Ni12 tetracubane cores with slow relaxation of magnetization and efficient charge utilization for photocatalytic hydrogen evolution

We report two Ni12 multicubane topologies enclosed in the polyanions [Ni12(OH)9(WO4)3(PO4)(B-α-PW9O34)3]21−{Ni12W30} and [Ni12(OH)9(HPO4)3(PO4)(B-α-PW9O34)(A-α-PW9O34)2]21−{Ni12W27} that magnetically behave as Ni12 units clearly distinguishing them from typical Ni4 cubanes as shown by magnetic studies together with high field and frequency electron paramagnetic resonance (HFEPR). Beyond the unprecedented static properties, {Ni12W30} shows the unusual coexistence of slow relaxation of the magnetization and a diamagnetic ground state (S = 0), providing the unique opportunity of studying the essentially elusive magnetic relaxation behavior in excited states. The cubane-topology dependent activity of {Ni12W30} and {Ni12W27} as homogeneous HER photocatalysts unveils the structural key features significant for the design of photocatalysts with efficient charge utilization exemplified by high quantum yields (QY) of 10.42% and 8.36% for {Ni12W30} and {Ni12W27}, respectively.


General Information
All reagents and chemicals were of high-purity grade and were used as purchased without further purification. K 14  were prepared according to literature procedures 1 and characterized using single-crystal X-ray diffraction (SXRD) ({Ni 4 W 18 }) and 31 P-NMR spectroscopy ({P 2 W 19 }) as well as ESI-MS ({Ni 4 W 18 }) ( Figure S1).
Attenuated total reflection Fourier−transform Infrared Spectroscopy: All FTIR spectra were recorded on a Bruker Vertex 70 IR Spectrometer equipped with a single−reflection diamond−ATR unit. Frequencies are given in cm -1 , intensities denoted as w = weak, m = medium, s = strong, br = broad.
Elemental analysis: Elemental analysis was performed using X-ray photoelectron spectroscopy (XPS). The analysis was performed with a Nexsa XPS system (Thermo-Fisher) using a radiation source guntype Al Kα operating at 72 W and a pass energy of 200 eV, a spot size of 400 μm, "Standard Lens Mode", CAE Analyzer Mode, an energy step size of 0.1 eV for the survey spectrum, and integrated flood gun. Analysis was performed after cleaning the surface with Ar-clusters (1000 atoms, 6000 eV, 1 mm raster size) for 60 s. The high-resolution C 1s spectrum was acquired with 10 passes at a pass energy of 50 eV and fitted using Thermo Avantage v5.9914, Build 06617 with Smart background and Simplex Fitting algorithm using Gauss-Lorentz Product. Elemental microanalysis of C/H/N/O contents was performed by Mikroanalytisches Laboratorium (University Vienna, Faculty of Chemistry). An EA 3000 (Eurovector) was used for C/H/N/S-analysis. O-determination was performed by high temperature digestion using the HT 1500 (Hekatech, Germany) pyrolysis system in combination with the EA 3000 system.
UV-Vis spectroscopy: UV−Vis spectra were collected on a Shimadzu UV 1800 spectrophotometer.
Thermogravimetric analysis (TGA): TGA was performed on a Mettler SDTA851e Thermogravimetric Analyzer under N 2 flow with a heating rate of 5 K min -1 in the region 298−973 K.
Single crystal X-ray diffraction (SXRD): The X-ray data were measured on a Bruker D8 VENTURE equipped with a multilayer monochromator, Mo Kα Incoatec Microfocus sealed tube, and Kryoflex cooling device. The structures were solved by direct methods and refined by full-matrix least-squares. Non hydrogen atoms were refined with anisotropic displacement parameters. The following software was used for the structure-solving procedure: frame integration, Bruker SAINT software package using a narrow-frame algorithm (absorption correction) 2 , SADABS 3 , SHELXS-2013 4 (structure solution), SHELXL-2013 5 (refinement), OLEX2 6 (structure solution, refinement, molecular diagrams and graphical user-interface), and SHELXLE 7 (molecular diagrams and graphical user interface). CCDC-codes are provided in Table S5. Experimental data are summarized in Tables S6-S9.
Powder X-ray diffraction was performed on an EMPYREAN diffractometer system using Cu Kα radiation (λ = 1.540598), a PIXcel3D-Medipix3 1 × 1 detector (used as a scanning line detector) and a divergence slit fixed at 0.1 mm. The scan range was from 5° to 50° (2θ).
Diffuse reflectance spectroscopy (DRS) was performed on a Jasco V-670 UV-Vis spectrometer using a diffuse reflectance unit containing an Ulbricht-sphere. The powdered samples were fixed in the micro sample holder with a diameter of 3 mm and MgSO 4 was used as a standard. and {Ni 12 W 27 } is outlined in Figure S32. Although the structural differences between these units are not very significant, J ia-c may be sufficiently different since the magnitude and nature of some of these interactions strongly depend on the Ni-O-Ni angle (α, Figure S35). To evaluate the 39 magnetic coupling constants, the calculation of at least 40 different spin configurations, one of reference and the remaining ones forming a linearly independent set of equations depending on J i , is required. Due to the large size of the complete molecular model, only 31 spin configurations were calculated, and only 13 different J i constants were assumed, that is, J ia = J ib = J ic . Difficulties in the correct description of tungsten atomic orbitals and weak interactions between second neighbors considering that the pathways between two adjacent neighbors are partially made up of a single atom mainly contribute to the standard deviations given for the magnetic coupling constants thereby providing information on the approximation's accuracy. The coexistence of tungsten atoms forces the use of an atomic basis set different from the rest of atoms causing a marked slowdown in the convergence of the wavefunction. Hence, a model was built employing hydroxo groups to replace the tungsten centers while maintaining the positions of the oxygen atoms and placing the hydrogen atom (d O-H : 0.98 Å) in the direction of the O-W bond, which allowed verifying the validity of the approximation that reduces the number of magnetic couplings to only thirteen.
Two approaches were subsequently applied: 1) 51 spin configurations were calculated in the simplified Ni 12 model, applying one configuration as reference (high-spin, S = 12) and the remaining ones with their relative energies being expressed as a function of the J i constants.

2)
In both {Ni 12 W 30 } and {Ni 12 W 27 }, all Ni II except the two Ni II centers involved in the corresponding calculated coupling were substituted by diamagnetic Zn II ions. This procedure was performed to simplify the complex magnetic structure endowed by the presence of multiple Ni II cations to build a Ni 2 Zn 10 model for each magnetic coupling without affecting the region involved in the magnetic interaction, considering that the charge of the system remains unchanged.
In {Ni 12 W 27  Complete active space (CAS) calculations were performed on NiZn 11 molecular models aiming at evaluating the axial (D) and rhombic (E) zfs parameters. These models were built from the original Ni 12 entity of {Ni 12 W 30 } replacing the Ni II by Zn II ions except for the one Ni II metal center of interest. The calculations were carried out with version 4.0 of the ORCA program 13 using the TZVP basis set proposed by Ahlrichs and the auxiliary TZV/C Coulomb fitting basis sets. 14 The spin-orbit coupling contributions to zfs from 10 triplet and 5 singlet excited states generated from an active space with eight electrons in five d-orbitals were included from an effective Hamiltonian. The g-tensors were calculated using Multireference Configuration Interaction (MRCI) wave functions with a first-order perturbation theory on the SOC matrix. 15 Magnetic Studies: Variable-temperature (2-300 K) direct current (dc) magnetic susceptibility measurements under applied magnetic fields of 0.5 T (above 30 K) and 0.025 T (below 30 K) and variable-field (0-8 T) magnetization measurements at 2.0 K on powdered crystalline samples were carried out using Quantum Design Superconducting Quantum Interference Device (SQUID) magnetometer and Physical Property Measurement System (PPMS). The samples were embedded in n-eicosane to prevent any crystal reorientation. Variable-temperature (2-6 K) and variable-field (0-0.75 T) alternating current (ac) magnetic susceptibility measurements under ± 5.0 Oe oscillating field at frequencies in the range 1-10 kHz were performed with a Quantum Design PPMS. The magnetic susceptibility data were corrected for the diamagnetism of the constituent atoms and the sample holder.
High-Frequency/High-Field Electron Paramagnetic Resonance: HFEPR spectra of powdered crystalline samples of {Ni 12 W 30 } and {Ni 12 W 27 } at temperatures ranging from ca. 5 to 280 K were recorded on a home-built spectrometer at the Electron Magnetic Resonance facility of National High Magnetic Field Laboratory, Tallahassee, Florida. The setup of this instrument has been described in detail previously. 16 The instrument is a transmission type device in which microwaves are propagated in cylindrical lightpipes. The microwaves are generated by a phase-locked Virginia Diodes source, generating a frequency of 13 1 GHz and producing its harmonics of which the 2 nd , 4 th , 6 th , 8 th , 16 th , 24 th , and 32 nd ± are available. A superconducting magnet (Oxford Instruments) capable of reaching a field of 17 T was employed.
Photocatalytic H 2 evolution: The visible-light-driven hydrogen evolution experiments were carried using a 5 mL batch reactor equipped with a monochromatic LED light source (445±13 nm, power 2.5 mW/cm 2 , incident light intensity 5 mW, Thorlabs SOLIS). The reactor volume was filled with a 2 mL solution mixture of 11  (2-20 μM). Exposure to ambient light was minimized during the solution mixture preparation and transfer to the reactor. The reaction volume was purged with Ar for 10 min to ensure the removal of headspace and dissolved oxygen prior to reaction start. The temperature of the reactor was maintained at 15 °C with a watercooling system. The reaction mixture was stirred at 1150 rpm. The H 2 produced was monitored by sampling the reactor headspace (100 L) and analyzing its composition via gas chromatography (Shimadzu GC 2030) equipped with a barrier ionization discharge detector and a Micropacked-ST column using helium as a carrier gas. Injections were done with an interval of 10 minutes. The calibration was done using a range of H 2 in argon gas mixtures. The H 2 concentrations in ppm (derived from the chromatograms) were converted to μmol and turnover numbers (TONs -expressed per catalyst cluster/species) based on reactor parameters and the ideal gas equation. Initial turnover frequencies (TOFs) were calculated after 10 minutes of illumination (in most of the cases a close to linear H 2 evolution trend within the first 20 minutes of HER was observed). The calculation of the quantum yields (QYs, better known as internal quantum efficiency IQE values) considered the ratio between the number of H 2 molecules produced and the number of photons absorbed by the reaction solution. The latter was extracted using a power meter PM100D (Thorlabs) by measuring photon flux at the reactor position.
X-ray fluorescence: Chemical analysis with total-reflection X-ray fluorescence (TXRF) was performed using an Atomika 8030C X-ray fluorescence analyzer to analyze the supernatant obtained upon precipitation and subsequent centrifugation of {Ni 12 W 27 } or {Ni 12 W 30 } (for experimental details see section 13.4). This spectrometer operates with a total reflection geometry using an energy-dispersive Si(Li) detector, and the measurements were done with monochromatized Mo-Kα excitation mode (20.2 keV) at 50 kV and 47 mA, for 100 s live time. All reflectors were washed thoroughly and measured to account for true blanks. 995 µL of each sample was pipetted into an Eppendorf tube and 5 µL of a Cr internal standard solution (c = 1000 ppm = 1000 mg/L) were added into the tube (total volume = 1000 µL) resulting in a final Cr concentration of 5 ppm. The Eppendorf tubes were vortexed for at least 1 min and 5 µL of the sample solutions containing the internal standard were pipetted in the middle of the reflector followed by subsequent addition of 45 µL Cr standard solution (c = 1000 ppm) giving a total volume of V = 1040 µL and a concentration of 50 ppm internal standard. After drying for 5 min on a hot plate and cooling, the dried samples were measured. The results are summarized in Table S15, section 13.4. entitled Total X-ray fluorescence (TXRF) experiments.
Photoluminescence (PL) spectroscopy: PL steady state measurements of 0.2 mM [Ir(ppy) 2 (dtbbpy)] + solutions (with and without quenchers) were performed using a Picoquant FluoTime 300 spectrophotometer with a Xe arc lamp (300 W power) as excitation source coupled with a double-grating monochromator. The detection system was composed of a PMA Hybrid 07 detector along with a highresolution double monochromator. The excitation wavelength utilized for all steady state measurements was 445 nm (2.79 eV photon energy). The concentration of the [Ir(ppy) 2 (dtbbpy)] + solution was set to be in the range to exclude any inner filter effects. Time-resolved PL spectra were obtained using a laser wavelength of 377 nm, keeping the detection wavelength at 590 nm for all measured solutions. The collected data was fitted using the EasyTau2 software. 17

Synthesis Procedure
When this paper was under preparation, a crystal structure identical with the anion of {Ni 12 W 30 } has been reported. 18 19 , propensity to dissociate into A-and B-isomers of {PW 9 }-units 20 and additional tungstate structural fragments, as well as its affinity towards Ni II electrophiles. 21 To an aqueous solution of {P 2 W 19 }, 3 eq. of NiCl 2 were added, and the pH of the resulting light green reaction mixture (pH = 6.8) was adjusted to 5.5 using HCl [1 M] to allow the use of increased PO 4 3-or CO 3 2amounts for the subsequent basification (pH = 9.1) and templated formation of {Ni 12 W 27 } (using PO 4 3-) or {Ni 12 W 30 } (using CO 3 2-) upon heat activation (Scheme S1). Note that control experiments lacking the acidification step via HCl yielded the same products {Ni 12 W 27 } (using PO 4 3-) 47 (13), 3918-3920) and the web of knowledge database (using the key words "homogeneous hydrogen evolution polyoxometalate" in the search engine) (August, 2022).
Note that various parameters such as the shape of the reaction vessel, light intensity, stirring rate as well as the ratio of gaseous head space to total volume render a direct comparison of the WRC performance difficult. 35 Figure S4. IR-spectrum of K 11 Na 10 -{Ni 12 W 30 } in the range of 3600 -300 cm -1 . The strong vibrational peaks at 1168 cm -1 and 1061 cm -1 can be associated with P=O and P-O stretching. 47 The broad vibrational peak at ~3400 cm -1 and the sharp peak at ~1600 cm -1 are characteristic of stretching vibration of (O-H) and bending vibration of (O-H) in the lattice and coordinated water molecules.   Figure S7. IR-spectrum of K 14 Na 7 -{Ni 12 W 27 } in the range of 3600 -300 cm -1 . The strong vibrational peaks at 1168 cm -1 and 1061 cm -1 can be associated with P=O and P-O stretching. 47 The broad vibrational peak at ~3400 cm -1 and the sharp peak at ~1600 cm -1 are the characteristic of stretching vibration of (O-H) and bending vibration of (O-H) in the lattice and coordinated water molecules.

Single-Crystal X-ray Diffraction (SXRD)
Single crystal X-ray diffraction studies revealed that {Ni 12 W 30 } crystallizes in the triclinic space group P1̅ (Tables S5-S7 Figure S14E) that encapsulate a Ni 12 core, which can be regarded as a structural isomer of the Ni 12 core in {Ni 12 W 30 }. Attributed to the different connectivity types between the Ni II metal centers and the POT isomers ( Figure S14B, E)

Ni12
O370-Ni12-O89 86.6(3) Figure S15. Comparison of the experimental and simulated PXRD pattern of K 11 Na 10 -{Ni 12 W 30 }. Note that differences between the simulated and the experimental PXRD patterns may be due to factors such as scanning speed, preferred orientation, and efflorescence of the crystals, which lose solvent molecules further leading to the collapse of the lattice. Figure S16. Comparison of the experimental and simulated PXRD pattern of K 14 Na 7 -{Ni 12 W 27 }. Note that differences between the simulated and the experimental PXRD patterns may be due to factors such as scanning speed, preferred orientation, and efflorescence of the crystals, which lose solvent molecules further leading to the collapse of the lattice. derived from the DRS spectra by applying Equations S1 and S2 and determining the intersection point between the energy axis and the line extrapolated from the linear portion of the absorption edge (Figures S20 -S22)

S is the scattering factor and R is the reflectance [%]
obtained from the DRS spectrum (Equation S1) where , , with being the corresponding x-axis value (nm)

Estimation of band gap position using cyclic voltammetry (CV)
Considering that the LUMOs of POMs are formally a nonbonding combination of symmetry-adapted d xy like orbitals centering on the metal (W) centers, 51 (Figures S26, S28), which are consistent with slow electron transfer rates likely due to high reorganization energies associated with Ni-PT based redox processes. A substantial overlap of the negative domain peaks corresponding to the reductions of W(VI) to W(V), W(V) to W(IV) and Ni(II) to Ni(I) renders them difficult to distinguish. 1b,53,54 The linear dependency of the peak current on the square root of the scan rates (R 2 ~ 0.998, Figures S27, S29) is consistent with diffusion-controlled interfacial redox processes. 1b Addition of 3 M H 2 O to a solution containing the corresponding Ni-PT leads to substantial current starting at -1.24 V, indicating onset of electrocatalysis ( Figure S30)

DFT -guided estimation of coupling constants (J i values)
The OXO exchange paths (X = P or W) are essentially not effective in transmitting the magnetic interaction rendering the monoatomic pathway primary in the mediation of magnetic couplings through μ-OX bridging ligands (J 1 -J 7 ) (Figures S33-S35). An accidental orthogonality situation in the μ-OX bridging ligands induces a dependence of nature and magnitude of the coupling on the Ni-O-Ni angle (α), 18 resulting in the interaction to become AF when a certain magic angle (ca 95°) is exceeded, which is supported by the simulations of  M T vs T for both compounds. Ferromagnetic couplings are more numerous than AF ones in {Ni 12 W 27 }, and even more pronounced in {Ni 12 W 30 } thereby explaining the increase in  M T for both Ni-PTs upon cooling as well as the initial decrease observed for {Ni 12 W 27 }. A singlet ground state occurs for {Ni 12 W 30 }, with very close triplet and quintet excited states in the Ni 4 subunits and excited states of even higher multiplicity for the Ni 12 metal-oxo core, which accounts for the observed non-saturation of the magnetization (Figure S36). This scenario also occurs for the best-fit parameters: g Ni = 2.24, J 1 = J 2 = -4.4 cm -1 , J 3 = +6.6 cm -1 , J 4 = J 5 = +1.0 cm -1 , J 6 = +6.2 cm -1 , and J 7 = +9.2 cm -1 (Figure 2A). Slight improvements are obtained with small changes of these parameters upon incorporating an axial zfs parameter (|D| = 0.45 cm -1 ) or dipolar intermolecular interactions through a mean-field approach (θ = -0.30 K). Considering the crystal structure of {Ni 12 W 30 }, the first upgrading seems more adequate. Moreover, this D value represents a minimum amount since the approach of parallel local zfs tensors is like that suggested from CAS calculations (D = -1.27 cm -1 ). The presence of competing interactions in the Ni 4 subunits of {Ni 12 W 27 } leads to a spin frustration topology, causing the emergence of a paramagnetic spin ground state (S = 2 or S = 1) for each Ni 4 subunit which is F coupled to reach an S = 6 ground state suggested by the experimental saturation value of the magnetization (Figure S36). In contrast to {Ni 12 W 30 } where the bulky diamagnetic spacers separate the Ni 12 clusters far away from each other in all directions, the crystal structure of {Ni 12 W 27 } displays {Ni 12 W 27 } 2 supradimers with short Ni … Ni distances of 6.414 Å (Ni9 … Ni9) and 6.535 Å (Ni2 … Ni5) ( Figure  S46). This structural feature of {Ni 12 W 27 } would account for a non-negligible dipolar AF coupling between Ni 12 units and the sharper downturn of  M T, which cannot be reproduced through zfs effects exclusively. A similar situation occurs for the best-fit parameters: g Ni = 2.20, J 1 = J 2 = J 3 = +11.9 cm -1 , J 4a = J 4b = J 5a = J 5b = J 6a = J 6b = -38.0 cm -1 , J 4c = J 5c = J 6c = -9.6 cm -1 , J 7 = +9.4 cm -1 , and  = -1.8 K (Figures 2A, S37), suggesting an S = 6 ground state with close excited states (S = 5 and S = 4) at 2.0 and 10.1 cm -1 (Figure S36).
Although the magnetic behaviors of these Ni 12 complexes seem simple, their intricate molecular geometries, together with the possibility of a wide variety of magnetic couplings, make rigorous and reliable analysis a difficult task. Therefore, J i values were first estimated from DFT calculations and used to analyze the experimental magnetic behavior. In both compounds, three Ni 4 groups linked together constitute the Ni 12 molecular entities. The connections interlinking the Ni 4 units involve PO 4 3and WO 4 2diamagnetic bridging ligands that establish OXO (X = P and W) or even monoatomic O exchange pathways (J 7-13 ). Figure S32 summarizes the topology of magnetic couplings found for K 11 Na 10 -{Ni 12 W 30 } and K 14 Na 7 -{Ni 12 W 27 }. A molecular description of these magnetic interactions and the most relevant geometric parameters that define them are detailed in Tables S12 and S13 and illustrated in Figures S33 and S34. A priori, thirteen different J i magnetic couplings grouped in six types (J A-F ) could describe the magnetic topology of these Ni 12 systems, but they became thirty-nine because of the lack of symmetry between Ni 4 units (J ia , J ib , and J ic ). This feature is more notable in K 14 Na 7 -{Ni 12 W 27 }, where the encapsulated phosphate group acting as a bridging ligand between three Ni II ions in each Ni 4 unit does so differently in one of them. Although the structural differences between these units are not very significant, J ia-c may be markedly different since the magnitude and nature of some of these interactions strongly depend on the Ni-O-Ni angle.
DFT calculations on the whole geometry and simplified Ni 12 and Ni 2 Zn 10 models of K 11 Na 10 -{Ni 12 W 30 } show qualitatively equivalent results with the strongest ferromagnetic (F) and antiferromagnetic (AF) interactions being intensified in the models ( Table S12). The small standard deviations of the J i values in the simplified Ni 12 model indicate that the possible magnetic coupling between second neighbors, although present, is not relevant and can be ignored. The fact that the J i values obtained on the Ni 2 Zn 10 model are like those for the simplified Ni 12 one indicates that no significant electronic effects have been added when replacing Ni II with Zn II ions. However, some standard deviations derived from deleting any coupling between second neighbors prevent a correct estimation of the weakest J [8][9][10][11][12][13] interactions. Consequently, the discussion will be mainly based on the results of the simplified models, and only results from them will be provided for K 14 Na 7 -{Ni 12 W 27 }.
The weakest magnetic couplings usually occur when only OXO pathways (X = P or W) connect two Ni II ions (J 8 -J 13 ), evidencing the unsuitability of these connectors, in contrast to what occurs through carboxylate (OCO). Several factors would be responsible for this different efficiency: the shorter X-O bond length and the more favorable overlap with the oxygen atomic orbitals for X = C with respect to P or W. Finally, it deserves to be noted that the geometric arrangement of the metal ions relative to the OXO group has a great influence on the magnetic coupling. Thus, notable differences in the J i values are expected in syn-syn, syn-anti, and anti-anti conformations (angle, Figure S35), all of them observed in K 11 Na 10 -{Ni 12 W 30 } and K 14 Na 7 -{Ni 12 W 27 }. Furthermore, the Ni II ion is located almost in the OXO plane ( angle, Figure S34) or significantly out of it. When each metal ion adopts one of these conformations, but being different from each other, very F interactions are expected in many cases due to an accidental orthogonality.
When μ-hydroxo and carboxylate groups connect two metal ions, particularly Cu II , the phenomenon of orbital counter-complementarity arises, 55 leading even to F couplings despite the fact that each bridging ligand separately favors AF interactions in their molecular conformation. However, phosphate or tungstate bridging ligands do not play this role here, as the magnetic coupling between two Ni II ions is governed only by the hydroxo ligand. In this case, as with the di--hydroxo, di--alkoxo, di--phenoxo or di--azido homodinuclear copper(II) or nickel(II) complexes, there must be a magic angle at which a transition from F to AF will occur. 56 This value will depend on the bridging ligand, being different for -OH than for μ-OPO 3 or μ-OWO 3 . Here, this magic value seems to be placed at ca.  = 95º (Tables S12 and S13). Thus, even though only a single μ-OH pathway transmits the magnetic communication in the J x coupling of K 14 Na 7 -{Ni 12 W 27 } because of the highly obtuse  angle (~127º), a strong AF coupling is mediated.
Other structural factors can modify the magnitude of the interaction, such as the butterfly distortion of the central unit Ni 2 O 2 (δ) or the out-of-plane displacement of the hydrogen atom (-OH) or X (-OXO 3 ) from the Ni 2 O 2 plane (γ) (Figure S33). However, these parameters do not change much in K 11 Na 10 -{Ni 12 W 30 } and K 14 Na 7 -{Ni 12 W 27 }. Besides, as observed in the past for other systems, they are usually strongly correlated to the angle. For example, δ, γ, or even , defined as the out-of-plane of the Ni atom from the exchange pathway plane, increases as  decreases (Table S12).
Only average values of the most intense couplings obtained by the DFT study were considered in the analysis of the magnetic behaviors of K 11 Na 10 -{Ni 12 W 30 } and K 14 Na 7 -{Ni 12 W 27 } and the J 8-13 couplings were neglected. With this consideration, both compounds can be visualized as Ni 4 units ferromagnetically coupled to each other. Although the searching for best-fit parameters to reproduce the experimental  M T vs T curves is viable for a twelve coupled S = 1 local spin momenta under the framework of a Heisenberg Hamiltonian ( ) applied on isotropic quantum spins, the required ̂= -̂t ime is too long to be helpful. Suppose these spin momenta undergo zfs effects, as occurs for the Ni II ion, the size of the generated matrix is too large to be stored in a conventional computer, and the time of a single simulation without applying highly advanced techniques together with simplifications would evolve from some tens of minutes to possibly quite a few months or years. This gets dramatically worse during a fitting. Thus, an approach based on effective Hamiltonians and developed in the past was applied to fit the spin Heisenberg models applied to recreate the observed behaviors of both compounds. 57 In this approach, some fragments (Ni 4 ) are exactly solved, and then considered as an effective spin (S eff ) with an effective g-factor (g eff ), which are temperature-dependent. In the whole system, these fragments are coupled to each other through an effective magnetic coupling (J eff ), related to the actual J 7 value. This J eff , also temperature-dependent, is extracted from the energies and wavefunctions of the S states in fragments. The treatment of effective coupling between Ni 4 S eff was done considering a classical spin approach through Langevin functions and the spin interaction topology of K 11 Na 10 -{Ni 12 W 30 } and K 14 Na 7 -{Ni 12 W 27 } being a triangle. 58 This procedure fails at low temperature because the small size of the cycle allows a fast emergence of an autocorrelation error; that is, a spin momentum vastly is correlated with itself, requiring the more difficult task to develop an exact law. However, it was not needed since our simulation above 2.0 K moved all the time within the limit of applicability of the first technique for a triangular topology ( ). The inclusion of ( + 1) > 0.57 a zfs for Ni II ions makes the labor more difficult. However, a fast and relatively efficient technique entails considering these effects in the exact solution of the fragments and then adding them on the g eff . Final verification is done for isotropic spin momenta by comparing the exact and approached simulations on the Ni 12 system with the obtained best-fit parameters.
Applying this methodology, the experimental  M T vs T curve for K 11 Na 10 -{Ni 12 W 30  However, the non-zero J 4 and J 5 F couplings compete with the rest, moving paramagnetic excited states closer ( Figure S32), a feature that accounts for the experimental dependence of the magnetization on the applied magnetic field and temperature.
The low symmetry of K 14 Na 7 -{Ni 12 W 27 } renders the analysis of magnetic behavior even more difficult. In such a case, there is a different thermal dependence of the effective factors, S eff and J eff , for each Ni 4 fragment, forcing the consideration of the classical heterospin model, which to the best of our knowledge has not yet been developed before. Following methodology based on Langevin function and the interaction model shown in Figure S32, the following analytical law has been deduced: noted that the Langevin function, that describes the spin correlation between two coupled centers, is normalized by a κ term that depends on their spin moments and g-factors, , M i being g i S i . This term takes the unit value when the two centers are equivalent. The validity of this approximation has been verified against the exact simulation. However, the real spin coupling model is too intricate and has too many parameters to determine. For semiquantitative analysis of the thermal dependence of the magnetic susceptibility, the model has been simplified considering a single g-factor and reducing the number of active couplings to those stronger (J 1-7 ). Moreover, from the information provided by DFT study, some equivalences were imposed between parameters (J 1 = J 2 = J 3 , J 4a = J 4b = J 5a = J 5b = J 6a = J 6b , and J 4c = J 5c = J 6c ). The best-fit was achieved with the values g Ni = 2.227, J 1 = +11.9 cm -1 , J 4a = -38.0 cm -1 , J 4c = -9.6 cm -1 , J 7 = +9.4 cm -1 , and  = -1.8 K. The agreement factor (F = 3.1 x 10 -4 ) was reasonable despite the high degree of simplification of the model. Note that equation 4 is not an empirical law or a standard polynomial but a physical law for a classical spin approach. Therefore, equation 4 is with physical meaning without introduction of any overparameterization in the fit process since it only presents a priori the J i variable. S eff and J eff , which are both temperature dependent variables, are estimated from a previous treatment, hence not being a consequence of the equation above.
The predominant AF interaction in two Ni 4 units produces a slight decrease in  M T from room temperature. The rest of the F interactions are responsible for the significant increase in  M T < x K. The sharp fall in  M T at T < x K cannot be reproduced only by the presence of a zfs for Ni II ions, which is undoubtedly acting. Only the dipolar or intermolecular interaction between two neighboring Ni 12 units creating a supra-dimeric entity can reproduce this abrupt drop. According to these results, the ground state of each Ni 4 unit would be S = 1 or S = 2, depending on the Ni 4 fragment, intermediate spin arising from a spin frustration topology, with other excited states relatively far apart (Figure S36). Because these units are ferromagnetically coupled, the ground state of K 14 Na 7 -{Ni 12 W 27 } is an S = 6 without any close excited state with larger spin multiplicity. The closest excited state (S = 5) is placed at 2.0 cm -1 (Figure S36). This result agrees with the observed reduced magnetization curves projecting toward a saturation value corresponding to a ground state S = 6. The non-collapse of these curves is a consequence of the small gap with the first excited states, the weaker intramolecular couplings, but mainly of the widely reported zfs in octahedral nickel(II) complexes. 59 The electronic effects in each Ni site are not equal (Tables S10, S11). While the surroundings of the vertex of each Ni 4 unity confirming the proposed Ni 3 core of {Ni 12 W 30 } (Ni1, Ni5 and Ni9, Figure S32) is composed of one OPO 3 , two OWO 3 and three OH groups; four hydroxo, and two OXO 3 groups (P:W ratio for X = 1:1 or 2:0) occur in the rest of the Ni II ions (Figure S14B), resulting in the presence of two groups of D values. Thus, in the latter, the coordination sphere can be defined as an elongated octahedron with four hydroxo ligands in the basal plane and OXO 3 of weaker ligand-field in more distant axial positions, leading to positive values of D. Meanwhile, Ni1, Ni2, and Ni3 sites exhibit a more compressed geometry but close to an ideal octahedron, so expecting a smaller value of D but of uncertain sign, which in our case is negative. There is a good correlation between these values and the distortion of the octahedral coordination sphere provided by shape measures (OC-6) 60 , even if this parameter also embraces other geometrical factors that do not affect the axial zfs ( Figure S33). From the calculated orientation of the local zfs tensors (Table S14), the D value for an S ground state would be D = -15.2/S 2 with E/D = 0.14. In the fit process in polynuclear complexes, it is usual to consider an average local D value in polynuclear complexes, equivalent to arranging all local tensors parallel. According to this approach and previous calculations, the average local D value for each Ni II ion would be D = -1.27 cm -1 . 61 This value may seem small, but in an ideal tetrahedral Ni 4 arrangement, a null D for any resulting state with D i therefore being null for the Ni 12 entities, as well, should be expected.
Simulations of the magnetic behavior were performed using an approach based on an effective Hamiltonian, where effective spin momenta (S eff ) of each Ni 4 unity and the effective coupling (J eff ) between them are temperature-dependent and obtained from the exact solution of Heisenberg Ni 4 systems. Accordingly, the thermal effect of the zfs of Ni II ions is included from an effective g-factor (g eff ) for each Ni 4 fragment. To simplify, the coupling between these fragments was obtained from a classical spin approach, developing  M T as a combination of Langevin functions.
In the less symmetrical {Ni 12 W 27 }, a classical spin law for a heterospin triangle was deduced.
Considering the short self-connecting pathway when cycling a triangle, the range of applicability is more limited (T/(J eff S eff (S eff + 1)) > 0.57) as compared to a 1D system. 58 However, J eff S eff (S eff + 1) decreases with temperature, ensuring the model's suitability for temperatures up to 2.0 K. Thus, a final verification for isotropic spin momenta shows a complete agreement between exact and approached simulations on the Ni 12 system with the obtained best-fit parameters.  Table S14). Labels are used to identify the data for each Ni site. Figure S34. Magnetic coupling pathways referred in Figure S32, Tables S12 and S13.     Figure S34. b Intermetalic distance in angstroms. c Angles (in degrees) described in Figure S35. d Figure S34. b Intermetalic distance in angstroms. c Angles (in degrees) described in Figure S35. d Average values in cm -1 calculated on the full experimental geometry. d Values (in cm -1 ) obtained on the simplified Ni 12 model. Standard deviations in parentheses. e Values (in cm -1 ) obtained on the simplified Ni 2 Zn 10 model. Table S14. Axial (D) and rhombic (E) contributions to the local zfs tensors and the average gfactor for the S = 1 ground state obtained from CASSCF calculations on the NiZn 11 model of compound {Ni 12 W 30 }, and geometrical distortions from the ideal octahedron (OC-6) estimated from shape measures (Sh). Note that an observable difference in D values for each Ni center arises from the central Ni II ions being non-equivalent in their coordination environment to the rest (Table S10)

Hydrogen Evolution (HER) experiments
HER performance of {Ni 12 W 30 } and {Ni 12 W 27 } was subsequently evaluated as a function of Ni-PT concentration in the lower range between 2 and 10 μM. Figure S48 indicates that the obtained HER profiles are similar to those from 20 μM experiments shown in Figure 3.

Post-catalytic studies
Post-catalytic studies and re-loading experiments were performed to elucidate the POTs' stability under photocatalytic conditions. First, the catalytic solution of {Ni 12 W 30 } or {Ni 12 W 27 } after the first HER cycle (point x in Figure 3) was re-loaded with a sensitizer-TEOA mixture. This second illumination cycle resulted in renewed H 2 evolution, whose extent and profile matched those from the first HER run (Figure  S49 A). In contrast, the addition of exclusively TEOA yielded only 25% of the original activity (Figure  S49 B). This proves that the H 2 saturation shown in Figure 3 is not a result of sole Ni-PT-deactivation but can instead be related to the sensitizer degradation or TEOA depletion. Second, following the completion of HER (point x, Figure 3), {Ni 12 W 30 } and {Ni 12 W 27 } were selectively precipitated from the catalytic solution using CsCl. 65 ATR spectra of the isolated Cs-salts match well with the initially recorded tungsten fingerprint areas in the range from 1000-300 cm -1 (Figures S49 A, B), suggesting structural integrity of both polyanions under turnover conditions. To provide a quantitative assessment of the Ni-PT integrity, the remaining solutions after separating the POT Cs-salts were further analyzed with X-ray fluorescence (XRF) concerning their Ni and W contents (  Figure S50, the observed Ni-PT degradation seems insignificant compared to the effect of sensitizer instability.
13.2 Post-catalytic precipitation of TBA 13 Na 8 -{Ni 12 W 30 } and TBA 13 Na 8 -{Ni 12 W 27 } The photocatalytic reaction was carried out with 100 μM of the corresponding catalyst to obtain the POM in sufficient quantity for post-analysis. After 30 min of illumination, 0.5 mL of a [0.5 M] solution of cesium chloride in a mixture of acetonitrile/H 2 O (2:1) was added resulting in the immediate formation of precipitates. The precipitate was centrifuged at 2500 rpm for 5 min and completeness of the precipitation was insured by adding a few drops of the cesium chloride solution to the supernatant. The precipitates were air dried and displayed to IR-spectroscopic analysis ( Figure S49). Figure S49. ATR-IR spectra showing the superimposed tungsten fingerprint areas (1000-300 cm -1 ) of A) K 11 Na 10 -{Ni 12 W 30 } and the precipitated cesium salt Cs{Ni 12 W 30 } as well as B) K 14 Na 7 -{Ni 12 W 27 } and the precipitated cesium salt Cs{Ni 12 W 27 }. A dominant band at ~660 cm -1 in the precipitated Cs-salts arises from residual DMF as shown by the IR spectrum of pure DMF. , the reaction volumes were re-charged with a photosensitizer/TEOA/CH 3 CN/DMF/water solution (as described above). After degassing, the second photocatalytic run (red curves) yielded significant H 2 evolution close to that of the first HER cycle for both compounds. When only TEOA was re-loaded (lila curve in B), the amount of generated H 2 only accounted to around a quarter of the original activity value.

Total X-ray fluorescence (TXRF) experiments
Following the post-catalytic precipitation experiments (see subsection 13.1. Post-catalytic precipitation of TBA 13 Na 8 -{Ni 12 W 30 } and TBA 13 Na 8 -{Ni 12 W 27 }), TXRF analyses of the Ni and W contents present in the isolated supernatants of the corresponding Ni-PT solutions were conducted to elucidate on potential leaching and provide a quantitative assessment of the Ni-PTs' post-catalytic stability (see General Information section X-ray fluorescence). The TXRF results are summarized in the following Table S15: The detected Ni/W contents before (2, in ppm) and after HER cycle (4, in ppm) were evaluated with regard to the theoretical amounts of Ni/W in case complete Ni-PT dissociation/decomposition would take place (1, in ppm). The part of the Ni-PT that underwent dissociation/leaching before (3, in %) and after the HER cycle (5, in %) provides a quantitative measure for PT stability. Expressing the Ni/W amounts found by TXRF in % (consideration of mol. % or wt. % would give identical results) of the total amounts of Ni/W present in the original catalytic solutions allows to evaluate instability of the Ni-PTs under the turnover condition.
Considering the precatalytic stability experiments (see sections 8 Cyclic Voltammetry and 9 UV-vis spectroscopy), which suggested long-term stability of both Ni-PTs, the observed Ni-and W contents in the solution before HER indicate incomplete precipitation of the anions during the extraction. Hence, the observed pre-catalytic Ni/W contents (3, in %) were subtracted from the determined post-catalytic contents (5, in %) to assess for the degree of Ni-PT leaching/decomposition (6, in %). Table S15 shows (see column 6) contents of 6.5% for Ni and 10.3% for W for TBA 13 Na 8 -{Ni 12 W 27 } as well as 5.0% for Ni and 3.6% for W for TBA 13 Na 8 -{Ni 12 W 30 } indicating that not more than ~10% of the Ni/W was leached over the course of the HER cycle. This implies that ~90 % of the polyanions stayed intact allowing for the long-term photocatalytic stability shown in Figure S50A.   15.