Electron Localization of Polyoxomolybdates with Îµ-Keggin Structure

Article pubs.acs.org/JPCA

Electron Localization of Polyoxomolybdates with ε‑Keggin Structure Studied by Solid-State 95Mo NMR and DFT Calculation Takahiro Iijima,†,‡,# Toshihiro Yamase,§,⊥ Masataka Tansho,∥ Tadashi Shimizu,∥ and Katsuyuki Nishimura*,†,‡ †

Institute for Molecular Science, Okazaki, 444-8585, Japan The Graduate University for Advanced Studies (SOKENDAI), Okazaki, 444-8585, Japan § Tokyo Institute of Technology, Nagatsuta, Yokohama 226-8503, Japan ⊥ MO Device Corporation, Kanazawa 920-0335, Japan ∥ National Institute for Materials Science, Tsukuba 305-0003, Japan ‡

S Supporting Information *

ABSTRACT: We report electron localization of polyoxomolybdates with ε-Keggin structure investigated by solid-state 95 Mo NMR and DFT calculation. The polyoxomolybdates studied are the basic ε-Keggin crystals of [Me3NH]6[H2Mo12O28(OH)12{MoO3}4]·2H2O (1), the crystals suggested to have a disordered {ε-Mo12} core of [PMo12O36(OH)4{La(H2O)2.75Cl1.25}4]·27H2O (2), and the paramagnetic Keggin crystals of [H2Mo12O30(OH)10{Ni(H2O)3}4]·14H2O (3). The spectra of 95Mo static NMR of these samples were measured under moderate (9.4 and 11.7 T) and ultrahigh magnetic fields (21.8 T). From spectral simulation and quantum chemical calculation, the NMR parameters of the chemical shift and quadrupole interactions for 95Mo were estimated. By the analysis based on the result for 1, it was found for 2 that although the {ε-Mo12} core is disordered, the eight d1 electrons in it are not completely localized on four Mo−Mo bonds. Furthermore, it was shown for 3 that the d1 electrons are localized to make the Mo−Mo bonds, while the unpaired electrons are also almost localized on the paramagnetic NiII ions.

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INTRODUCTION There are stable compounds for a group 6 transition-metal element of molybdenum with all integer valences from Mo0 to MoVI. Among them, many MoV species are included in polyoxometalates of ε-Keggin anions1−5 and nanosized oxides with characteristic shape such as ring, ball and tube.6−9 Localization of d1 electrons of the MoV species has attracted much attention in terms of molecular design and solid state physics like optic, electric and magnetic properties.10−12 Nuclear magnetic resonance (NMR) is a well-known powerful tool for analyzing local structures of materials in both liquid and solid states.13,14 Basically, the spectra of solidstate NMR are broadened by anisotropic nuclear-spin interactions that are usually averaged by fast motion in liquids. In particular, half-integer quadrupole nuclei (HIQN, I = 3/2, 5/ 2, ...) may have large quadrupole interactions that influence the behavior of nuclear magnetization and the NMR spectra.15 Lineshape of the NMR spectra for the central transition (1/2 ↔ −1/2) is affected by the second-order quadrupole interaction that is inversely proportional to the applied magnetic field. Thus, high magnetic field can improve resolution of the spectra due to the second-order quadrupole interaction. High field also improves sensitivity in NMR © 2014 American Chemical Society

measurements, which is especially efficient for the HIQN with low values of gyromagnetic ratio. Recent development of the high-field magnets has accelerated structural studies by solid-state 95Mo (I = 5/2, γ = −1.743 × 107 rad s−1 T−1) NMR.16−26 The NMR parameters of 95Mo NMR have also been obtained by quantum chemical calculations.16−18,27−32 Previously, 95Mo NMR for MoV species with d1 electrons has been measured only for several liquid samples.33−39 Recently, we have reported solid-state 95Mo magic-angle-spinning (MAS) NMR of mixed-valence polyoxomolybdates including MoV.40 In the that work,40 the high-field spectra of solid-state 95Mo NMR for ε-Keggin species of [Me3NH]6[H2MoV12O28(OH)12(MoVIO3)4] (1) with localized d1 electrons1,2 and blue species of [NMe4]2[NH4]8[(MoVI6MoVO23)2]·8H2O with delocalized ones41 were measured. It was found from spectral simulation and relativistic density-functional-theory (DFT) calculation that solid-state 95Mo NMR can be utilized for localization analysis of the d1 electrons.40 Received: October 8, 2013 Revised: March 10, 2014 Published: March 12, 2014 2431

dx.doi.org/10.1021/jp409969g | J. Phys. Chem. A 2014, 118, 2431−2441

The Journal of Physical Chemistry A

Article

Figure 1. Structure of (a) [PMo12O36(OH)4(La(H2O)2.75Cl1.25)4] by X-ray analysis,3 (b) [PMo12O36(OH)4(La(H2O)4)4]5+, and (c) [PMo12O36(OH)4(La(H2O)3Cl)4]+ expressed by atom-and-bond model. Mo, Ln, O, Cl and P atoms are indicated by magenta, green, gray, light blue, and yellow, respectively. In part a, all the disordered sites of Cl and O in the ligand are expressed. Parts b and c show the structures used for DFT calculation.

MAS can average second-rank interaction tensors to give high-resolution NMR spectra of solids, which is usually efficient for peak separation of different chemical sites. However, MAS may not resolve the NMR spectra, when the spectra exhibit inhomogeneous broadening due to the second-order quadrupole interaction with the fourth-rank tensor and homogeneous broadening due to the fast magnetic relaxation by paramagnetic species. In such a case, static NMR becomes advantageous, because the spectral line shape can be reliably captured and error of the NMR parameters estimated by simulation will decrease. In the present work, we applied solid-state 95Mo static NMR and DFT calculation to the study of three ε-Keggin polyoxomolybdates that have similar structures but significantly distinct properties. The structure of the ε-Keggin isomer can be obtained from the well-known α-Keggin anion [PMo12O40]3− by rotation of all four Mo3O13 groups with 60°.1−4,42 The materials treated here are the crystal with structural disorder of [PMo12O36(OH)4{La(H2O)2.75Cl1.25}4]·27H2O (2) and the paramagnetic crystal of [H2Mo12O30(OH)10{Ni(H2O)3}4]· 14H2O (3). The crystal of 2 is composed of the {ε-Mo12} core capped with four La(H2O)2.75Cl1.25 groups, where the decimal is due to disorder of the ligand of H2O and Cl.3 The structure obtained by X-ray diffraction is shown in Figure 1a. Seven-coordinate LaIII ions are bound to the Keggin core by three O atoms. Four remaining ligands of LaIII are H2O and Cl, where the occupation probabilities are 11/16 and 5/16, respectively. From the result of potentiometric titrations, the {ε-Mo12} core contains eight MoV and four MoVI centers.3 Since no intervalence charge-transfer bands for MoV → MoVI have been observed in electronic absorption spectroscopy and there is dispersion of the Mo−Mo distance among 2.697−2.780 Å, the {ε-Mo12} core is also suggested to be disordered; the disordered pairs of four MoV−MoV and two MoVI−MoVI result in the overall Td symmetry. Solid-state 95Mo NMR is expected to clarify the structure of the {ε-Mo12} core or localization of the d1 electrons. The main difference of 3 from 1 is the cap group with the paramagnetic NiII ions in 3 (Figure 2).4 In paramagnetic compounds, the hyperfine interaction is included in the internal nuclear-spin interactions.13,43 Fast paramagnetic relaxation can cause broadening of the NMR spectra, although in some cases it is advisedly used for speeding up NMR measurement.44,45 The hyperfine coupling also affects the spectra as a change of line shape by the anisotropic component and as a whole shift by

Figure 2. Structure of [Mo12O30(OH)10H2(Ni4(H2O)12)] expressed by polyhedral (a) and atom-and-bond model (b). (MoV atoms, MoVO6 octahedra) and (NiII, NiIIO6) are indicated by magenta and light green, respectively. In part b, gray circles show oxygen atoms. Thick lines denote MoV−MoV bonds.

the isotropic component. Although numerous structural studies of paramagnetic materials have been conducted by solid-state NMR with 7Li46−51 and other HIQN such as 51V,52−54 59Co,47 95 Mo,55 137Ba,56 and 139La,57 the spectra have not been simulated by considering both isotropic and anisotropic effects from the second-order quadrupole, chemical shift and hyperfine interactions as far as we know. The present work performing numerical simulation of the 95Mo spectra combined with DFT calculation58−60 for the paramagnetic crystal would be a challenging attempt. In the Results and Discussion, the crystal of 1 is discussed first. We will compare the NMR parameters obtained by static NMR and previous MAS NMR, and show the relation between the chemical shift and the electronic structure in detail. On the basis of the result of 1, localization of the eight d1 electrons in the {ε-Mo12} core of 2 is discussed. Finally, localization of both the d1 electrons of MoV and the unpaired electrons of NiII for 3 is shown.

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EXPERIMENTAL SECTION Solid State 95Mo NMR. The powder samples used in this study were [Me3NH]6[H2Mo12O28(OH)12{MoO3}4]·2H2O (1), [PMo12O36(OH)4{La(H2O)2.75Cl1.25}4]·27H2O (2) and [H2Mo12O30(OH)10{Ni(H2O)3}4]·14H2O (3) crystals, which were synthesized according to the methods in the previous reports.2−4 Solid-state 95Mo NMR measurements under magnetic field of 9.4, 11.7, and 21.8 T were performed by a 2432



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Varian Inova 400 spectrometer at a resonant frequency of ν0 = 26.060 MHz, a JEOL ECA 500 spectrometer at ν0 = 32.595 MHz, and a JEOL ECA 930 spectrometer at ν0 = 60.572 MHz, respectively. Single-tuned probes by JEOL and Doty were used for experiments under (9.4 and 21.8 T) and (11.7 T), respectively. To prevent acoustic ringing and acquire quite broadened spectra, a Hahn echo sequence (90°Q−τ−180°Q−τ− acq) was used. 90°Q and 180°Q are central transition pulse-widths for HIQN in solid samples with CQ ≫ ν1, which are scaled by (I + 1/2)−1 with respect to the pulse width in solution state.61,62 The rf pulses with ν1 of 33, 29, and 54 kHz were irradiated under 9.4, 11.7, and 21.8 T, respectively. The τ values were 80, 100, and 50 us under 9.4, 11.7, and 21.8 T, respectively. Under 9.4, 11.7, and 21.8 T, the 95Mo NMR signals of 150000−164000, 532000, and 220000−266000 transients were accumulated at room temperature with the repetition delay of 0.2−0.3, 0.4, and 0.3−0.5 s, respectively. Under 11.7 T, the 95Mo NMR spectrum at 173 K was also measured for the sample 2 with accumulation of 168000 transients. A 2.0 M Na2MoO4 solution was used for a reference of the 95Mo chemical shift (δics = 0 ppm) and a calibration of the pulse width. Spectral Simulation. Numerical calculations for the 95Mo NMR signals were carried out by a home-written Fortran90 program. Hamiltonian used for the calculation was (2) (2) 43,63−69 / = / (1) Here, / (1) Q and / Q Q + / Q + /S + /1. are the first and second order quadrupole interactions, respectively. / (1) Q that is irrelevant for the spectral line shape of the |1/2⟩ ↔ |−1/2⟩ central transition of the HIQN is needed, because it affects nutation behavior of the magnetization of 95Mo. The shift term /S includes both the chemical and paramagnetic shifts, each of which has the isotropic and anisotropic components. /1 is the Zeeman interaction with applied rf field. The tensors of electric field gradient (EFG), chemical shielding and dipolar coupling between the resonant 95Mo nuclei and electron spins in paramagnetic ions surrounding the nuclei are expressed with their principal components and orientation of the tensors with respect to the external field. The irreducible component of the EFG tensor was given by twostep Euler-angle rotations, that is from the principal axis system (PAS) to a molecular system, and from the molecular system to the laboratory frame. For the chemical shielding tensor, further transformation is needed in order to account for the relative orientation (α, β, γ) with respect to the EFG tensor. Each of the PAS of the dipolar coupling tensor between the resonant 95 Mo and the electron spins in the paramagnetic ions is transformed to the molecular axis system with respective Euler angles. For the EFG tensor we define |eq33| ≥ |eq22| ≥ |eq11| for its principal components and ηQ = (eq11 − eq22)/eq33 as an asymmetry parameter. The parameter CQ = e2Qq33/h is called as a quadrupole coupling constant. For the chemical shift interaction the principal components δii are taken as |δ33 − δics|≥|δ22 − δics| ≥ |δ11 − δics| with δics = (δ11 + δ22 + δ33)/3 and have relation of δcsa = δ33 − δics and ηcsa = (δ11 − δ22)/(δ33 − δics). In paramagnetic materials, the isotropic shift (δiso) of the spectra is a sum of the temperature-independent chemical shift (δics) and temperature-dependent paramagnetic shift (δihf) which is given for an isotropic g-tensor by58,70−73

δihf =

gμ B (γ /2π )3kBT

S(S + 1)Aiso

(1)

where μB, γ, kB, T, and S are the Bohr magneton, gyromagnetic ratio, Boltzmann constant, temperature, and spin number of the electron spin, respectively. Aiso is the isotropic value of the hyperfine coupling tensor (Aii) expressed in units of hertz, including a contribution from the Fermi contact and relativistic terms.74 For the anisotropic hyperfine interaction due to the nuclear-electron dipolar coupling, the coupling constant for the unpaired electrons localized on the jth paramagnetic ions, ωPj , can be given by ωjP =

2 2 ⎛ μ0 ⎞ 2γB0 g μB ⎜ ⎟ S(S + 1) ⎝ 4π ⎠ 3kBTrj 3

(2)

where μ0 and rj are the permeability of vacuum and distance between the 95Mo nuclear and the electron spins for the jth paramagnetic ion, respectively. The ASG tiling scheme75 was employed for powder distribution of molecular orientation and hemisphere was divided by ca. 62000 points. DFT Calculation. DFT calculations for the EFG and chemical shielding tensors were implemented with an Amsterdam density functional (ADF) software package.76,77 The local density approximation of Vosko−Wilk−Nusair (VWN) augmented with the Becke−Perdew generalized gradient approximation (GGA) was employed for the exchange-correlation functional.16,18,40 Relativistic calculations by zeroth-order regular approximation (ZORA) formalism78−80 including both scalar and spin−orbit corrections were performed. For open shell system, only scalar correction was included in the relativistic calculation. Isolated ions of [Mo 12 O 28 (OH) 12 {MoO 3 } 4 ] 8− ({Mo 16 }), [PMo 12 O 40 {La(OH2)3OH}4]3− ({Mo12(La)}), [PMo12O40{La(H2O)2ClOH}4]7− ({Mo12(LaCl)}), and [Mo12O28(OH)12{Ni(H2O)3}4] ({Mo12(Ni)}) were used for calculation. The tripleζ doubly polarized (TZ2P) Slater-type ZORA all-electron basis set was used. The Mo and O atomic coordinates were determined so that the ions take averaged structures with Td symmetry by adapting average bond lengths and bond angles obtained using structural data.2−4 For {Mo12(La)} and {Mo12(LaCl)}, asymmetric structures with distinct Mo−O lengths were also used (vide inf ra). Protons were added for convergence of self-consistent field (SCF) calculation; the H atoms were bonded to bridging oxygens in the {ε-Mo12} core for {Mo16}, to terminal oxygens in the cap for {Mo12(La)} and {Mo12(LaCl)}, and to both for {Mo12(Ni)}. Positions of the H atoms were determined by geometry optimization with nonrelativistic DFT using the frozen-core double-ζ basis set. The 95Mo chemical shift by DFT was referenced to an isolated Mo(CO)6 at −1854 ppm.16,40,81

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RESULTS AND DISCUSSION Mo NMR of Crystal 1. We start with the basic ε-Keggin crystals of sample 1, where the {ε-MoV12} core composed of the six MoV−MoV pairs is capped with MoVIO3. Figure 3(i-a) and Figure 3(ii-a) show the 95Mo static spectra of 1 measured under 9.4 and 21.8 T, respectively. These are wide spectra expanding about 2000 ppm. Since {Mo16} has chemically distinct two types of molybdenum (MoV and MoVI), spectral simulation was performed by a superposition of two components with the relative signal intensity of 3: 1 as in the case of our previous 2433

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acceptable limits. Discrepancy of the parameters estimated from the MAS and static spectra would be due to experimental error. A characteristic of the NMR parameters of 1 is the 95Mo chemical shielding tensor that is considerably different between the MoV and MoVI sites. The electronic state of {Mo16} helps us to understand such a difference. Figure 4 shows the energy and

Figure 3. 95Mo static NMR spectra of the sample 1 under (i) 9.4 and (ii) 21.8 T. (a) and (b) show the observed and simulated spectra, respectively. Parts c and d are the constituting spectra of part b.

MAS NMR study.40 Note that the Zeeman interaction with the B1 field was explicitly incorporated in simulation in order to take account of nutation behavior depending on the CQ value.61,62,82 In the experiments, we applied the simple echo sequence without adding a quadrupolar Carr−Purcell− Meiboom−Gill train83 to reduce effect of unwanted phase distortion due to the different nutation frequencies on the spectra. Simulation results and the spectral constituents are shown in Figure 3b−d. The obtained NMR parameters of the quadrupole interaction (CQ, ηQ), the chemical shift interaction (δics, δcsa, ηcsa) and the relative orientation (α,β,γ) are summarized in Table 1. As apodization of the spectra, the effective spin−spin relaxation times T2* for MoV and MoVI were assumed as 90 and 70 us, respectively. In Table 1, the NMR parameters40 by simulation of the MAS spectra and by relativistic DFT calculation are also shown for comparison. For the MoV site, the NMR parameters obtained by the static spectra were similar to those by the MAS spectra, although the asymmetry parameter ηQ and relative orientation (α, β, γ) could not be determined owing to the very small CQ value. On the other hand, the chemical shielding tensor and the β angle between σ33 and eq33 were estimated for the MoVI site by the static experiment. We consider that the parameter values obtained by spectral simulation and DFT calculation are within

Figure 4. Energy diagram and selected MOs (a−e) of {Mo16} obtained by relativistic DFT calculation.

some molecular orbitals (MOs) of {Mo16} obtained by DFT calculation. The molecular axes are chosen so that each of three orthogonal vectors connects the midpoints of the opposite MoV−MoV bonds. The energy of the lowest unoccupied molecular orbital (LUMO) is shifted to 0 eV. The energy of {Mo16} in Figure 4 can be divided into three bands; band-1 at −6.81 to −3.01 eV, band-2 at −2.28 to −1.94 eV and band-3 at 0.00−1.68 eV. The virtual orbitals of the band-3 are mainly composed by 5s, 6s, and 4d orbitals of molybdenum both in the ε-Keggin {MoV12} and MoVIO3 cap (Figure 4, parts d and e). The band-2, including the highest occupied molecular orbital (HOMO), is composed of six occupied orbitals that mainly make six MoV−MoV σ-bonds with dxy−dxy, dyz−dyz and dzx−dzx combinations by the localized d1 electrons (Figure 4c). The MOs in the band-1 are basically the oxygen 1p orbitals; those at ca. −6.2 to −3.0 eV are dangling lone-pair (Figure 4b). The

Table 1. 95Mo NMR Parameters of Crystal 1 Obtained by Spectral Simulation and Relativistic DFT Calculation ηQ

CQ/MHz MoV

MoVI

a

0.5 ± 0.2



δics/ppm 305

0.7 ± 0.1

0.2 ± 0.2

0.48a

0.24a

5.2 ± 0.4

0.2 ± 0.2

40

4.0 ± 0.2

0.15 ± 0.15

68

5.96a

0.00a

305

δcsa/ppm

By Static Spectra ± 30 −1060 ± 100 By MAS spectraa ± 10 −990 ± 40 By DFT 519a −1159a By Static Spectra ± 30 100 ± 100 By MAS Spectraa ± 10  By DFT 253a 102a

ηcsa

(α,β,γ)/deg

0.2 ± 0.15



0.4 ± 0.2



0.17a

(0, 55, 90)

0.2 ± 0.2

(, 15 ± 15, )

 0.00a

 (0, 0, 0)

Reference 40. 2434



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molybdenum 4d atomic orbitals (AOs) in MoVIO3 mix into several MOs at around −6.4 eV (Figure 4a) and lower edge of this band to form the Mo−O π- and σ-bonds in the MoVIO3 cap, respectively. In general, the chemical shift tensor is determined by a sum of diamagnetic, paramagnetic and spin−orbit contributions.16,18,79,84 Among these terms, the diamagnetic shielding term dominated by core electrons is large but almost independent of the chemical structure. The paramagnetic deshielding term is primarily responsible for the dependence of the chemical shift on the chemical structure in many cases including 95Mo.18 For {Mo16}, the dominant contribution that induces the difference of chemical shift values of MoV and MoVI was this paramagnetic term. The spin−orbit term corresponds to Fermi contact and spin-dipole terms at nonrelativistic limit. While the relativistic correction in chemical shift calculation has been reported to be important for the piano-stool complex,16 nonrelativistic calculations have given acceptable results for other compounds.17,18,26,32,84−87 In our case of {Mo16}, the contribution from spin−orbit term was smaller than that from the diamagnetic and paramagnetic terms by an order of magnitude and was almost independent of the molybdenum sites. The paramagnetic term is caused by magnetic-dipole allowed mixing of occupied and virtual orbitals of appropriate symmetry and the magnitude is inversely proportional to the difference of these orbitals.16,18,84 In the present case, the molybdenum 4d orbitals are relevant for the 95Mo chemical shift. The large shift interaction for MoV is due to the small gap for the MOs of the molybdenum 4d orbitals of, e.g., parts c and e of Figure 4, while the gap for the MOs of MoVI in the MoVIO3 cap (parts a and d of Figure 4) is large with more than 6 eV. The large anisotropy in the chemical shift interaction of MoV species is arising from directionality of the MoV−MoV bond. Considering a MoV site with the MoV−MoV bond formed by the two dxy AOs, the principal δ22 component was along this bond and δ33 parallel to the molecular z axis. The energy is 0.4 eV for the virtual MOs with significant portion of dyz and dzx AOs that are conjugated by the angular momentum operators of L̂ x and L̂ y to provide the principal values of δ11 (1000 ppm) and δ22 (1199 ppm). On the other hand, the virtual MOs with dx2−y2 AOs contributing to δ33 (−639 ppm) appear at 2.4 eV or higher, resulting in the weak deshielding of this principal component. The CQ values were very different between MoV in MoVO6 and MoVI in Mo VI O6 . According to the point-charge approximation,88 the EFG at nucleus in the center of the regular octahedral symmetry becomes zero. Distortion of octahedron of MoVO6 and MoVIO6 can result in the nonzero CQ value. In the crystals in this study, a correlation between the CQ value with simple average of Mo−O distance could not be obtained. For MoVIO6, three O atoms are bridging oxygens in the ε-Keggin core with the MoVI−O distance of 2.221 Å, and the other three O atoms are terminal oxygens with the distance of 1.746 Å (Supporting Information). Then, the O−MoVI−O angle from 78.0° to 104.2° would cause the large CQ value obtained. On the other hand, the MoVO6 octahedron has five bridging oxygens and one terminal oxygen. The MoV−O lengths are 1.686 Å for the terminal oxygen and 1.967−2.095 Å for four of the five oxygens. The length for the remaining oxygen opposite to the terminal oxygen is 2.167 Å. The O− MoV−O angles are 73.9−105.5°. The six oxygens in the

distorted octahedron and the neighboring MoV forming the MoV−MoV bond seem to cancel the EFG at the MoV site. 95 Mo NMR of Crystal 2 with Structural Disorder. Figure 5a shows the 95Mo NMR static spectra of sample 2 measured

Figure 5. 95Mo static NMR spectra of the sample 2 under (i) 9.4 and (ii) 21.8 T. (a) and (b) show the observed and simulated spectra, respectively. Parts c and d are the constituting spectra of part b.

under two different magnetic fields. The spectra spread about 4800 and 2300 ppm under 9.4 and 21.8 T, respectively. First, we tried simulating the spectra with only one component. However, a set of NMR parameters with which the calculated spectra simultaneously reproduce the two experimental spectra could not be obtained. Thus, we used two sets of the parameters and superimposed the components with a ratio of 2:1 (Mo(1):Mo(2)). The simulation results are shown in Figure 5b and the NMR parameters used are summarized in Table 2. As expected, quite large (CQ, δcsa) values of (7.2 MHz, −1360 ppm) for Mo(1) and (5.0 MHz, −710 ppm) for Mo(2) were estimated. For DFT calculation, molecular modeling of {Mo12(La)} or {Mo12(LaCl)} is needed because (i) the O and Cl atoms in the cap of 2 occupy multiple sites by the structural disorder (Figure 1a), (ii) 11 O and 5 Cl atoms are included in the four caps of(La(H2O)2.75Cl1.25)4, and (iii) the {ε-Mo12} core may also be disordered.3 Concerning localization of the d1 electrons in the {ε-Mo12} core, there can be two types of the model structure: one is the average structure with the delocalized d1 electrons, and the other has the structural disorder with the localized electrons on the MoV sites. For the former model, we used La(H2O)4 as a cap (Figure 1b) and imposed the Td symmetry for the {Mo12(La)} ion. However, we could not obtain any aufbau electron structures. In order to acquire the latter structure, we then tried geometry optimizations by molecular mechanics or DFT calculation without the Td symmetry. Unfortunately, the structure has never converged. Thus, we decided to create structure models with the disordered {ε-Mo12} core manually. Since apart from the Td symmetry many kinds of the {Mo12(La)} structure are possible to construct, we simply changed the Mo−Mo distances from the structure in Figure 1b. Considering eight d1 electrons for 12 Mo atoms, we prepared two long Mo−Mo distances (dS ) and four short ones (ds) that satisfy the equation (dS + 2ds)/3 = d̅, 2435



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Table 2. 95Mo NMR Parameters of Crystal 2 Obtained by Spectral Simulation and Relativistic DFT Calculation for Δd = 0.4 Å CQ/MHz Mo(1)

Mo(2)

7.2 ± 1.0

ηQ 0.5 ± 0.2

11.4

0.22

11.3

0.16

5.0 ± 1.0

0.7 ± 0.1

5.9

0.27

4.4

0.38

δics/ppm

δcsa/ppm

By Static Spectra 130 ± 260 −1360 ± 100 By DFT for {Mo12(La)} 433 −1150 By DFT for {Mo12(LaCl)} 506 −1252 By Static Spectra −310 ± 240 −710 ± 80 By DFT for {Mo12(La)} 475 −306 By DFT for {Mo12(LaCl)} 387 −280

where d̅ is the average Mo−Mo distance of the X-ray structure. There are two possible configurations; the two long-distance Mo−Mo are opposite or adjacent in the {Mo12(La)} ion. Among them, the SCF calculation was converged only for the former model. The NMR parameters were calculated by relativistic DFT with changing the difference Δd (= dS − ds) from 0.1 to 0.6 Å with a step of 0.1 Å. The calculation results are summarized in Figure 6.

ηcsa

(α,β,γ)/deg

0.3 ± 0.1

(0 ± 15, 10 ± 10, 0 ± 15)

0.22

(13, 8, −24)

0.28

(20, 9, 7)

0.1 ± 0.1

(, 10 ± 10, )

0.23

(−1, 6, 1)

0.32

(−1, 6, 4)

obtained by the spectral simulation of 2. With decreasing the Δd value, the ratios CQ(Mo(1))/CQ(Mo(2)) and |δcsa(Mo(1))|/|δcsa(Mo(2))| came close to those by the simulation, except for δcsa with Δd = 0.2 Å. This is consistent with the X-ray structure, where the Mo−Mo distances have been analyzed as 2.697−2.780 Å.3 For ηQ, δics, and ηcsa, significant correlation with the experimental values was not seen. Disagreements can be due to the fact that only the positions of Mo atoms were changed in the present structure model. The parameters with Δd = 0.4 Å are shown in Table 2. The relative orientation of chemical shift and EFG tensor obtained by simulation and DFT agreed well. The DFT calculation was also carried out for {Mo12(LaCl)} in Figure 1c, where one of the O atoms in the cap site was displaced with Cl and the La−Cl distance was adjusted to the value by the X-ray structure. The SCF calculation converged with Δd larger than 0.3 Å. The Δd dependence of the NMR parameters and the values with Δd = 0.4 Å for {Mo12(LaCl)} are shown in Figure 6 and Table 2, respectively. No significant difference of the parameters by this substitution was seen, except for ηcsa of Mo(2) that takes small values even with large Δd. Although five Cl atoms are coordinated to four La atoms in the cation statistically, only one or two Cl atom(s) could coordinate to each La atom for the SCF to converge in our DFT calculation. The energy diagram of {Mo12(La)} and some MOs are shown in Figure 7. The bonding orbitals for the Mo−Mo σ bond spread over six MOs from the HOMO-3 to LUMO+1,

Figure 6. Δd dependences of 95Mo NMR parameters (CQ, ηQ, δics, δcsa, ηcsa) obtained by DFT calculation for crystal 2. The circles and triangles show the values of {Mo12(La)} and {Mo12(LaCl)}, respectively. The closed and open symbols show the values for Mo(1) and Mo(2), respectively.

In this range of Δd for {Mo12(La)}, the larger the Δd value was, the easier the SCF calculation converged; the difference Δd = 0.1 Å was too short to converge the SCF, and the δcsa value for Mo(2) seems to deviate with Δd = 0.2 Å. The present calculation exhibited the large (CQ, δcsa) values and the magnitude relations of CQ(Mo(1)) > CQ(Mo(2)) and |δcsa(Mo(1))| > |δcsa(Mo(2))|, which agrees with features

Figure 7. Energy diagram and some MOs of {Mo12(La)} with Δd = 0.3 Å obtained by relativistic DFT calculation. 2436



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where the eight d1 electrons mainly occupy four orbitals from the HOMO to HOMO-3. Similar to the case of {Mo16}, the d1 electrons are considered to lead to the large δcsa value of 95Mo NMR, because |δcsa(Mo(1))| > |δcsa(Mo(2))| holds (Figure 6). It is notable that although HOMO-1 − HOMO-3 are the bonding orbitals of Mo(1), the HOMO includes the 4d AOs of both Mo(1) and Mo(2). The degree of mixing of the 4d AOs of Mo(2) into the HOMO increased with decreasing the Δd value (data not shown), resulting in the increased |δcsa(Mo(2))| value as shown in 6. Indeed, from the spectral simulation we estimated the large |δcsa(Mo(2))| value that cannot be for the pure MoVI state. Therefore, the d1 electrons are not completely localized and the valences of Mo(1) and Mo(2) are considered to be 5 + κ and 6 − 2κ, respectively, where κ is a small quantity. The CQ values are large for both of Mo(1) and Mo(2). The structures of MoO6 of {Mo12(La)} are similar to that of MoVO6, except for the Mo−O length for the oxygen opposite to the terminal oxygen with the value of 2.513−2.519 Å at Δd = 0.4 Å (Supporting Information). This elongation of the Mo−O distance would lead to the large EFG of {Mo12(La)}. The difference of CQ between Mo(1) and Mo(2) should be due to Mo−Mo distance. 95 Mo NMR of Paramagnetic Crystal 3. Figure 8(a-i) and Figure 8(b-i) show the 95Mo NMR static spectra of sample 3

performed with and without considering the hyperfine interaction between 95Mo nuclei and electron spins in NiII ions. For the paramagnetic interaction due to the dipole coupling, contributions from the NiII ions in 4a × 8b × 12c unit cells around the resonant nucleus were considered, where (a, b, c) = (29.755 Å, 18.050 Å, 12.226 Å). The Euler angles for the transformation of the dipole coupling tensor from the PAS to the molecular system were calculated using the structural data by assuming the unpaired electron spins localized on NiII. The molecular system was set to coincide with the PAS of the EFG tensor, where the orientation of the tensor was assumed that (i) the eq22 axis is parallel to the MoV−MoV bond axis and (ii) the eq33 is parallel to the vector from the center of the ion to the midpoint of MoV−MoV. We used S = 1 and the isotropic g value of 2.23.4 Note that the contribution from this paramagnetic interaction is not a simulation parameter but can be calculated using information about crystal structure and electron state. The results of spectral simulation with T2* = 50 μs are shown in Figure 8(ii) and the best-fit parameters are listed in Table 3. The effect of the paramagnetic shift due to the 95Mo−NiII dipole coupling on the spectra was not a drastic change of the line shape but rather some broadening. This would be caused by the following reasons; (i) the maximum of the dipole coupling (ωPj ) was 267 ppm for the low-γ nuclei of 95Mo with the nearest NiII ion, (ii) the dipole couplings from the four NiII ions in {Mo12(Ni)} occupying the Td-symmetry sites are partially canceled, and (iii) the spectra are already largely broadened by the quadrupole interaction and, especially, the chemical shift anisotropy. The huge isotropic shift of 4200 ppm can be due to both chemical shift and hyperfine interactions. In order to separate these contributions, the 95Mo NMR spectrum was measured at 173 K. No significant shift of the spectrum, however, was observed as shown in Figure 8(c-i), which indicates small contribution of the isotropic hyperfine interaction to the 95Mo NMR. The spectrum at 173 K was also reproduced with the parameters in Table 3. Note that the theoretical spectrum at 173 K (Figure 8(c-ii)) was slightly broader than that at 301 K (Figure 8(b-ii)), because the paramagnetic shift due to the dipole coupling is inversely proportional to temperature (eq 2). Also, the quadrupole interaction may increase in magnitude as temperature decreases, resulting in broadened line width at 173 K. The relativistic DFT calculation was performed for the open shell of {Mo12(Ni)} and the obtained parameters are shown in Table 3. The relatively small CQ and quite large |δcsa| values are consistent with the experimental results. The isotropic shifts due to chemical shift and hyperfine interactions were separately calculated by DFT as δiso = 662 ppm and Aiso = −182 kHz. Similar to {Mo16} and {Mo12(La)}, the molybdenum d1 electrons of {Mo12(Ni)} largely occupied higher energy orbitals

Figure 8. 95Mo static NMR spectra of the sample 3 under (a) 21.8 and (b, c) 11.7 T. Parts a−c show the spectra at RT, 301 and 173 K, respectively. (i and ii) Observed and simulated spectra, respectively. The solid and broken lines in part ii show the theoretical curves with and without considering the paramagnetic shift interaction, respectively.

under 21.8 and 11.7 T, respectively. Under the both fields, the considerably broadened spectra spreading over several thousands of ppm were observed. Spectral simulation was

Table 3. 95Mo NMR Parameters of Crystal 3 Obtained by Spectral Simulation and Relativistic DFT Calculation

b

CQ/MHz

ηQ

1.5 ± 0.4

0.3 ± 0.3

0.61

0.59

δiso/ppm 4200 ± 200 880b (301 K) 1040b (173 K)

δcsa/ppm By Static Spectra −2200 ± 200 By DFT −1370

ηcsa

(α,β,γ)/deg

0.6 ± 0.1

(0 ± 15, 50 ± 15, 80 ± 40)

0.49

(90, 15, 0)

The δics value is 662 ppm (see text). 2437



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forming the MoV−MoV bonds (Supporting Information). The 4d AOs of Mo in the highest 12 spin−orbitals and the HOMO−LUMO gap of 1.3 eV seem to lead to the large |δcsa| value. Regrettably, there were some discrepancies in the value of δics and (α,β,γ) between spectral simulation and DFT. The {Mo12(Ni)} molecules around the target molecule may be important for the calculation of these values in the open shell system. With the calculated value of Aiso and eq 1, the δihf value was estimated as 218 and 378 ppm at 301 and 173 K, respectively. The spin density distribution of the unpaired electrons in the {Mo12(Ni)} molecule was also calculated. The electron spins were almost localized in the four NiII ions as drawn in Figure 9. Localization of the unpaired electrons results in the small δihf values and small temperature dependence of them, which is again consistent with the NMR measurement.

*(K.N.) E-mail: [email protected]. Present Address #

Yamagata University, Yamagata 990−8560, Japan

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors thank JEOL RESONANCE Inc., Probe Laboratory Inc. and Tuskuba Magnet Laboratory in Japan for their technical supports. This work was supported in part by The Graduate University for Advanced Studies (SOKENDAI). This work was financially supported by JST CREST, Grant-in-Aid for Young Scientists (B) No. 24750026 and Nanotechnology Support Project of MEXT in Japan.

The CQ value for Mo of {Mo12(Ni)} obtained by the DFT calculation (Table 3) is comparable to that for MoV of {Mo16} (Table 1). This is consistent with the fact that the structures of Mo V O 6 are similar between {Mo 12 (Ni)} and {Mo 16 } (Supporting Information).

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ASSOCIATED CONTENT

REFERENCES

(1) Khan, M.; Müller, A.; Dillinger, S.; Bögge, H.; Chen, Q.; Zubieta, J. Cation Inclusion within the Mixed-Valence Polyanion Cluster [(Mo VI O 3 ) 4 Mo 12 VO 28 (OH) 12 ] 8− : Syntheses and Structures of and (NH4)7[NaMo16(OH)12O40]·4H2O (Me2NH2)6[H2Mo16(OH)12O40]. Angew. Chem., Int. Ed. 1993, 32, 1780−1782. (2) Yamase, T.; Ishikawa, E. Photoreductive Self-Assembly from [Mo7VIO24]6− to Anti-Tumoral [H2Mo12VO28(OH)12(MoVIO3)4]6− in Aqueous Media. Bull. Chem. Soc. Jpn. 2008, 81, 983−991. (3) Mialane, P.; Dolbecq, A.; Lisnard, L.; Mallard, A.; Marrot, J.; Sécheresse, F. [ε-PMo12O36(OH)4La(H2O)44]5+: The First εPMo12O40 Keggin Ion and Its Association with the Two-ElectronReduced α-PMo12O40 Isomer. Angew. Chem., Int. Ed. 2002, 41, 2398− 2401. (4) Müller, A.; Beugholt, C.; Kögerler, P.; Bögge, H.; Bud’ko, S.; Luban, M. [Mo12VO30(μ2-OH)10H2(NiII(H2O)3)4], A Highly Symmetrical ε-Keggin Unit Capped with Four NiII Centers: Synthesis and Magnetism. Inorg. Chem. 2000, 39, 5716−5717. (5) Lopez, X.; Carbo, J. J.; Bo, C.; Poblet, J. M. Structure, Properties and Reactivity of Polyoxometalates: A Theoretical Perspective. Chem. Soc. Rev. 2012, 41, 7537−7571. (6) Yamase, T.; Prokop, P. Photochemical Formation of Tire-Shaped Molybdenum Blues: Topology of a Defect Anion, [Mo142O432H28(H2O)58]12−. Angew. Chem., Int. Ed. 2002, 41, 466−469. (7) Yamase, T.; Yano, Y.; Ishikawa, E. Photoreductive Self-Assembly from [Mo7O24]6− to Carboxylates-Coordinated Mo142 Mo-Blue Nanoring in the Presence of Carboxylic Acids. Langmuir 2005, 21, 7823−7832. (8) Müller, A.; Beckmann, E.; Bögge, H.; Schmidtmann, M.; Dress, A. Inorganic Chemistry Goes Protein Size: A Mo368 Nano-Hedgehog Initiating Nanochemistry by Symmetry Breaking. Angew. Chem., Int. Ed. 2002, 41, 1162−1167. (9) Liu, T.; Diemann, E.; Li, H.; Dress, A. W. M.; Müller, A. SelfAssembly in Aqueous Solution of Wheel-Shaped Mo154 Oxide Clusters into Vesicles. Nature 2003, 426, 59−62. (10) Pope, M. T., Müller, A., Eds. Polyoxometalate Chemistry: From Topology via Self-Assembly to Applications; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001. (11) Yamase, T., Pope, M. T., Eds. Polyoxometalate Chemistry for Nano-Composite Design; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2002. (12) Borrás-Almenar, J. J., Coronado, E., Müller, A., Pope, M., Eds. Polyoxometalate Molecular Science; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2003. (13) Abragam, A. The principles of Nuclear Magnetism; Clarendon: Oxford, U.K., 1961.

Figure 9. Spin density distribution of {Mo12(Ni)} by relativistic DFT calculation.

CONCLUSION

AUTHOR INFORMATION

Corresponding Author

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Article

In this paper, we studied solid-state 95Mo NMR of some polyoxomolybdates with ε-Keggin structure using high magnetic fields up to 21.8 T. The parameters about the chemical shift and quadrupole interactions for 95Mo of the crystals 1, 2 and 3 were obtained by DFT calculation and spectral simulation with or without considering the hyperfine interaction. It was concluded for 2 that the eight d1 electrons contained in the {ε-Mo12} core is not completely localized to result in 8 MoV + 4 MoVI but slightly delocalized to 8 MoV+κ + 4 MoVI−2κ. For the paramagnetic crystals of 3, we showed possibility of structural analysis of paramagnetic materials by solid-state 95Mo NMR.

S Supporting Information *

Tables of Mo−O distance of the MoO6 octahedron and a figure showing an energy diagram and some MOs of {Mo12(Ni)}. This material is available free of charge via the Internet at http://pubs.acs.org. 2438



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Electron Localization of Polyoxomolybdates with Îµ-Keggin Structure

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