Temperature dependence of spherical electron transfer in a nanosized [Fe14] complex

The study of transition metal clusters exhibiting fast electron hopping or delocalization remains challenging, because intermetallic communications mediated through bridging ligands are normally weak. Herein, we report the synthesis of a nanosized complex, [Fe(Tp)(CN)3]8[Fe(H2O)(DMSO)]6 (abbreviated as [Fe14], Tp−, hydrotris(pyrazolyl)borate; DMSO, dimethyl sulfoxide), which has a fluctuating valence due to two mobile d-electrons in its atomic layer shell. The rate of electron transfer of [Fe14] complex demonstrates the Arrhenius-type temperature dependence in the nanosized spheric surface, wherein high-spin centers are ferromagnetically coupled, producing an S = 14 ground state. The electron-hopping rate at room temperature is faster than the time scale of Mössbauer measurements (<~10−8 s). Partial reduction of N-terminal high spin FeIII sites and electron mediation ability of CN ligands lead to the observation of both an extensive electron transfer and magnetic coupling properties in a precisely atomic layered shell structure of a nanosized [Fe14] complex.

T o date, numerous nanosized transition metal complexes have been synthesized 1 , which can be predetermined to have various fascinating structures via molecular selfassembly process 2,3 . One of the challenges in realizing their functions is the introduction of fast electron transfer over a long distance that ubiquitously occurs in chemical and biological systems 4,5 . The low-nuclearity compounds have been intensively investigated as intramolecular electron transfer systems [6][7][8][9][10][11][12][13] . The recent interesting work on the [Fe 2 ] V mixed-valence compound exhibited changes in the electron transfer rate observable by Mossbauer spectroscopy with a ferromagnetic S = 9/2 ground state 14 . It is still challenging to isolate nanoarchitectures where electron transfer occurs over more metal centers, toward revealing extraordinary spectral and electronic behavior 15 . In the presence of intermetallic coupling in high-nuclearity complexes, the number of hopping d electrons and their interactions would be expected to increase. This would be accompanied by some intriguing processes, such as electron transfer along topologyspecific pathways, many-electron transfer processes, and externally induced charge separation in a confined nanospace [16][17][18] . However, intermetallic electron transfer-mediated through bridging ligands are normally weak; thus, properties related to confined electron transfer processes in discrete nanosized complexes have remained hypothetical thus far 19,20 .
Prussian blue analogs have received considerable attention as they can demonstrate the coexistence of electron transfer and exchange interaction through a cyanide bridge 21,22 . The realization of partially reducing or oxidizing the interacting metal centers in a nanoarchitecture is proposed as a route to achieve the extensive multielectron transfer with novel magnetic and electronic properties 23,24 . Here, we report a cyanide-bridged complex [Fe II (Tp)(CN) 3  The key feature of this complex is that only two of the six Nterminal Fe-hs sites in the Fe II-ls -CN-Fe hs structure are successfully reduced (hs = high spin and ls = low spin), thereby reducing the potential barrier for two-electron hopping at the six N-terminal Fe-hs sites. Furthermore, the rates of the intramolecular electron transfer exhibit a distinct temperature dependence that can be described with an Arrhenius law in the nanosized complex. Another important characteristic is that a ferromagnetic interaction operates in [Fe 14 ] with a ground spin S = 14, which implies that extra 3d electrons hop around the exchange-coupled atomic layer shell.  25 .

Results
Electronic behavior. To confirm the valences and spin states of the Fe ions in the complex, 57 Fe Mössbauer spectroscopic measurements were performed at various temperatures under zero magnetic field (Fig. 2a) 26 . As a result, the well-fitted profiles were produced with the Fe II vs. Fe III area ratio fixed at 2:4. A few additional parameter constraints were necessary to prevent divergence in the calculations for the spectra at 245−297 K because of strong parameter correlations, especially between the linewidth and relaxation rate. The results indicate that the electron-hopping rate at room temperature is comparable to or faster than the fast-exchange limit (~10 −8 s) of the Mössbauer time window. On the other hand, the fluctuation rate below 144 K is slower than the lower limit (τ =~3 × 10 −7 s) of the time window, and the electron-hopping relaxation model no longer describes the system (Fig. 2c). Figure 2d summarizes the QS and IS values from the spectral analysis. A sudden change in the temperature dependences of IS and QS for Fe II -hs and Fe III -hs was observed at around 220 K, whereas there was no such abrupt change for Fe II -ls. This change seems to correlate with the electron hopping at the B sites of the complex. On cooling, the IS values of Fe III -hs and Fe II -ls increased almost linearly according to a second-order Doppler shift, except for the sudden change. In contrast, the IS values of Fe II -hs anomalously rise upon an increase in the temperature and do not obey a second-order Doppler shift effect at high temperatures. However, the average Fe II 27 , where the slope of the second-order Doppler shift was calculated as 6.3 × 10 −4 mm s −1 T −1 , comparable to the value of 5.6(3) × 10 −4 mm s −1 K −1 for [Fe 14 ]. The electron-hopping relaxation model provides a good fit in the temperature range of 164-297 K, with a relaxation time of τ as shown in Fig. 2e. A typical Mössbauer time window was observed to range from~3 × 10 −7 to~1 × 10 −8 s for the system. Actually, in a previous study using the relaxation model, it was indicated that such dynamics are detectable as spectral changes in the range of~6.5 < −log(τ/s) <~8.0 28 , which is comparable to the case of [Fe 14 ]. The electron-hopping activation energy (U eff ) was successfully evaluated using the Arrhenius equation, ln(τ) = ln(τ 0 ) + U eff /k B T. The best fit of the experimental data yielded U eff = 943(47) cm −1 with a preexponential factor of τ 0 = 5.0(16) × 10 −11 s. Hence, the temperature dependence of the rates of intramolecular electron transfer in the Mössbauer spectroscopic analysis clearly demonstrated that six B-site Fe ions form a class II mixed-valence system according to the Robin-Day classification 29 . Electronic spectroscopy in the domain of intervalence transitions exhibits a wide peak centered at 11,100 cm −1 (900 nm) with a pronounced absorption tail due to the superposition of adjacent IVCT (Fe II -CN-Fe III ) and remote IVCT (Fe II -NC-Fe II -CN-Fe III ), as indicated in the reported cyanide-bridged systems with N-terminal mixed-valence state 24,30,31 . (Supplementary Fig. 3) The crystal structure was additionally analyzed to probe whether a temperature-induced charge separation occurs in [Fe 14 ] at lower temperature, that is, 25 K, a temperature at which the electrons should be completely frozen (τ~10 13 s) according to aforementioned Arrhenius equation. However, no crystallographic differences in the coordination environment of the B-site Fe ions were observed between the structures at low and room temperature. At 25 K, the B-site Fe ions stay at the crystallographically identical sites in the unit cell as in the case of the RT (room temperature) structure. Therefore, although two Fe II are expected to be located in the trans positions of the [Fe 6 ] octahedron to minimize Coulombic repulsion, the positions of the Fe II atoms cannot be assigned by X-ray diffraction. This is mostly due to the random distribution of the localized electrons at six B-site irons in the lattice. Thus, the charges at each B-site Fe virtually hold site occupation factors of 0.333 for Fe II and 0.667 for Fe III , respectively. The heat capacity of [Fe 14 ] under zero field at 7-300 K was investigated (Fig. 3a). No distinct anomaly was observed in the heat capacity data, further indicating no firstor second-order phase transition. The observation is consistent with the thermal dependence of the rate of intramolecular electron transfer as indicated in the Mössbauer spectra.
To elucidate the electron-hopping behavior in the [Fe 14 ] complex, temperature-dependent infrared (IR) spectroscopic measurements were carried out at 78-350 K. The IR spectrum of [Fe 14 ] at 78 K exhibits several strong ν CN stretches at 2101, 2078, 2068, 2053, and 2042 cm −1 (Fig. 3b) (dpp = 1,3-di(4-pyridyl)propane), wherein the valence-trapped Fe II-ls -CN-Fe III-hs structure was preserved across the whole temperature range 32 ( Supplementary  Fig. 4). Furthermore, the ν CN stretching frequency in Prussian blue with a Fe II-ls -CN-Fe III-hs structure has been previously observed to be slightly higher compared with that in Prussian white with a Fe II-ls -CN-Fe II-hs structure 33 . The additional ν CN stretching bands for [Fe 14 ], which lack in [Fe 42 ], indicates the presence of a Fe IIls -CN-Fe III-hs and Fe II-ls -CN-Fe II-hs mixed linkage, by in situ Fourier-transform infrared spectroscopy. These results mean that the electron-hopping rate is slower than the time scale of the IR technique (10 −12 -10 −13 s) 34 .
Iron L-edge X-ray absorption spectra (XAS) were measured between 3.5 and 300 K to further characterize the electronic structure (Fig. 3c). Spin-orbit coupling of the 2p 5 final state (2p 6 3d n → 2p 5 3d n + 1 ) leads to the splitting of L 2,3 edges into L 3 (J = 3/2) and L 2 (J = 1/2) absorption regions, which are separated in energy by~12 eV. The L 3 and L 2 absorption edges of [Fe 14 ] were found to have maxima at 708.5 and 722 eV, respectively. The [Fe 14 ] L edge includes overlapping contributions from the A and B sites. The XAS spectra measured between 3.5 and 300 K are identical, confirming that there is no resolvable change in the local Fe coordination symmetry or crystal field splitting at the A or B sites between the low-and high-temperature states. Furthermore, no temperature-induced changes in the spectra were observed for the Kβ 1,3 emission spectroscopy and highresolution K-edge X-ray absorption near-edge structure measurements ( Supplementary Fig. 5). The lack of evidence for the thermal transition by these techniques indicates that the electronhopping rate is slower than the time scale of the X-ray spectroscopy measurements ( 14 ], magnetization data were collected and were plotted as reduced magnetization (M/Nμ B ) vs. applied field in the range of 0-5 T at 2 K, as shown in Fig. 4b. The onset of magnetization in the applied field is greater than that of six magnetically isolated centers (red line in Fig. 4b) and is closer to the Brillouin curve for one isotropic S = 14 center (blue line in Fig. 4b). Inclusion of weak ferromagnetic exchange coupling (green line) between B sites suitably reproduces the measured magnetization curve, indicating a ferromagnetic S = 14 ground state. The presence of a ferromagnetic interaction was also confirmed using X-ray magnetic circular dichroism (XMCD), a technique that is a probe of magnetization at the atomic level. Since they are diamagnetic, the A-site Fe ions have no XMCD intensity. Hence, the [Fe 14 ] XMCD spectrum provides direct spectroscopic access to only the B-site Fe ions. The left and right circularly polarized total fluorescence yield (TFY) detected XAS at 3.5 K, and 14 T is shown in Fig. 4c, alongside the XMCD spectra at various applied magnetic fields. At 3.5 K, the B sites are in the valence-trapped state in a ratio of 4:2 (Fe III vs. Fe II ). The onset of the L 3 edge for the octahedral Fe II -hs component is known to be lower in energy than that of Fe III -hs by~1 to 2 eV. Hence, the lower energy region of the L 3 XMCD spectrum is expected to exhibit Fe II -hs contributions with respect to the higher energy region, which is expected to show Fe III -hs contributions. The magnitude of the XMCD signal across the L 3 edge increases monotonically with an applied field indicating that the ferrous and ferric spins at the B sites are ferromagnetically exchange coupled 40 . (Supplementary  Fig. 7) The field dependence of the XMCD data is in accordance with that observed for the superconducting quantum interference device (SQUID) magnetization.
It should be noted that the maximum χ M T at low temperatures is significantly reduced compared to the expected χ M T value for an isolated S = 14 ground state (~105 cm 3 K mol −1 ). (Supplementary Fig. 8) The susceptibility measurements conducted down to 0.5 K exhibits a sharp peak in χ M at 0.8 K (Fig. 4d), showing a  typical feature of antiferromagnetic long-range magnetic ordering. Heat capacity measurements were carried out and showed a λ-type anomaly centered at T N = 0.85 K in the zero field (Fig. 4e), revealing the onset of weak long-range magnetic ordering. The magnetic nature of this feature was confirmed by its disappearance upon the application of a strong magnetic field. The intermolecular interaction was also suggested by the highfrequency electron paramagnetic resonance spectra of [Fe 14 ] (Supplementary Fig. 9). Since the high-spin sites are coordinated via diamagnetic [Fe II-ls (Tp) (CN) 43 . However, the value of such an analysis is limited due to the onset of 3D magnetic ordering at low temperature.
In summary, we report on the synthesis and electronic behavior of a nanosize [Fe 14 ] complex with the two-electron, four-hole mixed-valence state. Two extra 3d electrons in the complex are found to hop at N-terminal Fe centers on its atomically thin spheric surface. The valence of the A-site Fe is basically static, while the valence electrons on the B-site Fe exhibit thermal dependence of the rate of intramolecular electron transfer. Furthermore, [Fe 14 ] has a high-spin ground state with S = 14, meaning that the two electrons are hopping around the exchange-coupled atom-layer thin surface. The nanoarchitecture in this work may be useful for application in future molecular electronic and chemical devices using the intermetallic electronic and magnetic interactions in the framework and precise nanospace.   X-ray crystal structure determination. X-ray diffraction data at room temperature and 123 K for [Fe 14 ] were collected on a BRUKER APEX-II CCD (Bruker Corp.) equipped with a graphite-monochromated Mo-Kα radiation source (λ = 0.71073 Å) [44][45][46][47] . Diffraction data at 25 K were collected under a cold helium gas stream on a Rigaku HPC X-ray diffractometer, using multi-layer mirror monochromated Mo-Kα radiation (λ = 0.71073 Å). Bragg spots were integrated using the CrysAlisPro program package, and empirical absorption correction (multi-scan) was applied using the SCALE3 ABSPACK program. The structures were solved by direct methods (SHELXT Version 2014/4) using full-matrix least-squares refinement (SHELXL Version 2018/1) 48 . The H atoms were geometrically placed on organic ligands in riding mode, and all of the non-H atoms were anisotropically refined by full-matrix least-squares refinement on F 2 using the SHELXTL program 49 . A summary of the crystallographic data and refinement parameters is presented in Extended Data Table 1.

Methods
Computational details. Spin-polarized DFT calculations were carried out using the PWscf module in the Quantum Espresso 6.1 program package 50 6 contained 348 atoms in total. Atomic optimizations were carried out, starting from the experimental cell parameters. Integration in the first Brillouin zone for geometry optimizations was performed using 2 × 2 × 2 point Monkhorst-Pack sampling 53 . The SCF (self-consistent field) convergence and the total force convergence were set to be 1.0 × 10 −6 (Ry) and 1.0 × 10 −3 (Ry/ au), respectively. The total magnetization was constrained to be 28.00 Bohr mag per cell. The spin-polarized DFT calculations further provided reliable information as to the charge and the spin state on each iron atom in [Fe 14 ]. The singly occupied electrons at the B-site Fe III components partially delocalizes on the A-site Fe II ions.
Magnetic analysis. The magnetic measurements of the samples were performed using a SQUID (MPMS-5S) magnetometer (Quantum Design Inc., USA). The magnetic susceptibility measurements shown in Fig. 4d were performed using MPMS-XL7AC (Quantum Design Inc., USA) apparatus with a 9 mm diameter 3 He insert 54 . The data were corrected for diamagnetic contributions, calculated using Pascal's constants 55 .
Simulation of magnetization. The field dependence of magnetization for [Fe 14 ] follows neither the Brillouin function for an S = 14 spin moment or the sum of uncoupled moments (four S = 5/2 and two S = 2). Inclusion of a weak ferromagnetic exchange interaction, acting between high spin sites was found to reproduce the measured magnetization curve. The magnetization curve was fit assuming one exchange constant J = 0.9 K and g = 2.0, based on the following Hamiltonian: where S 1 and S 6 represent the S = 2 sites and S 2 , S 3 , S 4 and S 5 represent the S = 5/ 2 sites, B is the applied magnetic field and µ B is the Bohr magneton. 57 Fe Mössbauer spectroscopy. The 57 Fe Mössbauer spectra were measured using a conventional Mössbauer spectrometer (Topologic Systems, Kanagawa, Japan) in transmission mode with a 57 Co/Rh γ-ray source. Low-temperature measurements were performed upon a CryoMini/CryoStat cryogenic refrigerator set (Iwatani Industrial Gases, Osaka, Japan). The samples were tightly sealed with silicon grease in an acrylic holder and the spectra were calibrated using α-Fe foil as a reference at room temperature. The spectral fitting was carried out using the MossWinn 4.0 program and the full zero-field 57 Fe Mössbauer spectra at all investigated temperatures were provided in Supplementary Fig. 10 Supplementary   Fig. 11) or two quadrupole doublets (10-144 K). The area ratio was fixed at the ideal value (Fe II /Fe III = 1/2) according to the chemical formula in order to avoid overparameterization. Some parameter correlations were found, especially between the linewidth and relaxation rate, through curve fittings of the spectra at 245-297 K. Therefore, the linewidth and IS values for Fe II -hs at the relevant temperatures were fixed using those at 224 K. For the analyses at 10-144 K, the Fe II -hs doublet was regarded as an asymmetric doublet, rising as a result of paramagnetic relaxation because an alternative symmetric doublet was tried but presented no sufficient result. Heat capacity calorimetry. Heat capacity measurements were performed with a laboratory-made adiabatic microcalorimeter in the temperature range of 9-300 K (adiabatic method) and with a PPMS (Quantum Design Inc., USA) in the temperature range 0.36-100 K under magnetic fields of 0-9 T (relaxation method). In the adiabatic calorimetry, 0.06356 g of a polycrystalline sample, which was made a buoyancy correction, was loaded into a 0.09 cm 3 gold-plated copper cell and sealed with an indium wire under helium gas atmosphere. Thermometry was performed using a rhodium-iron alloy resistance thermometer (nominal 27Ω, Oxford Instruments) calibrated on the basis of the international temperature scale of 1990 (ITS-90). In the relaxation calorimetry (PPMS), we used buoyancy-corrected 1.1031 mg of a polycrystalline sample formed into a pellet of 2.5 mm in diameter. For the measurements below 10 K, a 3 He insert was employed 56 .
X-ray absorption spectra and X-ray magnetic circular dichroism. XAS and XMCD measurements at the Fe L absorption edges (703-740 eV) were measured on beamline I10 at the synchrotron Diamond Light Source of the Harwell Science and Innovation Campus in Oxfordshire in the United Kingdom. The XMCD spectra were obtained by flipping the helicity of circularly polarized X-rays exhibiting a 100% degree of polarization in the case of fixed applied magnetic fields.
The measurements were performed with the temperature of the sample holder being regulated between 3.5 and 300 K. The total electron yield was obtained by measuring the drain current of the sample, whereas the TFY was obtained using a photodiode. The powdered samples of [Fe 14 ] were attached with indium, to a copper sample holder. Radiolysis was controlled through the attenuation of the incident X-ray flux to 7% of the optimized value. Multiple scans were performed at each sample location to maintain control of the radiolysis, which was indicated by an increase in intensity at the low-energy portion of the L 3 edge. TFY-detected measurements were found to be less susceptible to radiolysis and were hence adopted for XMCD measurements.
High-frequency electron paramagnetic resonance. High-frequency electron paramagnetic resonance (HF-EPR) measurements were performed on a locally developed spectrometer at the Wuhan National High-magnetic Field Center with a pulsed magnetic field of up to 30 T.

Data availability
The data that support the findings of this study and its Supplementary