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Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Solid-State 1H NMR Study of Structures and Dynamics of Proton Sites in Group II Salts of 12-Tungstophosphoric Acid and Related Compounds Steven F. Dec*,† and Andrew M. Herring*,‡ †

Department of Chemistry and Geochemistry and ‡Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States

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S Supporting Information *

ABSTRACT: The group II salts of 12-tungstophophoric acid were studied in the limiting state of hydration using a suite of 1 H solid-state NMR experiments, theoretical analysis, and density functional theory (DFT) energy calculations. Various nonspinning (NS) 1H NS NMR, magic-angle spinning (MAS) 1 H MAS NMR, and rotational-echo double-resonance (REDOR) 1 H{ 31 P} REDOR NMR experiments were performed. Chemical shift and spinning sideband patterns and comparison of 1H MAS two-pulse sequence NMR results with predictions of average Hamiltonian theoretical calculations definitively show that the limiting hydrated form of the group II salts of 12-tungstophosphoric acid contain only H+-protons and H2O-protons. Density matrix methods were used to derive expressions for the 1H NMR signal for a two-pulse NMR experiment as a function of the second pulse length under both NS and MAS conditions for H+-protons and H2O-protons. NMR structural parameters were obtained from the fit of theoretical expressions to the 1H NS two-pulse sequence NMR data where it was found that all H2O molecules have an interproton distance of 167 pm and the hydrogen atoms have a chemical shift asymmetry parameters of 0.5−1.0. DFT energy calculations consistent with the 1H{31P} REDOR NMR results were performed to determine the most stable H+-proton and H2O-proton structures in Keggin anion dimers (KA2−6). For the MgHPW, SrHPW, and BaHPW salts, the H+-protons are found to be in static, surface sites with multiple hydrogen-bonding interactions with oxygen atoms of the 1165 pm KA2−6 dimer in the monoclinic unit cell. Each hydrogen atom of the rotating H2O molecules of MgHPW and BaHPW has multiple hydrogenbonding interactions with one KA−3 of the 1400 pm KA2−6 dimer, whereas each hydrogen atom of the static H2O molecules of SrHPW has multiple hydrogen-bonding interactions with one KA−3 of the 1165 pm KA2−6 dimer. Similar analysis for CaHPW could not be performed probably because the H+-protons and H2O-protons are very mobile in this salt and no 1H{31P} REDOR dephasing was observed. For the BeHPW salt, the H+-proton and H2O-proton resonance lines are not resolved but analysis of the 1H NS two-pulse sequence NMR data shows that there is one H+-proton for each H2O molecule in this salt.

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INTRODUCTION

Employing HPA’s as the proton source in hydrogen fuel cells has been the subject of extensive recent research where often the goal is to use these materials in devices that operate at high temperatures and low hydration conditions.19 Whereas these studies indicate that the catalytic activity, bulk conductivity, and bulk diffusivity of HPA’s and HPA-containing composites can be measured using a variety of techniques, the structural basis for efficient catalytic activity and proton transport in HPA’s is of fundamental interest. An efficient proton-conducting material is presumably one that has a number of equivalent proton-binding sites distributed throughout the material with a sufficiently low energy activation barrier for proton transport between two

Heteropoly acids (HPAs) such as 12-tungstophosphoric acid (H3PW12O40·xH2O) are a structurally diverse, highly acidic, thermally stable set of materials.1 The application of HPA’s as acid catalysts for a variety of chemical reactions and as proton conductors is well known.2,3 Salt-substituted HPA’s have been found to be effective acid catalysts in a wide range of chemical reactions such as methanol conversion to the lower hydrocarbons and Friedel−Crafts reactions.4−8 The often high proton conductivity and diffusivity behaviors of the acid forms as well as many of the cation-substituted HPA’s have been extensively studied.9−15 More recent interest in HPA’s involves the environmentally friendly application of these materials to industrially important synthetic processes and the hydrogen economy. The HPA’s are attractive green chemistry acid catalysts16−18 because they are readily recycled, have minimal waste products involved with their use, and are low in toxicity. © XXXX American Chemical Society

Received: May 8, 2018 Revised: June 15, 2018 Published: June 18, 2018 A

DOI: 10.1021/acs.jpcc.8b04370 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

between a KA−3 at the corner and a KA−3 at the center of the structure. Figure 1d shows that substitution of the alkaline earth cation Mg2+ for two H+ cations dramatically reduces the symmetry of the parent cubic H3PW12O40·6H2O structure to a monoclinic structure.30 The group I salts of 12-tungstophosphoric acid have been studied using both solid-state 1H and 31P NMR techniques.31 In those studies, the highly substituted salts, that is, salts with about three group I countercations per unit cell, were investigated in the limiting hydration state to investigate the residual protons present in the salt structures. In each of the highly substituted group I salts, both water molecule protons (H2O-protons) and lone protons (H+-protons) were found to be present. In the case of the Li, Na, and Rb salts, all protons were assigned as part of the bulk structure, whereas the protons of the K and Cs salts were found to reside in surface sites. These results are consistent with the two models that are often used to describe the locations of protons in these materials, that is, a solid solution model and a model where a residual acid phase coats the surface of the salt-substituted HPA.2,32 The group I salt study showed that the more appropriate of the two models used to describe the materials can be unambiguously determined on the basis of a suite of 1H and 31 P NMR experiments. The group II salts of HPA’s are expected to have a limited number of structures because it is only possible to substitute one group II countercation per unit cell of an HPA because of charge balance constraints. The reaction of 12-tungstophosphoric acid with a group II cation M2+ is given by

sites.20 In many cases, HPA’s and their salts as well as HPA’s added or incorporated into other materials to form ionomers fulfill one or both of these conditions. Building on earlier work where simple physical addition of 12-tungstophosphoric acid to Nafion as well as other polymers proved to increase the proton conductivity,21−24 Herring and co-workers synthesized an array of ionomers where the HPA moiety was part of the polymer chain.25,26 This research found that the highest conductivity was obtained from ionomers with high concentrations of the HPA moieties that are clustered with inter-HPA anion distances similar to those in pure HPA’s. In addition, ionomers with higher water concentrations had proton conductivities apparently because the water network provided a lower energy barrier pathway for proton transport between proton-binding sites.27 Because the inter-HPA moiety distances in ionomers with high proton conductivity are similar to those of pure HPA’s, it is probable that the ionomer proton structures (for example H+, H2O, H3O+, H5O2+, etc.) are also similar to those of pure HPA’s. The Keggin anion (KA−3) structure,28 depicted in Figure 1a for the 12-tungstophosphoric acid anion, is the basic

H3PW12O40 ·x H 2O + M2 + → MHPW12O40 ·x H 2O + 2H+ (1) 2+

The stoichiometric addition of M has not been confirmed in some cases. For example, a single-crystal X-ray diffraction study of the addition of Ba2+ to 12-tungstomolebdic acid showed that the product is a mixture of the parent acid and a divalent chemical compound instead of pure BaHMoW12O40·xH2O.33 The goal of this work is to investigate the structures and dynamics of various proton sites in 12-tungstophophoric acid (MHPW) that has been reacted with a stoichiometric amount of group II cations, defined in eq 1. The product of the reaction described by eq 1 is heated at 383 K to remove physisorbed water. In this way, the limiting hydrated form (LHF) of the group II salts of H3PW12O40·xH2O is formed. The results from a set of 1H solid-state NMR experiments, theoretical analysis, and density functional theory (DFT) calculations are used to investigate the structure and dynamics of the LHF of group II salts of H3PW12O40·xH2O.

Figure 1. (a) Schematic diagram of the Keggin anion. (b) Schematic diagram of interpenetrating simple cubic structures of H3PW12O40· 6H2O. Crystal data: cubic Pn3̅m, a = 1215 pm (ref 29). (c) Schematic diagram of one face of H3PW12O40·6H2O showing hydrogen bonding of H5O2+. (d) Schematic diagram of MgHPW12O40·10H2O. Crystal data: monoclinic P21/c, Z = 4, a = 986.8 pm, b = 2198.0 pm, c = 1928.9 pm, βac = 90.63° (ref 30).

structure for many HPA’s. KA−3 contains four different types of oxygen atoms;28 four Oa atoms tetrahedrally coordinated to the central phosphorus atom, two types of bridging oxygen atoms, Ob and Oc (12 each), and 12 terminal Od atoms. Neutron diffraction has been used to determine the cubic structure of hexa-aquo-12-tungstophophoric acid, H3PW12O40· 6H2O,29 which can be considered to be two different interpenetrating simple cubic structures, each with lattice parameter a. As shown schematically in Figure 1b, the corner of one simple cubic unit cell lies at the center of the second simple cubic unit cell. Figure 1c indicates that the protons in H3PW12O40·6H2O are all part of Zündel cations that lie in planes of the simple cubic unit cell; the H2O protons are hydrogen-bonded to Od atoms of two different KA−3’s. It is noteworthy that no protons of any type are found in the space

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THEORETICAL BACKGROUND Anticipating structural assignments and potential motional narrowing of proton NMR resonance lines in the LHF of MHPW, we define the Hamiltonians,34 in frequency units, for an isolated proton with a charge of +1 (H+-proton) and water molecule protons (H2O-protons). The Hamiltonian Ĥ H for an H+-proton (I = 1/2) is ĤH = ωHIẑ

(2)

where ωH is the H+-proton chemical shift (CS) frequency ωH = ΔωH,iso + ωH,csa B

(3) DOI: 10.1021/acs.jpcc.8b04370 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C The term ΔωH,iso is the offset of the H+-proton isotropic chemical shift frequency relative to the radio frequency (RF) carrier frequency in the rotating frame. The H+-proton chemical shift frequency anisotropy term ωH,csa is ωH,csa =

The orientation of the H2O-proton dipolar PAS in its chemical shift (CS) PAS can be determined by application of the spherical harmonic addition theorem36,37 using the angles defined in Figure 2a yielding

δH (3 cos2(βH) − 1 − ηH sin 2(βH)cos(2αH)) 2

1 (3 cos2 (βH O) − 1)(3 cos2 (Θ) − 1) 2 2 + 6 cos(βH O)(1 − cos2(βH O))1/2 cos(Θ)(1 − cos2(Θ))1/2

3 cos2(βD) − 1 = (4)

2

where δH is the H -proton chemical shift anisotropy, ηH is the H+-proton chemical shift asymmetry parameter, and (αH, βH) are the azimuthal and polar angles, respectively, defining the orientation of the external magnetic field Bo in the principal axis system (PAS) of the H+-proton chemical shift tensor. The Hamiltonian, Ĥ H2O, for a dipolar coupled proton pair of equivalent nuclei, such as those in a water molecule or H2Oprotons, is +

Ĥ H2O = ωH2O(I1̂ z + I2̂ z) + ωD(3I1̂ zI2̂ z − I1̂ ·I2̂ )

2

3 cos(αH2O − Φ) + (1 − cos2(βH O))(1 − cos2(Θ)) cos(2 2 2 (αH2O − Φ)) (12)

(5)

where ωH2O is the H2O-proton chemical shift frequency and ωD is the dipolar coupling frequency. The chemical shift frequency is defined as ωH2O = ΔωH2O,iso + ωH2O,csa

(6) Figure 2. (a) Angles of relevance for H2O-protons in a magnetic field Bo. (b) Relative orientation of the water molecule rotation axis and ZPAS.

The term ΔωH2O,iso is the offset of the H2O-proton isotropic frequency relative to the RF carrier frequency in the rotating frame. The H2O-proton chemical shift frequency anisotropy is ωH2O,csa =

δ H 2O 2

It will prove to be useful to calculate the effect of motion on the H2 O line shape for the special case where the transformation matrix relating the H2O-proton dipolar and chemical shift PAS’s is the identity matrix; eq 12 then simplifies to 3 cos2(βD) − 1 = 3 cos2(βH2O) − 1. Figure 2b shows the coordinate system and angles used to define the rotational motion of a water molecule. If the axis of rotation, Zrot, bisecting the two O−H bonds, is perpendicular to ZPAS and if ηH2O ≅ 0, then the classical model for rotation37 yields after averaging over αrot 1 ⟨3 cos2 (βH O) − 1⟩ave = − (3 cos2(βrot ) − 1) 2 (13) 2 Therefore, the proton spectrum for one rotating H2O molecule consists of two signals at

(3 cos2(βH O) − 1 2

− ηH Osin 2(βH O)cos(2αH2O)) 2

2

(7)

where δH2O is the H2O-proton chemical shift anisotropy, ηH2O is the H2O-proton chemical shift asymmetry parameter, and (αH2O, βH2O) are the azimuthal and polar angles, respectively, defining the orientation of the external magnetic field Bo in the PAS of the H2O-proton chemical shift tensor. The dipolar coupling frequency is defined as ωD =

ℏγH2 3 rHH

(1 − 3 cos2(βD))

(8)

where ℏ is Planck’s constant divided by 2π, γH is the proton gyromagnetic ratio, rHH is the distance between the two protons, and βD is the polar angle defining the orientation of the external magnetic field Bo in the PAS of the dipolar tensor. The time evolution of the H2O-proton magnetization can be determined by calculating the density operator at time t, ρ̂H2O ̂ + I2x ̂ , from35 (t), with an initial condition ρ̂H2O (0) = I1x ̂ ̂ ρ̂H O (t ) = e−iHH2Ot (I1̂ x + I2̂ x) e iHH2Ot 2

ΔωH2O,iso −

(9)

(10)

and therefore the proton spectrum for one H2O molecule consists of two signals at ω H 2O

3 ± ωD 2

(14)

which shows that both the proton chemical shift anisotropy and proton−proton dipolar coupling constant of H2O-protons are scaled by a factor of −1/2. The two-pulse sequence shown in Figure 3a can be used to differentiate Hamiltonians that are either linear or bilinear in the spin operators, which are well known to have maximum echo signals at 2te for ϕx = π and π/2, respectively.35 In some cases, it is possible to extract structural information from twopulse sequence signal intensity data obtained as a function of ϕx.38−40 For example, for a single H+-proton, the density matrix ρ̂H (2te) is for ρ̂H (0) = Ix̂ 38

It is shown in the Supporting Information (SI) that the time domain signal FH2O(t) is FH2O(t ) = e i(ωH2O − (3/2(ωD)))t + e i(ωH2O + (3/2(ωD)))t

1 ijj δ H2O 3 ℏγ 2 yzz ∓ jj z(3 cos2(βrot ) − 1) 2 jk 2 2 r 3 zz{

̂

̂

̂

̂

̂

̂

ρ̂H (2te) = e−iHHte e iϕxIx e−iHHte I x̂ e iHHte e−iϕxIx e iHHte

(15)

It can be shown (SI) that the normalized, real part of the echo signal for a single H+-proton at 2te is

(11) C


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Figure 3. (a) Two-pulse sequence. (b) 1H{31P} rotational-echo double-resonance (REDOR) pulse sequence.

fH (2te) = (1 + cos(ϕx)) cos2(ωHte) − cos(ϕx)

Under MAS, the H+-proton and H2O-proton Hamiltonians become time-dependent, Ĥ H(t) and Ĥ H2O(t), respectively, and can be written as

(16)

For an isotropic distribution of H+-protons in an amorphous or powdered sample, the signal is calculated from the powder average ⟨fH (2te)⟩ave =

(1 + cos(ϕx))

2π

π

H

H

= ΔωH2O,iso(I1̂ z + I2̂ z) + ωH2O,csa(t )(I1̂ z + I2̂ z) + ωD(t )(3I1̂ zI2̂ z − I1̂ ·I2̂ )

ωi(t ) = C1i cos(γi + ωR t ) + C2i cos(2γi + 2ωR t ) + S1i sin(γi + ωR t ) + S2i sin(2γi + 2ωR t )

1 fH O (2te) = (1 − cos2(ϕx))(2 − cos(3ωDte) + 2 cos(2ωH2Ote) 2 4 1 − cos(2ωH2Ote) cos(3ωDte)) + (1 − cos(ϕx))2 cos(3ωDte) 4 1 2 + (1 + cos(ϕx)) cos(2ωH2Ote) cos(3ωDte) (18) 4

1 4π

∫α

2π H2O = 0

dα H 2 O

sin(βH O)fH O (2te) 2

2

∫β

π

H2O = 0

(22)

The angles γi belong to the set of Euler angles that define the orientation of the PAS of interaction i relative to the RF frame. As will become clear, the exact forms of C1i, C2i, S1i, and S2i are not of interest in the context of this work and will not be discussed in any detail. The average Hamiltonian is calculated by integrating Ĥ H(t) and Ĥ H2O(t) over the appropriate time interval, which for the two-pulse sequence of Figure 3a with te = TR is simply one rotor period TR. In general, the average of any Hamiltonian over one rotor period is given by42−44

For an isotropic distribution of H2O-protons in an amorphous or powdered sample, the signal is calculated from the powder average

2

(21)

The time-dependent frequencies, ωi(t) (i = H, H2O, and D), are all of the form41

(17)

The normalized, real part of the proton signal for a two-pulse sequence for one H2O molecule at 2te is (see SI)

⟨fH O (2te)⟩ave =

(20)

Ĥ H2O(t ) = ωH2O(t )(I1̂ z + I2̂ z) + ωD(t )(3I1̂ zI2̂ z − I1̂ ·I2̂ )

∫α =0 dαH ∫β =0 dβH sin(βH)

ÅÄÅi l o δH o 2Å ÅÅjjΔω cos (3 cos2(βH) − 1 − ηH sin 2(βH) m ÅÅj H,iso + o o Å 2 k Å Ç n É o y ÑÑÑ| cos(2αH))zzzteÑÑÑÑo } o − cos(ϕx) Ñ { ÑÖo ~ 4π

ĤH(t ) = ωH(t )Iẑ = ΔωH,isoIẑ + ωH,csa(t )Iẑ

dβH O

(0)

(1)

Ĥ ̅ = Ĥ ̅ + Ĥ ̅ + higher order terms TR TR 1 i = Ĥ (t ) dt − dt 2 TR 0 2TR 0 + higher order terms

2

∫

(19)

It is also possible to obtain echo-signal maximum amplitudes at ϕx = π/2 from three or more dipolar coupled protons depending on the magnitude of the internuclear dipolar interactions and the time te.35 This may lead to ambiguities in structural assignments for various resonance lines in 1H nonspinning (NS) two-pulse sequence NMR spectra. In some cases, it may be possible to differentiate signals due to two coupled protons, such as those in H2O, and, for example, three protons, such as those in H3O+, using a two-pulse sequence with magic-angle spinning (MAS) of the sample. Under MAS, the angles αH, βH, αH2O, and βH2O and therefore ωH, ωH2O, and ωD become time-dependent but analysis using average Hamiltonian theory simplifies the task of determining the effect of MAS on the two-pulse sequence signal at 2te when te = TR, the MAS rotor period.

∫

∫0

t2

dt1[Ĥ (t 2), Ĥ (t1)] (23)

Because [Ĥ H(t2), Ĥ H(t1)] = 0, [Ĥ H2O(t2), Ĥ H2O(t1)] = 0, and all higher-order terms on the right-hand side of eq 23 are also functions of these commutators, the average Hamiltonians for Ĥ H(t) and Ĥ H2O(t) are equal to the zeroth-order term of eq 23. The integral over one rotor period for each trigonometric function of eq 22 is zero; therefore ̅ = ΔωH,isoIẑ ĤH

(24)

Ĥ ̅ H2O = ΔωH2O,iso(I1̂ z + I2̂ z)

(25)

The normalized real parts of the signals from a two-pulse sequence with MAS for H+-protons and H2O-protons calculated using their average Hamiltonians at time 2TR are D



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fH̅ (2TR ) = (1 + cos(ϕx)) cos2(ΔωH,isoTR ) − cos(ϕx)

fH̅ O (2TR ) = (1 + cos(ϕx)) cos2(ΔωH2O,isoTR ) − cos(ϕx) 2

(27)

Eqs 26 and 27 show that the signal for an MAS two-pulse experiment recorded on-resonance for any ϕx for both H+protons and H2O-protons is an MAS-averaged, unattenuated resonance line. For three or more coupled protons, analysis using average Hamiltonian theory becomes much more complicated because the commutators on the right-hand side of eq 23 do not commute and higher-order terms must be included. As will be shown, it is more expedient to use simulation programs such as SIMPSON45 to determine the effect of MAS on the signal from the two-pulse experiment for three or more coupled protons. Rotational-echo double-resonance (REDOR) NMR experiments can be used to determine internuclear distances in HPA’s and salt-substituted HPA’s.46,47 The REDOR pulse sequence employed in this work is shown in Figure 3b.48 Goetz and Schaefer have provided theoretical REDOR expressions to calculate the REDOR fraction, ΔS = (So − S)/So, for a number of cases.49 So is the signal without dephasing π-pulses, and S is the signal with dephasing π-pulses. For an isolated, static I−S spin pair, the REDOR fraction is given by49 1 4π

2π

π

∫α =0 dαIS ∫β =0 dβIS sin(βIS)

ÄÅ ÉÑ ÅÅ 2 ÑÑ Å ωDNcTR sin(2βIS) sin(αIS)ÑÑÑÑ cosÅÅÅ ÅÅÇ π ÑÑÖ IS

EXPERIMENTAL SECTION

Sample Preparation: Group II Salts of 12-Tungstophosphorice Acid. The 12-tungstophosphoric acid used to synthesize the group II salts was obtained from Aldrich and dried in air at 393 K for at least 2 weeks before use. The 12tungstophosphoric acid group II salts were obtained by simple substitution by mixing stoichiometric amounts of a group II cation chloride and 12-tungstophosphoric acid in water according to eq 1. Each group II salt was crystallized and allowed to dry at 393 K in air for 2 weeks and subsequently stored in the oven at 393 K prior to use. For NMR spectroscopy, the samples were transferred rapidly from the oven to a MAS rotor. While spinning the sample at an MAS speed of 10.0 kHz in the NMR probe, the sample was heated to 393 K for 0.5 h to eliminate any atmospheric water that may have condensed onto the sample during the sample transfer process. The sample temperature of the probe was then changed to the temperature of interest to record NMR spectra. Thus, only structural water of the limiting hydrated form of the group II salts of 12-tungstophosphoric acid was present while recording NMR spectra. Sample Preparation: Quasi-Model Compounds. The completely dehydrated form of 12-tungstophosphoric acid, H3PW12O40 or HPW, and its sodium-substituted limiting hydrated form, H0.5Na2.5PW12O40·4H2O or NaHPW, have been studied in sufficient detail such that for the purposes of the NMR experiments described here they may be considered to be model compounds.46,47,50−56 HPW was synthesized from the as-received 12-tungstophosphoric acid by heating in an oven at 500 K in air for 48 h. NaHPW (Fluka, lot 90600) was dried in air at 383 K for at least 17 days. Both HPW and NaHPW were stored in an oven at 393 K prior to use and then transferred to an MAS rotor and heated in the NMR probe as described above for the group II salts before recording NMR spectra at the temperature of interest. NMR Spectroscopy. All NMR spectra were recorded on a two-channel Chemagnetics CMX Infinity 400 NMR spectrometer operating at 400.0 and 161.8 MHz for 1H and 31P, respectively. With one exception (see below), all nonspinning (NS) and MAS 1 H spectra were obtained using a Chemagnetics 5 mm double-resonance, MAS probe equipped with a Pencil spinning module. The spectrometer was equipped with Chemagnetics solid-state variable temperature and MAS speed controllers. The equivalent single-pulse excitation 1H NS NMR spectra were recorded using the DEPTH pulse sequence57 to suppress 1 H probe background signals. The 90° pulse widths and relaxation delays were 4.5−4.8 μs and 5 s, respectively. The temperature was 298 K. The 1H NS NMR spectrum of NaHPW was recorded with a home-built probe using 3.70 μs 90° pulses and 5 s relaxation delays.47 The 1H MAS NMR spectra were also recorded using the DEPTH pulse sequence.57 The 90° pulse widths and relaxation delays were 4.5−5.0 μs and 5 s, respectively. The MAS speed was 10.0 kHz. The temperature was 310 K. The two-pulse sequence NMR experiment (Figure 3a) for both the 1H NS and MAS experiments employed a 50 kHz 1H RF field corresponding to 90° pulse lengths of 5.0 μs. For the NS experiments, te = 40 μs. In the MAS experiments, the MAS speed was 10.0 kHz and rotor synchronization was achieved by setting TR = 100 μs. The two-pulse sequence 1H NS NMR spectra were recorded as a function of ϕx (9° increments) at a

(26)

ΔS = 1 −

Article

IS

(28) γγ

The heteronuclear dipolar coupling is ωD = ℏ rI3S , where γI and IS

γS are the gyromagnetic ratios of the I and S spins, respectively, and rIS is the distance between the I and S spins. Nc is the number of rotor cycles and (αIS, βIS) are the azimuthal and polar angles, respectively, that describe the orientation of the I−S internuclear vector relative to the rotor axis. For a single, static I-spin coupled to N different, static S-spins, the REDOR fraction is49 ÄÅ N ÅÅ 2 i 1 ΔS = 1 − ωDNcTR sin(2βISi ) dΩ ∏ cosÅÅÅÅ 2 ÅÅÇ π 8π i=1 ÉÑ Ñ i Ñ sin(αIS)ÑÑÑÑ ÑÑÖ (29)

∫

where dΩ is the element of solid angle for powder averaging. For a single I-spin in relative motion with N S-spins, the REDOR fraction is49 ÄÅ N ÅÅ n Å 1 2 2 j ΔS = 1 − ωDNcTR dΩ ∏ cos i ÅÅÅÅ ∑ 2 Å 8π ÅÅÅ j = 1 n π i=1 Ç ÉÑ ÑÑ j Ñ j sin(2βIS) sin(αIS)ÑÑÑÑ ÑÑ ÑÑÖ (30)

∫

There is one cosine term for each of the N S-spins, and n is the number of steps that the S-spin moves through in its trajectory in some time interval. E


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Figure 4. 1H NS NMR spectra (400 MHz) of group II salts of 12-tungstophosphoric acid obtained at 298 K.

temperature of 298 K, and the two-pulse 1H MAS NMR spectra were obtained for ϕx = 180° at a temperature of 310 K. The 1H{31P} REDOR spectra, Figure 3b, were recorded using 1H 90° pulses of 5 μs, 31P 180° pulses of 5.8−7.2 μs, and relaxation delays of 5 s. The MAS speed was 10.0 kHz, and TR was 100 μs. The temperature was 310 K. The 1H chemical shift reference was obtained by sample substitution of H2O(l) that was assigned a chemical shift value of 4.8 ppm at 298 K. Therefore, the chemical shifts reported here for 1H are relative to tetramethylsilane (0.0 ppm). Calibration of the temperature at the sample position has been described.58 Simulations and Computational Methods. Simulations of 1H NS and MAS NMR spectra were performed using SIMPSON.45 Parameters used in particular simulations are provided as needed. Various Keggin anion dimer (KA2−6) structures were generated with ORTEP-3.59 The fractional coordinates used with ORTEP-3 for the KA2−6 structures of HPW and NaHPW (both cubic Pn3̅m) were those of H3PW12O40·6H2O.29 The lattice parameters, a, were obtained from neutron diffraction (HPW)29 and X-ray diffraction (NaHPW).47 For the group II salts, MHPW (monoclinic P21/c, Z = 4, a = 986.8 pm, b = 2198.0 pm, c = 1928.9 pm, βac = 90.63°),30 the fractional coordinates used with ORTEP-3 were calculated from the transformation60 ij 1 jj jj jj a jj x ij yz jjjj jj y zz jj jj zz = jj 0 jj zz jj k z { jjjj jj jj 0 jj j k

yz zz zz a 1 − cos2(βac) zzz zzi X y zzzjj zz zzjj zz 1 zzjjY zz 0 zzjjj zzz b zz Z zzk { zz 1 zz 0 z 2 c 1 − cos (βac) zz { 0

coordinates of the structures for which calculations were performed are provided in the Supporting Information. Avogadro68,69 was used to analyze some results and generate figures obtained from the density functional theory calculations.

■

RESULTS AND DISCUSSION An overview of the experimental results is provided before discussion of the results for each of the individual salts and model compounds. Figure 4 shows the 1H NS NMR spectra of the group II salts of 12-tungstophosphoric acid recorded at 298 K. With the exception of the SrHPW salt, all spectra can be simulated with one broad and one narrow resonance line; the line fitting parameters are listed in Table 1, and the relative intensities should only be considered to be qualitative because of the overlap of the two spectral lines. The broadest lines for the BeHPW, CaHPW, and BaHPW salts are all about 20 kHz, whereas those for the MgHPW and SrHPW salts are greater than 30 kHz. Figure 5 shows 1H MAS NMR spectra of the group II salts of HPW. Figure 5a displays both the isotropic region of the spectra and the associated spinning sidebands. Figure 5b shows only the isotropic region of the spectra. All spectra are similar in appearance in that one peak or set of overlapping peaks dominates the spectral intensity. With the exception of the BeHPW salt, this peak has a chemical shift in the range of ∼4− 6 ppm; the most intense feature for BeHPW has a peak position near 7 ppm. In addition, all spectra except for the BeHPW spectrum show lower-intensity resonance lines in the ∼6−10 ppm range. Peak positions and their relative intensities are provided in Table 1. Figure 6 shows 1H NS NMR relative intensities versus the refocusing pulse angle ϕx for the two-pulse sequence of Figure 3a of the group II salts of HPW. All salts show a maximum intensity at ϕx ∼ 90° except for BeHPW where the maximum relative intensity occurs at ϕx ∼ 108°. These results suggest that the signal intensity is dominated by a Hamiltonian that is bilinear in the spin operators.35 Figure 7 shows 1H MAS NMR spectra for the group II salts of HPW for the two-pulse sequence of Figure 3a with ϕx = 180°. The spectra were recorded by adjusting the spectrometer so that the most intense resonance line of Figure 5 was onresonance. In addition, only zeroth-order phase corrections were applied to each spectrum because the spinning sidebands for this choice of phase correction have a characteristic appearance for a particular proton type (see below). All of the spectra in Figure 7 have the same general appearance. Quasi-Model Compounds. Anhydrous HPW, H3PW12O40. The quasi-model compound anhydrous HPW contains only H+-protons, and although it has been extensively stud-

−cos(βac)

(31)

where (x, y, z) are the fractional coordinates of the MHPW and (X, Y, Z) are the Cartesian coordinates of any KA−3 monomer obtained from the HPW system. The single point energy (E) of a number of KA2−6 structures and KA2−6 structures containing either H+-protons or H2Oprotons was calculated using density functional theory methods using the CP2K package.61 All calculations were performed using the Perdew, Burke, and Ernzerhof functional62,63 and molecularly optimized double-ζ Gaussian basis sets.64 The core electrons for each atom were modeled with pseudopotentials65−67 where H, P, O, and W have 1, 5, 6, and 14 valence electrons, respectively. Because of the large number of calculations that were performed, the target accuracy for the self-consistent field convergence was defined as 0.3 eV. The F


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rPP for a KA−3 at each of two adjacent corners of one simple

Table 1. 1H NS and MAS NMR Spectral Parameters for the LHF Group II Salts of 12-Tungstophosphoric Acid NS parametersa

MAS parametersb

line width (kHz)

relative area

δiso (ppm)

relative area

proton typec,d

BeHPW

5.4 18.1

0.66 0.34

6.7 3.0

MgHPW

13.4 33.6

0.75 0.25

9.2 5.3 4.5

CaHPW

2.7 22.1

0.32 0.68

9.3 8.1 6.7 5.4 4.5 3.8

SrHPW

5.4 45e

0.86 0.14

8.9 8.7 8.4 8.1 7.9 7.5 6.6 6.0 5.1 4.1

BaHPW

3.8 22.1

0.38 0.62

8.8 6.7 6.0 5.4 4.5

0.84 0.03 0.13 0.07 0.25 0.46 0.22 0.03 0.02 0.04 0.12 0.38 0.33 0.08 0.02 0.01 0.03 0.07 0.05 0.02 0.01 0.03 0.02 0.41 0.03 0.30 0.22 0.02 0.01 0.02 0.49 0.24

H+ + H2O H2O SSB(H+,H2O) H+ H2O H2O SSB(H2O) H+ H+ H+ H2O H2O H2O SSB(H2O) H+ H+ H+ H+ H+ H+ H2O H2O H2O H2O SSB(H+) SSB(H2O) H+ H+ H2O H2O H2O SSB(H2O)

salt

(3)1/2

cubic structure and r′PP = 2 rPP for a KA−3 at both the center and the corner of the two interpenetrating simple cubic structures. A model where the H+-protons can hop between two different sites is also shown in Figure 10a. For a single dipolar 1H−31P coupling (denoted H+P), only the distance rHP1, for example, needs to be considered and the experimental REDOR data is fit to eq 28 by adjusting rHP1 until the goodness-of-fit parameter χ2 is minimized. For two static dipolar 1H−31P couplings, only site 1 (denoted static H+P2) needs to be considered, and for any value of rPP or r′PP, both rHP1 and rHP2 are adjusted to provide the best fit of eq 29 to the experimental data with the constraint rHP1 + rHP2 ≥ rPP (or r′PP). For two 1H−31P dipolar couplings where the H+-proton hops between sites 1 and 2 (denoted hopping H+P2), rHP1 and rHP2 are adjusted for a given value of rPP or r′PP to obtain the best fit of eq 30 to the experimental data with the constraint rHP1 + rHP2 ≥ rPP (or r′PP). H3PW12O40·6H2O has a cell parameter a = 1215 pm that has been found to be the same for anhydrous HPW.71 Therefore, rPP = 1215 pm and r′PP = 1052 pm were used to fit the 1H{31P} REDOR data. The results of the analysis of the 1H{31P} REDOR NMR data as shown in Figure 9 are provided in Table S1 (SI). Figure 9 and Table S1 (SI) clearly show that the static H+P2 model gives the best fit to the experimental data for both rPP and r′PP because of the inclusion of a second 1H−31P dipolar coupling. However, it is not possible to determine the pair of 31P nuclei that the H+protons are coupled to on the basis of this analysis alone. To further refine the H+-proton structure, the change in energy, ΔEH, for the reaction H+ + KA −2 6 → HKA −2 5

(32)

for selected HKA2−5 structures was calculated. Because of the crystal symmetry of anhydrous HPW, the orientation of the central PO4 tetrahedron can be used to describe the relative orientation of each KA−3 in a KA2−6 dimer.28 For the rPP = 1215 pm dimer, an edge of each PO4 tetrahedron points toward the edge of the second one, which is rotated by 90° relative to the first, with the two P atoms and two Oa atoms all lying in the same plane; this is denoted the edge dimer. For the r′PP = 1052 pm dimer, there are two relative orientations of the two PO4 tetrahedrons. One has an apex of one PO4 pointing at the apex of the second PO4; this is denoted the nose dimer. The other r′PP = 1052 pm dimer has the base of one PO4 tetrahedron pointing at the base of the second one, which is rotated 60° relative to the first; this is denoted the base dimer. The 1H{31P} REDOR analysis yields ∠1HPP = 17° for the nose and base dimers (Table S1, SI). This means the position of the H+-proton is restricted to lie on the circumference of the circle that forms the base of a right cone where the radius of this circle is given by rHP1 sin(∠1HPP). In a coordinate system where the P−P internuclear vector is the z axis ∠1HPP is the polar angle of the P−H internuclear vector. The azimuthal angle of the P−H internuclear vector, ϕPH, is the relevant parameter to locate the position of the H+-proton on the circumference of the circle described above. Because ∠1HPP = 0° for the edge dimer, the H+-proton lies on the line connecting the two P atoms of the edge dimer. Figure 11 shows ΔEH calculated as a function of ϕPH with an angular resolution of 10°. Note that ΔEH was calculated for each P atom chosen as the coordinate system origin, that is, the P atom of each Keggin anion monomer of the dimer, which are

a

Line widths and relative areas from deconvolution analysis of spectra. bRelative areas from deconvolution analysis of spectra. cSee the text for structural assignments. dSSB = spinning sidebands, SSB(H2O) = H2O isotropic peak spinning sidebands, SSB(H+) = H+ isotropic peak spinning sidebands, SSB(H+,H2O) = H+ isotropic peak plus H2O isotropic peak spinning sidebands. eSeparation of the horns of the Pake pattern.

ied,46,50−56 new results and methods are presented here in part to provide the basis for applying these new procedures to the structural refinement of the proton structures in the MHPW’s. Figure 8a shows the 1H NS NMR spectrum of anhydrous HPW at 298 K as well as the simulation obtained with SIMPSON.45 A good fit to the experimental spectrum was obtained for δH = −10 ppm and ηH = 0.8. Figure 8b shows that a good fit of the two-pulse sequence data using eq 17 is obtained for these values of δH and ηH. The 1H MAS NMR spectrum of anhydrous HPW shows a single resonance line at 9.3 ppm (Figure S1, SI), which indicates that the H+-protons are highly acidic.70 The structure of the H+-protons in HPW can be refined with the aid of the results and analysis of the 1H{31P} REDOR NMR experiment shown in Figure 9. The REDOR analysis using eqs 28−30 is based on the PHP triangle model that has its parameters defined in Figure 10a. Figure 1b indicates that two different P−P internuclear distances must be considered; G


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Figure 5. 1H MAS NMR spectra (400 MHz) of group II salts of 12-tungstophosphoric acid obtained at 310 K. (a) Large-scale display showing both isotropic peaks and spinning sidebands (*). (b) Expanded-scale display showing the isotropic region.

denoted KA1 and KA2. Addition of an H+-proton stabilizes all HKA2−5 structures considered. It is instructive to discuss in some detail the structure of the most stable HKA2−5, which is the base dimer (P of KA1 at the origin) with ϕPH = 209°. Figure 12 depicts this dimer, and Table 2 provides relevant structural data. The simple view is that the H+-proton is hydrogen-bonded to an Od oxygen of one of the KA−3 of the dimer with an Od(65,KA1)−H+ internuclear distance of 151 pm. As indicated in Figure 12, a more complete description is one where the H+-proton is enclathrated by a cage formed by six oxygen atoms of the two KA−3’s of HKA2−5. The six Oi−H+ distances have a range of 151−296 pm, which are strong to moderately strong hydrogen bond distances.72−74 There are also five Oi−H+ distances in the range 349−396 pm that are considered to be weak hydrogen bond distances.74 Notably, the results presented here show that the H+-proton resides in the space between a KA−3 at the center and a KA−3 at the corner of the two interpenetrating simple cubic structures of HPW. The majority of the ΔEH for the various sites considered lie in an energy band of about 2 eV with differences of only a few tenths of an electronvolt in the ΔEH values of the various

Figure 6. Plot of 1H NS NMR relative intensity vs ϕx for the twopulse sequence of Figure 3a for the group II salts of 12tungstophosphoric acid.

Figure 7. Two-pulse sequence MAS NMR spectra (400 MHz) for the group II salts of 12-tungstophosphoric acid recorded at 310 K using the twopulse sequence of Figure 3a with ϕx = 180°. H


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Figure 8. (a) 1H NS spectrum (400 MHz, 298 K) and simulation of HPW. (b) Plot of the two-pulse sequence relative intensity vs ϕx for HPW at 298 K.

Figure 9. Plot of the 1H{31P} REDOR fraction vs NcTR for H+-protons of HPW and H2O-protons of NaHPW at 310 K and 10.0 kHz MAS.

Figure 10. (a) Schematic diagram of the PHP triangle model used to calculate the REDOR fraction for an 1H nucleus dipolar coupled to one or two 31P nuclei. (b) Schematic diagram of the H2P2 isosceles trapezoid model used to calculate the REDOR fraction for two 1H nuclei dipolar coupled to two 31P nuclei.

HKA2−5 structures, similar to the hydrogen bond energy of about 0.3 eV of ice.75 Therefore, HPW fulfills one of the criteria for a good proton conductor, that is, it has a number of proton sites with similar hydrogen-bonding energies.20 Limiting Hydrated Form of NaHPW, Na2.5H0.5PW12O40· 4H2O. The LHF of the NaHPW material has the interpenetrating cubic structure29 with lattice parameter a = 1197 pm, Figure 1b, and contains 4 H2O molecules and 0.5 H+protons.47 Figure 13 shows the 1H MAS NMR spectrum of NaHPW at 310 K, whereas Figure S2 (SI) shows the 1H NS NMR spectrum and Figure S3 (SI) shows the 1H NS NMR

two-pulse sequence results of NaHPW at 298 K. The neutron diffraction results obtained for H3PW12O40·6H2O show that two protons of an H5O2+ molecule and two P atoms of two KA−3’s approximately form an isosceles trapezoid, Figure 1c. This H2P2 isosceles trapezoid model is used to analyze 1H{31P} REDOR NMR data of H2O-protons in this work, and its parameters are defined in Figure 10b. For the case where the P−P internuclear distance is rPP, it is readily shown that rHP2 = (rHHrPP + r2HP1)1/2. Using rHH = 167 pm (see the two-pulse sequence 1H NS NMR results below) and the H2O H−O internuclear distance rHO = 95.1 pm29 along with the constraint I


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Figure 11. Plot of ΔEH vs ϕPH for various HKA2−5 dimers of HPW. HPW legendnose dimer: red bullet with hyphen, P of KA1 at origin; gray bullet with hyphen, P of KA2 at origin. Base dimer: black bullet with hyphen, P of KA1 at origin; yellow bullet with hyphen, P of KA2 at origin. Edge dimer: blue bullet with hyphen, P of KA1 at origin; green bullet with hyphen, P of KA2 at origin. Plot of ΔEH2O vs ϕPH for various KA2−6· H2O’s of NaHPW. NaHPW legendred bullet with hyphen, nose dimer; black bullet with hyphen, base dimer; dark blue bullet with hyphen, edge dimer.

Figure 12. Ball-and-stick models of most stable structures of HKA2−5 for HPW and SrHPW and KA2−6·H2O for NaHPW and SrHPW. Values of ΔEH, ΔEH2O, and ϕPH are provided in Tables 2 and 3. 1

and r′PP (Table S2, SI), indicating that the H2O molecules are rotating in NaHPW at 310 K. Further evidence of this motional assignment is provided by a comparison of the experimental 1H NS NMR spectrum with SIMPSON45 simulations shown in Figure S2 (SI). The peak at 0 ppm in the experimental 1H NS spectrum has previously been assigned to H+-protons.47 The static H2O simulation used the parameters δH2O = −20.6 ppm, ηH2O = 1.0, and ωD = 26 kHz (see two-pulse sequence 1H NS NMR results below), whereas the rotating H2O simulation used these NaHPW values of δH2O and ωD scaled by a factor of −1/2, eq 14. The horns of the

rHP1 ≥ 2 (rPP − rHH), eqs 29 and 30 were used to fit the experimental 1H{31P} REDOR NMR data for static H2O H2P2 and rotating H2O H2P2 models. The same analysis of the 1 H{31P} REDOR NMR results follows for a P−P internuclear distance of r′PP. The best fit parameters for both the static H2O and rotating H2O models are provided in Table S2, and the experimental data and theoretical curves are shown in Figure 9. Figure 9 indicates that both the static and rotating H2O models give reasonable fits of the 1H{31P} REDOR NMR data. However, the χ2 value for the rotating H2O model is about 3 times smaller than that for the static H2O model for both rPP J


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The Journal of Physical Chemistry C Table 2. ΔEH and Structural Parameters for Most Stable HKA2−5 Structures material

dimer b,c

ϕPHa

Oi(j,KAk)

rHO (pm)

ΔEH (eV)

209

Od(65,KA1) Ob(38,KA1) Ob(52,KA1) Ob(63,KA2) Od(42,KA2) Od(69,KA2) Od(35,KA2) Ob(24,KA2) Oc(25,KA2) Od(31,KA1) Oc(76,KA2) Ob(72,KA2) Ob(53,KA2) Oc(54,KA2) Od(78,KA1) Od(35,KA2) Ob(24,KA2) Oc(25,KA2) Od(31,KA1)

151 251 227 263 296 257 270 321 370 326 327 353 375 385 369 248 339 359 325

−17.2

HPW

base

MgHPW

static 1165d

338

SrHPW

static 1165d

222

BaHPW

static 1165d

28

rHH and rHO for the rotating H2O molecule used were 167 pm (see two-pulse sequence 1H NMR results below) and 95.1 pm,29 respectively. The results of the ΔEH2O calculations are shown in Figure 11. The symmetry of the various KA−6 2 ·H2O structures is most evident for the nose and base dimers where the ΔEH2O values show a sinusoidal-type oscillation as a function of ϕPH. Because of the arbitrary choice of the ϕPH values, some nose and base dimer structures considered are very unstable because of the physically unrealistic nature of the structures; for example, the distance between H2O-protons and oxygen atoms of the Keggin anion is much too small in some structures. All KA−6 2 ·H2O edge dimer structures are stable, and the ΔEH2O values show the oscillatory behavior as a function of ϕPH, with those equal to 26, 116, 206, and 296° at least 1 eV more stable than all other values and with their respective ΔEH2O ∼ −17 eV. The most stable structure considered is shown in Figure 12 and shows that each of the H2O-protons is hydrogen-bonded to two oxygen atoms of each KA−3. The strong and moderately strong72−74 hydrogen bond distances of this structure are provided in Table 3. Each H2O-proton also has two Oi−H distances in the weak hydrogen bond range.74 This structure is more detailed than that described for the H2O-proton hydrogen-bonding arrangement in H3PW12O40· 6H2O where the H2O-protons are hydrogen-bonded to Od oxygen atoms only. The H2O-protons for the ϕPH = 26, 116, and 206° KA−6 2 ·H2O are similarly hydrogen-bonded to pairs of oxygen atoms of the two different KA−3’s. Assignment of Proton Structures in MHPW’s to Resonance Line Types. Two of the criteria for structural assignment of 1H NMR resonance lines under MAS conditions are that H+-protons have minimal spinning sideband intensity, whereas resonance lines of H2O-protons can have large spinning sideband arrays.31 Clusters of many 1H nuclei can also have large spinning sideband arrays with MAS,76 so the possibility that the MHPW’s contain dipolar coupled clusters of three or more 1H nuclei was investigated by comparing a 1H MAS-only NMR spectrum of NaHPW with the two-pulse sequence 1H MAS NMR spectrum of NaHPW as well as two-pulse sequence 1H MAS NMR SIMPSON simulations45 for H2O and H3O+. The results are shown in Figure 13. As predicted by average Hamiltonian theory, eq 27, the two-pulse sequence spectrum and the MAS-only 1H NMR spectra are essentially the same. The SIMPSON45 simulation used chemical shift

−16.7

−16.6

−16.7

a

Degree. br′PP = 1052 pm. cP of KA1 at origin of coordinate system. P of KA2 at origin of coordinate system.

d

Pake powder pattern for the rotating H2O molecule simulation more closely align with those of the experimental spectrum, indicating that the H2O molecules are rotating in NaHPW at 310 K, in agreement with the conclusion of the 1H{31P} REDOR NMR analysis. As was the case for anhydrous HPW, the 1H{31P} REDOR analysis of NaHPW does not uniquely determine the structure of the dimer containing H2O but does provide the H−P internuclear distances and constrains each proton of the H2O molecule to reside on the circumference of the circle at the base of right cone with the radius of the circle equal to rHPi sin(∠HiPP). The structure of the H2P2 isosceles trapezoid is therefore further refined by considering the change in energy, ΔEH2O, of the reaction H 2O + KA −2 6 → KA −2 6·H 2O

(33)

for selected structures. To simplify the DFT ΔE H 2 O calculations, the two P atoms of KA2−6 and all atoms of H2O were constrained to lie in the same plane. The values of

Figure 13. DEPTH and two-pulse sequence 1H MAS NMR spectra of NaHPW and simulations of H2O and H3O+ for the two-pulse sequence. MAS speed of 10.0 kHz. K


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The Journal of Physical Chemistry C Table 3. ΔEH2O and Structural Parameters for Most Stable KA2−6·H2O Structures material

dimera

ϕPHb

NaHPWc

edged

296

MgHPWc

1400

38

SrHPWe

1165

281

BaHPWc

1400

48

Oi(j,KA1)···HOwH and HOwH···Ok(m,KA2)

rHOj (pm)

Oc(25,KA1)···HOwH Od(44,KA1)···HOwH HOwH···Ob(31,KA2) HOwH···Od(39,KA2) Od(59,KA1)···HOwH Ob(37,KA1)···HOwH HOwH···Od(27,KA2) HOwH···Oc(52,KA2) HOwH···Oc(41,KA2) Oc(34,KA1)···HOwH Od(55,KA1)···HOwH HOwH···Ob(38,KA2) HOwH···Od(9,KA2) Od(10,KA1)···HOwH Ob(37,KA1)···HOwH Od(59,KA1)···HOwH HOwH···Od(27,KA2) HOwH···Oc(41,KA2) HOwH···Oc(52,KA2)

202 249 244 231 237 292 187 275 317 296 282 314 311 314 299 308 180 297 330

nuclei are not present and will therefore no longer be considered. Chemical Shift and Dipolar Tensor Parameters of H2OProtons in the MHPW’s. The 1H NS NMR two-pulse sequence results for the MHPW’s are shown in Figure 6. Because only H+-protons and H2O-protons are present in the MHPW’s, the two-pulse sequence data can be fit to the sum of eqs 17 and 19 weighted to the number of H+-protons and H2O-protons present, respectively, to obtain the 1H chemical shift and dipolar tensor information for H2O-protons. For each MHPW data set, the H+-proton δH and ηH values of anhydrous HPW were used in eq 17. The values of ΔωH,iso were determined from the chemical shift separation of the centersof-gravity of the isotropic resonance intensity of the H+protons and H2O-protons observed in the 1H MAS NMR spectra combined with the resonance offset (ΔωH2O,iso) observed in the 1H NS NMR two-pulse sequence spectra recorded at ϕx = 90°. Plots of the fit of the 1H NS NMR twopulse sequence data for each MHPW are shown in Figure S3 (SI), and the parameters obtained from the fit are provided in Table 4. The values of δH2O range from −13.8 to −25.6 ppm, which are in the range reported for hexagonal ice Ih and H2O in crystalline hydrates.73 The ηH values are markedly different from zero, indicating that the hydrogen bond angles between an H2O-proton and an oxygen atom of the KA−3 are less than 180°;73 it will be shown below that the hydrogen bonding for the H2O-protons in the MHPW’s are to more than one oxygen atom of a KA−3. The H2O-protons of all MHPW’s were found to have rHH = 167 pm, and the angle between ZPAS of the chemical shift tensor and ZPAS of the dipolar tensor of the MHPW has a range of 30−45°, consistent with the nonlinearity of the Ow−H···O hydrogen bonds in these salts. Individual LHF of MHPW. Figure 5 shows that SrHPW has relatively sharp 1H MAS NMR resonance lines compared to those of the other four MHPW’s, indicating that SrHPW is the most ordered of the group II salts of 12-tungstophosphoric acid. The high resolution of the 1H MAS NMR spectrum of SrHPW should provide the most detailed description of the proton structures in any of the MHPW’s. Therefore, discussion of the SrHPW results will be presented first. SrHPW. Figure 4 shows the 1H NS NMR spectrum of SrHPW. There is a dominant resonance line centered at about 0 ppm and two spectral features at about ±60 ppm that are the horns of a Pake powder pattern.77 The observed separation of 45 kHz (Table 1) is the value expected for rigid H2Oprotons.77 Previous work on the group I salts of 12tungstophosphoric acid shows that H+-protons have isotropic chemical shifts greater than 5 ppm and minimal spinning

ΔEH2O (eV) −17.2

−17.7

−29.9

−18.0

a P of KA1 at origin of coordinate system. bDegree. cRotating H2O H2P2. drPP = 1197 pm. eStatic H2O H2P2.

anisotropies of 4.12 kHz and dipolar couplings of 13 kHz (rotating H2O for NaHPW, see two-pulse sequence 1H NS NMR results below). For the H2O simulation, ZPAS of the chemical shift and dipolar tensors were taken to be the same (rotating case). For the H3O+ simulation, the three 1H nuclei were placed at the vertices of an equilateral triangle and the z axis of the molecular frame coordinate system was taken to coincide with one of the O−H bonds; the three 1H−1H dipolar vectors therefore have polar angles of 90, 150, and 210°. It is clear from Figure 13 that the H2O simulation provides a very good match to the experimental NaHPW twopulse sequence 1H MAS NMR spectrum and that the H3O+ simulation does not fit the experimental spectrum at all. For the MHPW’s, the two-pulse sequence 1H MAS NMR spectra (Figure 7) are essentially the same as the MAS-only 1H NMR spectra (Figure 5a) and the H2O simulation does and H3O+ simulation does not provide a very good match to the dominant resonance line for each of the two-pulse sequence 1 H MAS NMR spectra of the MHPW’s shown in Figure 7. Thus, only H+-protons and H2O-protons are present in the MHPW’s, that is, dipolar coupled clusters of three or more 1H

Table 4. Parameters for Fit of 1H NS Two-Pulse Sequence Data for LHF Group II Salts of 12-Tungstophophoric Acid and Related Materials salt

NH/NH2Oa

ΔωH,iso/2πb

ΔωH2O,iso/2πc

δH2Od

ηH2Oe

rHHf

Θg

Φg

NaHPW BeHPW MgHPW CaHPW SrHPW BaHPW

0.125 1.0h 0.15 0.20 0.61 0.63

−2.32 −2.59 −4.33 −3.50 −2.50 −2.60

0 −2.59 −2.59 −0.73 −0.90 −0.99

−20.6 −25.6 −18.8 −21.2 −13.8 −22.5

1.0 0.9 1.0 0.5 0.8 1.0

167 167 167 167 167 167

35 35 30 45 40 40

0 0 0 0 0 0

a

Ratio of H+-protons to H2O molecules, from 1H MAS NMR data except for BeHPW. bkHz, from combination of 1H NS and MAS NMR data. kHz, from 1H NS NMR two-pulse sequence data. dppm, from fit of 1H NS NMR two-pulse sequence data. eFrom fit of 1H NS NMR two-pulse sequence data. fpm. gDegree, from fit of 1H NS NMR two-pulse sequence data. hFrom fit of 1H NS NMR two-pulse sequence data. c

L


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Figure 14. MgHPW, CaHPW, SrHPW, and BaHPW 1H{31P} REDOR NMR for H+-protons (left column) and H2O-protons (right column).

sideband intensity in their 1H MAS NMR spectra.31 Group I salt H2O-protons were found to have isotropic chemical shifts in the 1−5 ppm range and large spinning sideband arrays in 1H MAS NMR spectra for rigid H2O molecules or for systems where the H2O molecular motion is restricted.31 The chemical shift range for H2O-protons in the group II salts must be

increased to lower shielding values (see below), but the other criteria are valid. Figure 5 and Table 1 show that SrHPW has six resonance lines in the isotropic chemical shift range of 7.5− 8.9 ppm that have minimal associated spinning sideband intensity; these resonance lines are therefore assigned to H+protons. Figure 5 and Table 1 also show that SrHPW has M


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Figure 15. ΔEH (left column) and ΔEH2O (right column) vs ϕPH for MgHPW, SrHPW, and BaHPW. HKA2−5 legendP of KA1 at origin: [1165 pm: black bullet with hyphen, static; orange bullet with hyphen, hopping. 1400 pm: red bullet with hyphen, static; yellow bullet with hyphen, hopping. 1405 pm: sky blue bullet with hyphen, static; gray bullet with hyphen, hopping]. P of KA2 at origin: [1165 pm: dark blue bullet with hyphen, static; light green bullet with hyphen, hopping. 1400 pm: navy blue bullet with hyphen, static; purple bullet with hyphen, hopping. 1405 pm: brown bullet with hyphen, static; dark green bullet with hyphen, hopping]. KA2−6·H2O legend [black bullet with hyphen, 1165 pm; red bullet with hyphen, 1400 pm]. 1

H{31P} REDOR NMR data of H+-protons and H2O-protons of SrHPW provided that rPP for a KA2−6 dimer can be determined. Although the crystal structure of SrHPW has not been solved, the similarity of the X-ray powder diffraction patterns of all of the MHPW’s78 and the 1H NS and MAS NMR spectra reported in this work suggest that the MHPW’s have similar crystal structures. Therefore, we assume that the MgHPW crystal structure parameters can be used to estimate

resonance intensity in the 4.1−6.6 ppm range that has large associated spinning sideband intensity; these resonance lines are assigned to H2O-protons on the basis of the observed chemical shifts and the spinning sideband pattern. The chemical shifts of the H+-proton peaks indicate that they are very acidic.70 With these basic structural assignments, the methods developed for the model compounds can be applied to N


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The Journal of Physical Chemistry C rPP values for KA2−6 dimers for all of the MHPW’s. Analysis using ORTEP-359 shows that there are three KA2−6 dimers with relatively small rPP values in the MgHPW unit cell, denoted 1165, 1401, and 1405 pm dimers. The H2O-proton 1H{31P} REDOR NMR results for SrHPW are shown in Figure 14. The experimental data were fit to both static H2O and rotating H2O H2P2 isosceles trapezoid models using eqs 29 and 30, respectively, for the three different dimers identified in the unit cell. Figure 14 and Table S2 (SI) show that the fit for all six possibilities are virtually the same. The rotating H2O H2P2 isosceles trapezoid model can be eliminated by consideration of the 1H NS NMR spectra and simulations shown in Figure S2 (SI). The simulations in Figure S2 (SI) used the parameters δH2O, ηH2O, and ωD (Table 4) obtained from the fit of the two-pulse sequence 1H NS NMR data of Figure S3 (SI) for the static H2O simulation, whereas the rotating H2O simulation used the scaled values of these parameters according to eq 14. The static H2O simulation agrees very well with the experimental spectrum, indicating that the H2O molecules in SrHPW are static. The KA−6 2 ·H2O structure of SrHPW can be refined by calculating ΔEH2O as a function of ϕPH, Figure 15. The most stable structure is that for the 1165 pm dimer when ϕPH = 281°. The hydrogen bonding of the H2O-protons in SrHPW is similar to that found for NaHPW, that is, each H2O-proton is hydrogen-bonded to a pair of terminal and bridging oxygen atoms of each KA−3, Figure 12 and Table 3. The hydrogen bond distances are in the moderately strong range.74 There are also three weak hydrogen bond distances present. The 1405 dimer results are not shown in Figure 15 because the ΔEH2O values are all greater than 90 eV for this KA2−6·H2O dimer. The 1H{31P} REDOR NMR results for the H+-protons of SrHPW are analyzed by grouping together the six resonance lines with chemical shifts of 7.5−8.9 ppm (Table 1). Figure 14 shows the experimental data and the theoretical curves obtained from the parameters provided in Table S1 (SI) from the best fit of eqs 28−30 for the H+P, static H+P2, and hopping H+P2 models, respectively. All seven models provide equally good fits of the experimental data. The H+-proton 1 H{31P} REDOR NMR results for HPW clearly show that the 1 H nucleus is dephased by the two 31P nuclei of KA2−6. Therefore, the SrHPW H+-proton structure was refined with DFT ΔEH calculations using only the static H+P2 and hopping H+P2 models. The results of DFT calculations are shown in Figure 15 where it is noted that the hopping H+P2 ΔEH values correspond to the average of the values for the two different sites. Although there are some unstable structures, addition of H+ to KA2−6 generally yields a stable structure. The static H+P2 model for the 1165 pm dimer yields the most stable structure with ΔEH = −16.6 eV at ϕPH = 222° (P of KA2 at origin). This structure is shown in Figure 12. Figure 12 and Table 2 indicate that the H+-proton is hydrogen-bonded to five oxygen atoms with weak hydrogen bond lengths in the range 327−385 pm. The H+-proton in SrHPW is located on the surface of the dimer in contrast to that of HPW where the H+-proton is caged between the two KA−3’s of the dimer. The surface location of the H+-protons in SrHPW suggests that these protons are more readily accessible to substrates for use as acid catalysts compared to the H+-proton in HPW, and this type of location of H+-protons may also provide a lower-energy pathway for proton transport in hydrogen fuel cell applications. Figure 15 also shows that there are a number of H+-proton

sites in SrHPW with similar energies, which is also a requirement for an efficient proton conductor.20 The SrHPW H+-proton structure is similar to that found for the NaHPW H+-proton structure, where it was determined with IR spectroscopy that the H+-proton is hydrogen-bonded to two Od oxygen atoms of two different KA−3’s.47 Note that rotation of the H+-proton about the P−P internuclear vector of this dimer shows that there are six structures similar to those shown in Figure 12, which is consistent with the six H+-proton resonance lines observed for SrHPW (Figure 5 and Table 1). MgHPW. On the basis of the chemical shift and spinning sideband patterns discussed for SrHPW, the resonance lines for the 1H MAS NMR spectrum of MgHPW in Figure 5 are assigned and listed in Table 1. Visual inspection of Figure 5 shows that the resonance lines assigned to the H+-protons and H2O-protons are significantly broader than those observed in SrHPW, indicating that MgHPW is a relatively more disordered salt. The chemical shift of the H+-proton peak indicates that it is very acidic.70 Possible structures for the H+-protons and H2O-protons in MgHPW can be determined with an analysis analogous to that for SrHPW. Figure 14 shows 1H{31P} REDOR NMR data for H+-protons and H2O-protons for MgHPW. The H2O-proton REDOR data was fit to eqs 29 and 30 for the static H2O H2P2 and rotating H2O H2P2 isosceles trapezoid models, respectively, for the 1165, 1400, and 1405 pm dimers, and the best fit parameters are provided in Table S2 (SI). Figure 14 and Table S2 (SI) indicate that the six cases considered yield indistinguishable results. Therefore, DFT calculations to obtain ΔEH2O for eq 33 subject to the constraints of the P−H internuclear distances obtained from the 1H{31P} REDOR NMR analysis are used to refine the structure of KA2−6·H2O for MgHPW. Estimates of ωD, δH2O, and ηH2O are obtained from the fit of the 1H NS two-pulse sequence NMR data to eq 19, Figure S3 (SI) and Table 4, and used to simulate the 1H NS NMR spectrum, Figure S2 (SI). For the H2O-protons, Figure S2 (SI) indicates that the 1H NS NMR spectrum has a Pake doublet with discontinuities that closely align with the rotating H2O simulation, indicating that the H2O molecules are rotating in MgHPW. Figure 15 shows ΔEH2O obtained as a function of ϕPH for rotating H2O H2P2 isosceles trapezoid KA−6 2 ·H2O structures of MgHPW. The 1400 pm dimer structures are all stable with the most stable structure at ϕPH = 38° where ΔEH2O = −17.7 eV. Figure S4 (SI) and Table 3 show that there are multiple hydrogen-bonding interactions of the H2O-protons and oxygen atoms of KA2−6. That the H2O molecules in MgHPW rotate in contrast to those in SrHPW may be because the 1400 pm dimer has more space between the KA−3’s than that in the 1165 pm dimer. Note that the 1405 pm dimer results are not shown in Figure 15 because the ΔEH2O values are all greater than 59 eV for this KA2−6·H2O dimer. Figure 14 shows the 1H{31P} REDOR NMR experimental data and the theoretical curves obtained from the parameters provided in Table S1 (SI) for the best fit of eqs 28−30 for the H+P, static H+P2, and hopping H+P2 models, respectively, of MgHPW. All seven models provide equally good fits to the data. Because previous results have shown (see above) that the 1 H nucleus is dephased by the two 31P nuclei of KA2−6, the MgHPW H+-proton structure was refined with DFT ΔEH calculations using only the static H+P2 and hopping H+P2 O


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Figure 14 shows that the 1H{31P} REDOR NMR data cannot be used to determine definitive H+-proton and H2Oproton structures in CaHPW because no 1H−31P dipolar coupling is observed. The theoretical curves of Figure 14 were obtained using the 1165 pm dimer and arbitrary values of rHP = 1000 pm for the H+P model and rHP1 = 1000 pm and rHP2 = 1092 pm for the rotating H2O H2P2 isosceles trapezoid model. These H−P internuclear distances do not seem physically realistic because they are of the same order of magnitude as the unit cell parameters.30 The total collapse of the static H2O Pake powder pattern, Figure 4, and observed line widths of the H+-proton and H2O-protons resonance lines, Table 1, of the 1 H NS NMR spectrum strongly suggest that the protons in CaHPW are very mobile, which is consistent with the lack of significant 1H−31P dipolar coupling. This conclusion is considered tentative, however, because BaHPW has readily observed 1H−31P dipolar couplings and its 1H NS NMR spectrum is similar to that of CaHPW. BeHPW. It was alluded to above that despite the similarity of the BeHPW 1H MAS NMR spectrum to the other MHPW spectra, Figure 5, the dominant peak in the BeHPW spectrum is more deshielded and there is no apparent resonance line that can be assigned to H+-protons. Because there are spinning sidebands associated with the 6.7 ppm resonance line, some or all of the resonance intensity at this position must be due to H2O-protons. To balance the charges of eq 1, H+-protons must be present in BeHPW. Figure 6 shows that the maximum in the 1H NS two-pulse sequence NMR spectrum for BeHPW occurs at about 108° in contrast to the 90° maximum observed for the other MHPW’s, suggesting that H+-protons may be contributing to the resonance intensity because the maximum in the two-pulse sequence curve shifts from that expected for H2O-protons (90°) toward that of H+-protons (180°). In contrast to the other MHPW’s, the fit of the BeHPW 1H NS two-pulse sequence NMR data of Figure S3 (SI) to the sum of eqs 17 and 19 cannot be weighted according to the relative intensities of the H+-protons and H2O-protons because resolved resonance lines for these two types of protons are not observed in the BeHPW 1H MAS NMR spectrum. Therefore, the relative amounts of the two types of protons were allowed to vary to help determine the best fit. The fit of the BeHPW 1H NS two-pulse sequence NMR data is shown in Figure S3 (SI), and it was found that there is one H+-proton for each H2O molecule in BeHPW, Table 4; there are 1.6−6.7 more H+-protons per H2O molecule in BeHPW than in the other MHPW’s. The collapse of the Pake doublet in the 1H NS NMR spectrum, Figure 4 and Table 1, suggests that the H2Oprotons in BeHPW are very mobile.

models. The results of DFT calculations are shown in Figure 15, where it is noted that the hopping H+P2 ΔEH values correspond to the average of the values for the two different sites. The static H+P2 model for the 1165 pm dimer yields the most stable structure with ΔEH = −16.7 eV at ϕPH = 338° (P of KA2 at origin). This structure is shown in Figure S5 (SI). Figure S5 (SI) and Table 2 indicate that the H+-proton is hydrogen-bonded to three oxygen atoms of one of the KA−3’s and one oxygen atom of the second KA−3; the hydrogen bond lengths are in the range of 270−370 pm. The H+-proton in MgHPW is located on the surface of the dimer, which may provide for enhanced acid catalytic activity and proton conductivity. BaHPW. Comparison of the chemical shift and spinning sideband patterns discussed for SrHPW permit the resonance lines for the 1H MAS NMR spectrum of BaHPW in Figure 5 to be assigned and listed in Table 1. Inspection of Figure 5 shows that the resonance lines assigned to the H+-protons and H2Oprotons are significantly broader than those observed in SrHPW, indicating that BaHPW is a more disordered salt. The chemical shift of the H+-proton peaks indicates that the H+protons are acidic.70 The procedures established previously for HPW, NaHPW, SrHPW, and MgHPW are used to determine possible structures for the H+-protons and H2O-protons in BaHPW. Figure 14 shows 1H{31P} REDOR NMR data for H+-protons and H2O-protons for BaHPW. As with the other materials discussed in this work, the fit of eqs 28−30 to the 1H{31P} REDOR NMR data does not clearly determine what model best describes either the H+-proton or the H2O-proton structure (Figure 14 and Tables S1 and S2 (SI)). For the H2O-protons, ΔEH2O was calculated as a function of ϕPH for the rotating H2O H2P2 isosceles trapezoid (Figures S2 and S3 (SI) and Table 4), and the results are shown in Figure 15. The 1400 pm dimer is the most stable structure with ΔEH2O = −18.0 eV at ϕPH = 48°. This structure is shown in Figure S6 (SI), and the hydrogen bonds that the H2O-protons make with oxygen atoms of each KA−3 are provided in Table 3. The H2Oprotons have significant hydrogen bond interactions with five oxygen atoms of KA2−6, and the hydrogen bond lengths are in the range of 180−330 pm. The observed motion of the H2O molecules is probably due to the relatively large amount of space between the KA−3’s of the 1400 pm dimer. Figure 15 shows that the most stable H+-proton structure is the static H+-proton 1165 pm dimer structure with ΔEH = −16.7 eV at ϕPH = 28°. This structure is depicted in Figure S7 (SI), and the hydrogen-bonding interactions of the H+-protons with the oxygen atoms of the KA−3 are provided in Table 2. The H+-protons have multiple hydrogen-bonding interactions with the oxygen atoms of KA2−6; this structure is similar to that found in MgHPW. The H+-protons are located on the surface of the 1165 pm dimer. This location of the H+-protons may yield increased proton acid catalytic activity and proton mobility. CaHPW. The resonance lines of the 1H MAS NMR spectrum of CaHPW, Figure 5, are assigned on the basis of the chemical shift and spinning sideband patterns described above, and these assignments are provided in Table 1. The H+-proton and H2O-proton resonance lines are broad, indicating that the CaHPW is relatively disordered and the chemical shifts of the H+-protons are in the range expected for acidic H+-protons.70

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CONCLUSIONS The structure and dynamics of protons in the limiting hydrated form of the group II salts of 12-tungstophosphoric acid were investigated using the results of 1H NS NMR, 1H MAS NMR, 1 H NS two-pulse sequence NMR, 1H MAS two-pulse sequence NMR, and 1H{31P} REDOR NMR experiments; modeling of the results based on theoretical expressions of these NMR experiments; and DFT energy calculations. The MHPW’s were found to contain only H+-protons and H2O-protons. A range of motional characteristics were found for the protons in the MHPW’s, from static to highly mobile H+-protons and H2Oprotons. The H+-protons and H2O-protons in MgHPW, SrHPW, and BaHPW were found to have hydrogen bond P



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interactions with multiple oxygen atoms in two different Keggin anions that form a Keggin anion dimer. The static H+protons of the MgHPW, SrHPW, and BaHPW salts are located on the surface of the 1165 pm dimer, which suggests that these salts may have enhanced acid catalytic activity and proton mobility. The static H2O-protons of the SrHPW salt form an isosceles trapezoid with two P-atoms of the 1165 pm dimer. The rotating H2O-protons of the MgHPW and BaHPW salts form an isosceles trapezoid with the two P-atoms of the 1400 pm dimer. The H+-protons and H2O-protons in CaHPW are probably very mobile, whereas only the H2O-protons in BeHPW were definitively shown to exhibit motional narrowing in its 1H NS NMR spectrum. The H2O-protons of all of the MHPW’s have an interproton distance of 167 pm and chemical shift anisotropies with a range of −13.8 to −25.6 ppm. The asymmetry parameter range of the MHPW’s is 0.5−1.0, consistent with observations that ZPAS of the chemical shift and dipolar tensors of the H2O-protons are not collinear and that each H2O-proton has multiple hydrogen-bonding interactions with oxygen atoms of a Keggin anion. The model compound HPW has H+-protons that are enclathrated by six oxygen atoms of two different Keggin anions, one at the center and one at the corner, of the two interpenetrating simple cubic unit cells. The H2O-protons of the model compound NaHPW form an isosceles trapezoid with P-atoms of an edge dimer with multiple hydrogen-bonding interactions of each H2O-proton with the oxygen atoms of the two Keggin anions of the dimer.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b04370.

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Article

Derivation of theoretical background expressions, tables of parameters for best fit of 1H{31P} REDOR NMR data for H+-protons and H2O-protons, 1H MAS NMR spectrum of H3PW12O40, 1H NS NMR spectra and simulations of NaHPW and MHPW’s, 1H NS two-pulse sequence NMR data and fits of NaHPW and MHPW’s, ball-and-stick figures of most stable HKA2−5 and KA2−6· H2O of MgHPW and BaHPW, and coordinates used in DFT calculations (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: 303-664-1054 (S.F.D.). *E-mail: [email protected]. Tel: 303-384-2082 (A.M.H.). ORCID

Steven F. Dec: 0000-0001-6413-1307 Andrew M. Herring: 0000-0001-7318-5999 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially funded by Department of Energy Grants DE-FC02-0CH11088 and DE-FG36-06GO16032. Q


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