  classied according to the cation charge. It becomes apparent that in absolute values DE def is much smaller than DE dehyd and DE bind , and that these two latter terms are very dependent on the cation charge. The complexation energy for di-and trivalent cation guests is respectively two or three times more exothermic than for monovalent cations, due to increasing charge-dipole and charge-charge interactions.
The dehydration energy (DE dehyd ) of the cation guest M and the electrostatic interaction (DE bind ) between M and the Pd 12 nanocage exhibit large values, and in all cases DE bind is larger than the sum DE dehyd + DE def , consequently, the E com term is always negative and hence exothermic. However, this does not mean that DE bind alone is sufficient to describe the E com trend. In Table 2 three examples are shown indicating that in absolute value DE bind is indeed dominant, but this term alone does not allow predicting the correct trend for E com . For example, let us consider the cation guest pair Ga 3+ /In 3+ , for which experiments clearly demonstrated that In 3+ is captured preferentially over Ga 3+ . The more negative value for E com for In 3+ originates essentially from the large deformation energy of 25.7 kcal mol À1 for Ga 3+ (vs. 8.4 kcal mol À1 for In 3+ ). The other two energy terms (DE bind and DE dehyd ) are signicantly larger in absolute terms for Ga 3+ than In 3+ , but they cancel each other out. Notice that the Pd 12 host cage deforms signicantly more for Ga 3+ than In 3+ , because the former is rather small.
For the Lu 3+ /Yb 3+ pair, it can be noticed from the values in Table 2 that Lu 3+ has a more negative complexation energy by 12 kcal mol À1 . The radii of both ions are virtually identical and the deformation and binding energies are rather similar, and so it can be concluded that the dehydration energy is the critical term in this case.
Finally, the third ion pair Ce 3+ /La 3+ allows to identify the relevance of electronic structure. The La 3+ and Ce 3+ ions have the same charge and essentially identical ionic radii, but the larger atomic number for Ce 3+ leads to a higher effective nuclear charge and due to the low shielding of f electrons Ce 3+ has a larger (more negative) binding energy than La 3+ , which in turn leads to a higher (more negative) complexation energy for the former.
In summary, E com depends mainly on the following four properties of the metal ion guest: (i) effective ionic radius, (ii) valence state, (iii) dehydration ability, and (iv) electronic conguration and resulting charge-accepting ability. The selectivity for a given cation guest is the result of a delicate balance between the cation-polyoxopalladate and the cationsolvent interactions.

Conclusions
In hostguest or template-based chemistry, one of the challenges is to know the exact role that ions or small fragments play in the formation of a given species. Ever since the discovery in 2008 of the archetypal polyoxopalladate [H 6 Pd II 13 O 8 (As V O 4 ) 8 ] 8À (Pd 13 ), which can be described as a {Pd 12 O 8 (AsO 4 ) 8 } nanocube encapsulating a central Pd 2+ ion with square-planar coordination geometry, about 50 more polyoxopalladate nanocubes {MPd 12 L 8 } with different central metal ion guests M and capping groups L have been reported. However, the main factors that govern the experimental formation of a particular polyoxopalladate (and the non-formation of others) are not well understood. Here, combining experimental and computational chemistry, we have been able to rationalize why a polyoxopalladate shell self-assembles around a particular cation template guest more preferentially than others.
The prototype Pd 13 is formed by condensation of [Pd(H 2 O) 4 ] 2+ complex cations in the presence of arsenate anion heterogroups. Nevertheless, if the solution contains other cations M n+ , then in principle {MPd 12 L 8 } type species may also be formed, determined by the favourable complexation energy and the relative competition with respect to Pd 2+ ions. Aer an exhaustive computational analysis of complexation and dehydration energies for a series of cation guests we were able to identify the most promising cations to be encapsulated inside the Pd 12 nanocube shell. Trivalent and tetravalent cations are easily trapped inside Pd 12 , whereas monovalent cations are largely elusive. As based on the calculations, we also performed target-oriented synthetic studies and we were able to isolate four novel polyoxopalladates: (i) the La 3+ -centered nanocube [LaPd 12 O 8 (PhAsO 3 ) 8 ] 5À (LaPd 12 -closed), the La 3+ -centered "open" nanocube [LaPd 12 O 6 (OH) 3 (PhAsO 3 ) 6 (OAc) 3 ] 3À (LaPd 12open), the Ga 3+ -centered [GaPd 12 O 8 (PhAsO 3 ) 8 ] 5À (GaPd 12 ), and the In 3+ -analogue [GaPd 12 O 8 (PhAsO 3 ) 8 ] 5À (InPd 12 ). All four compounds were fully characterized in the solid state, in solution, and in the gas phase. In particular 115 In and 75 Ga NMR combined with mass spectrometry were very useful, as these techniques allowed to perform speciation studies. We demonstrated that in solutions containing In 3+ and Ga 3+ ions only the former is incorporated in the Pd 12 shell, due to its more suitable size and higher complexation energy. DFT method also predicted that the large La 3+ ion should t in the Pd 12 host shell. The experimental work following the computations indeed resulted in the successful synthesis of the regular nanocube LaPd 12 -closed as well as the open-shell structure LaPd 12 -open. These results reemphasize that size and dehydration energy of the cation guest are the key driving forces in the formation mechanism of nanocuboid polyoxopalladates of the type {MPd 12 L 8 }. Our work has demonstrated how powerful the interplay between theory and experiment can be. We predict that other cations such as Cd 2+ , Tl 3+ , Sn 4+ , Zr 4+ , Hf 4+ , U 4+ , and Th 4+ amongst others are potential candidates for encapsulation inside the Pd 12 host and our efforts are geared in this direction.