PCCP View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PAPER

Cite this: Phys. Chem. Chem. Phys., 2015, 17, 10118

View Journal | View Issue

Solid-state 185/187Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal–metal bond† Cory M. Widdifield,*‡ Fre ´de ´ric A. Perras and David L. Bryce* Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I 4 1/2), such as

185/187

Re remain far from fully developed due to the exceedingly strong interaction between

the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed highfield (B0 = 21.1 T) experimental SSNMR study on several perrhenates (KReO4, AgReO4, Ca(ReO4)2
2H2O), as well as ReO3 and Re2(CO)10. We propose solid ReO3 as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp 185/187Re NMR resonances. We show that for KReO4, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., ZQ) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO4 and Ca(ReO4)2
2H2O enable us to comment on the effects of counter-ions and hydration upon Re(VII) chemical shifts. Calcium-43 and

185/187

Re

NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO4)2
2H2O, which would be considered as distinct, are in fact the same structure. Study of Re2(CO)10 provides insights into the effects of Re–Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the 185/187Re EFG tensor of Re2(CO)10, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH4ReO4, NaReO4 and RbReO4. These calculations are able to reproduce many of the experimental trends in rhenium Received 30th January 2015, Accepted 11th March 2015

diso values and EFG tensor magnitudes. Using KReO4 as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|c|) and the nuclear electric quadrupolar

DOI: 10.1039/c5cp00602c

coupling constant (CQ), which enables the refinement of the structure of ND4ReO4. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for

www.rsc.org/pccp

calculating rhenium NMR tensor parameters are identified for Re2(CO)10.

Introduction Rhenium exists in a wide range of oxidation states ( 1 to +7).1 Additionally, rhenium can participate in metal–metal bonding, with K2Re2Cl8 being recognized as the first example of a compound Department of Chemistry and Centre for Catalysis Research and Innovation, University of Ottawa, 10 Marie Curie Pvt., Ottawa, Ontario, Canada. E-mail: [email protected], [email protected]; Fax: +1 613 562 5170; Tel: +1 613 562 5800 ext. 2018 † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c5cp00602c ‡ Present address: Department of Chemistry, Durham University, Stockton Road, Durham, UK. Tel: +44 (0)191 334 2056.

10118 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

containing a bond with an order of greater than 3.2 Rhenium metal possesses very high thermal stability, and thus is a component in the alloys used to make jet engine parts.3 Rhenium-containing compounds have been used as catalysts,4–18 can facilitate CO2 reduction,19–23 and possess appealing properties for organic light-emitting diode24,25 and dye-sensitized solar cell26 applications. Rhenium-containing systems also show potential as therapeutic agents,27–29 bioimagers,30–32 in in vivo diagnosis,33 single-molecule magnets,34–36 and in hydrogen storage applications.37 While these attractive applications make the solid-state nuclear magnetic resonance (SSNMR) characterization of rhenium-containing compounds highly relevant, the quadrupolar nature of the two NMR-active nuclides

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

(185Re and 187Re) has significantly hampered the development of this technique to date. All quadrupolar nuclei possess greater than one half a unit of spin angular momentum (i.e., I 4 1/2). While the vast majority of routine SSNMR experiments are performed using spin 1/2 nuclei, ca. 74% of NMR-active nuclei are quadrupolar.38 As such, further development of SSNMR methods to characterize quadrupolar nuclei would benefit the chemical community. SSNMR experiments on quadrupolar nuclei can offer tremendous insights into local structure and dynamics due to the unique ability of quadrupolar nuclei (i.e., relative to I = 1/2 nuclei) to probe the electric field gradient (EFG) at the nuclear site.39 Recent examples can be found where SSNMR experiments on quadrupolar nuclei have been used to study a variety of important materials and interesting systems. For example, SSNMR experiments on the receptive 11B nucleus (I = 3/2) offered insight into the surface chemistry of double-layer capacitors,40 and a very detailed picture of short-range interactions in frustrated Lewis pairs.41 Likewise, 7Li (I = 3/2) SSNMR experiments involving spinning sideband suppression techniques were used to comment on Li+-containing batteries.42 SSNMR experiments on integer quadrupoles such as 2H and 14N (both I = 1) are established methods which can provide information on dynamical processes on the ms–ms time scale.43–46 While further development of SSNMR methods for quadrupoles is important, it is also beneficial to exploit the complementary relationship between SSNMR observables and other techniques such as X-ray diffraction (XRD) measurements and quantum chemical calculations.47–56 While probing quadrupolar nuclei using SSNMR experiments is informative and widely applicable, the additional information comes with a cost, due to the quadrupolar interaction (QI) between the nuclear electric quadrupole moment (Q) of a quadrupolar nucleus and the EFG.57–59 The QI broadens the SSNMR signal, sometimes to the point that SSNMR experiments become impractical or uninformative. In addition to resolution and sensitivity issues, standard analytical line shape simulation tools (which treat the QI as a perturbation to the Zeeman eigenstates to second-order) are unable to correctly model the observed SSNMR line shapes when the QI becomes comparable to the Zeeman interaction.60,61 Until recently, this issue of line shape modeling was of little practical importance, as experimental sensitivity did not warrant the observation of SSNMR signals which were broadened to such an extreme extent. However, due to advances in magnet technology62 and sensitivityenhancing pulse sequences,63–65 observation of SSNMR signals broadened by very large QIs is becoming increasingly common. At present, the most dramatic examples of strongly QI-broadened SSNMR signals belong to the 185/187Re nuclides (I(185/187Re) = 5/2).66,67 In certain cases additional fine structure, due to highorder quadrupole-induced effects (HOQIE), was observed in these 185/187Re SSNMR spectra, in agreement with earlier theoretical models.68 The nuclei of the two most stable isotopes of rhenium are NMR-active, are present in high natural abundance (37.398(16)% and 62.602(16)% for 185Re and 187Re, respectively),69 and possess relatively high magnetogyric ratios (g(185Re) = 6.1057  107 rad s 1 T 1; g(187Re) = 6.1682  107 rad s 1 T 1).70

This journal is © the Owner Societies 2015

PCCP

However, very few literature reports of 185/187Re SSNMR exist, and they are primarily restricted to very high symmetry rhenium environments and/or low temperature conditions.71–80 The dearth of 185/187Re SSNMR information is attributed to the very large Q for both NMR-active nuclides (Q(185Re) = 2180(20) mb; Q(187Re) = 2070(20) mb).81 As such, a very small EFG can result in a rhenium QI that broadens the SSNMR powder pattern to the point that it is undetectable. In this study, we focus on the novel information which can be obtained when analyzing 185/187Re SSNMR spectra under the conditions of a very strong QI. Due to the inconvenience of using a dilute solution standard, we present an argument for the use of a new solid standard, ReO3, and include discussion of the field- and temperature-dependence of its 185/187Re SSNMR resonances. We provide additional discussion on several highsymmetry perrhenate systems (KReO4, AgReO4, Ca(ReO4)2
2H2O), as well as Re2(CO)10, which possesses a rhenium–rhenium bond. By precisely measuring the 185/187Re EFG tensor in Re2(CO)10, we quantify rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample, and compare the present value to prior single-crystal SSNMR measurements.82 Discussions pertaining to rhenium chemical shifts as a function of the rhenium oxidation state are briefly put forth. Lastly, we comment upon the utility of modern quantum chemical approaches for calculating important rhenium NMR observables (e.g., CQ(185/187Re), diso, etc.), provide some discussion of the limitations of these quantum chemical approaches, and show that the knowledge gained in the present study can be applied to refine the neutron diffraction structure of ND4ReO4.

Experimental 1. Sample preparation ReO3 (99.9%), KReO4 (99.9%), AgReO4 (99.995%) and Re2(CO)10 (98%) were purchased from Strem Chemicals, while Ca(ReO4)2
2H2O was purchased from Aldrich. All were received as powders and used without modification (further details are given in the ESI,† Additional experimental). All compounds are stable under normal laboratory conditions. Depending upon the experiment, the powdered samples were tightly packed into 4 mm or 7 mm outer diameter Bruker magic-angle spinning (MAS) ZrO2 rotors. 2. Solid-state

43

Ca and

185/187

Re NMR

Experimental data were primarily acquired at the National Ultrahigh-field NMR Facility for Solids in Ottawa, with additional experiments being performed at the University of Ottawa. The Ultrahigh-field Facility experiments used a standard bore Bruker AVANCE II spectrometer, which operates at B0 = 21.1 T (n0(1H) E 899.95 MHz; n0(185Re) = 202.71 MHz; n0(187Re) = 204.75 MHz; n0(43Ca) = 60.57 MHz), and either a 4 mm Bruker HX MAS probe (185/187Re) or a 7 mm Bruker single-channel MAS probe (43Ca). Experiments performed at the University of Ottawa used a wide bore Bruker AVANCE spectrometer, which operates at B0 = 11.75 T (n0(1H) E 500.13 MHz; n0(185Re) = 112.65 MHz;

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10119

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

n0(187Re) = 113.79 MHz), and a 4 mm Bruker HXY MAS probe. The 185/187Re SSNMR signals were referenced to a 0.1 mol dm 3 solution of NaReO4 in D2O (diso(185/187Re) = 0 ppm); however, during the course of this study it was found that the sharp rhenium SSNMR signals from solid ReO3 may be used instead. The 43Ca SSNMR signal was referenced to 2.0 mol dm 3 CaCl2(aq) (diso(43Ca) = 0.0 ppm). The 185/187Re pulse lengths used for experiments on AgReO4, Ca(ReO4)2
2H2O, Re2(CO)10, and KReO4 (at 21.1 T) were established using the solution reference, and include a scaling of the optimized solution pulse by 1/[I + 1/2] = 1/3 to selectively excite the central transition (mI = 1/2 2 1/2; CT) of the solid. Calcium-43 pulse lengths were determined using saturated CaCl2(aq) and scaled (as above) by 1/4 (I(43Ca) = 7/2) to be selective for the CT of the solid. Due to the extensive breadth of the 185/187Re SSNMR signals of KReO4 at B0 = 11.75 T, the pulse lengths were also calibrated using the high- and low-frequency CT and satellite transition (ST) discontinuities of the actual KReO4 sample. For further details on the frequency-dependence of the pulse lengths used to generate this 185/187Re SSNMR spectrum, see the ESI,† Table S1. For samples exhibiting a broad line shape (i.e., all solids other than ReO3), the 185/187Re SSNMR signals were acquired using either Solomon (i.e., ‘‘solid’’) echo (i.e., p/2–t1–p/2–t2–acq)83–85 or Hahn echo (i.e., p/2–t1–p–t2–acq)86 pulse sequences. The Solomon echo experiment was preferred at B0 = 21.1 T, where experimental sensitivity was not of great concern. For a given radiofrequency field strength, this sequence yields a larger uniform excitation bandwidth relative to the Hahn echo sequence. The Hahn echo sequence was preferred at B0 = 11.75 T, as it is a more sensitive experiment at offsets near the transmitter frequency (although this comes at the expense of a reduced uniform excitation bandwidth). Due to the very rapid 185/187 Re spin–spin relaxation in these materials, whole echo data acquisition was not used. Typical parameters for these experiments were as follows: p/2 = 0.8 to 1.5 ms; spectral window = 2 MHz; t1 = 13.2 to 13.8 ms; recycle delay = 50 ms, and 1024 complex time-domain data points were collected per scan. The 43Ca SSNMR data for Ca(ReO4)2
2H2O were collected using a simple Bloch decay experiment (i.e., p/2–acq) under MAS conditions (MAS frequency of 5 kHz). Final 185/187Re SSNMR spectra were prepared using variable offset cumulative spectrum (VOCS) data acquisition methods.66,87,88 The VOCS offsets varied from 200 to 300 kHz for Hahn and Solomon echo experiments, respectively, and were chosen in such a fashion so as to ensure that the final co-added VOCS possessed a uniform excitation profile over the region of the SSNMR signal. Depending on the compound, for each transmitter setting, between 4000 and 19 000 transients were collected, but note that for each sub-spectrum in a given VOCS, the same number of transients was collected. Each sub-spectrum was processed as usual and combined in the frequency-domain via co-addition to produce the VOCS. Due to the temperature dependence of the 185/187Re QI for these compounds, all experiments were performed at T = 291.8(0.2) K, as monitored via a Bruker ‘type-T’ thermocouple and regulated using a standard Bruker variable temperature unit.

10120 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

Paper

For ReO3 only, it was possible under certain conditions to use a Bloch decay experiment due to its narrow 185/187Re SSNMR signals, while in other cases the Solomon echo experiment was used. Regardless of the signal acquisition method, SSNMR experiments on this material rapidly yielded high signal-tonoise ratio (S/N) spectra (e.g., at B0 = 21.1 T, 16 transients with a recycle delay of 100 ms resulted in a S/N of ca. 40). Variable temperature experiments were performed on ReO3 to assess the sensitivity of its rhenium diso value to temperature. For full experimental details, see the ESI,† Table S1. 3. Solid-state

185/187

Re nuclear quadrupole resonance (NQR)

All experiments were carried out at the University of Ottawa using either the AVANCE spectrometer outlined above, or an AVANCE III spectrometer. NQR experiments used either 4 mm Bruker HX or HXY MAS probes, or a 7 mm Bruker HX static probe. Unless specified otherwise, all spectra were acquired using the Hahn echo pulse sequence at T = 291.8(0.2) K. For single-quantum NQR experiments, short (r1.8 ms), highpowered pulses were used as the radiofrequency transmitter was varied until a particular resonance was detected. The offset used while searching for 185/187Re NQR signals was 200 kHz. For overtone NQR experiments on Re2(CO)10, relatively long (10 ms), high-powered pulses were used, for reasons outlined in prior literature.89 To acquire the 185/187Re NQR spectra for Ca(ReO4)2
2H2O only, the VOCS data acquisition method was necessary. For further details, see the ESI,† Table S1. 4. NMR/NQR line shape fitting and parameter determination The 185/187Re SSNMR spectra were typically modeled using the ‘Quadrupolar Exact Software’ (QUEST) program, which is numerical simulation software that treats the combined Zeemanquadrupole Hamiltonian exactly, and includes the effects due to chemical shift anisotropy.90 Conveniently, QUEST allows for the automatic inclusion of a 187Re site when a 185Re spectrum is calculated. Observed signals primarily correspond to the CT, although contributions from the satellite and other allowed transitions are implicitly considered in the line shape modeling in QUEST. The 43Ca MAS SSNMR spectrum was modeled using WSolids.91 Contributions to line shape broadening such as J and dipole–dipole were deemed insignificant and not considered. Uniquely for KReO4, a region containing only ST signal was directly acquired. The relevant SSNMR parameters considered in these fits are outlined in the footnotes to Table 1 and 2. To model the 185Re and 187Re NQR spectra and extract the relevant EFG tensor parameters, both QUEST and the closedform solutions to the secular equations provided by Semin92 were used and found to produce equivalent results. 5. Quantum chemical calculations Calculations of EFG and magnetic shielding tensors were carried out using gauge-including projector augmented-wave (GIPAW) density functional theory (DFT),93,94 as implemented in the Cambridge Serial Total Energy Package (CASTEP),95–98 version 4.1 or 5.5. Input files were generated using the CIF2Cell program (v. 1.2.2),99 and all calculations used ultrasoft

This journal is © the Owner Societies 2015

View Article Online

Paper Table 1

PCCP Experimental

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Compound

185/187

n1(185Re)/MHz

— ReO3 KReO4 28.380(0.010) 39.811(0.007) AgReO4 Ca(ReO4)2
2H2O Site 1 27.502(0.014) Site 2 34.789(0.017) f 29.287(0.015) Re2(CO)10

Re EFG tensor parameters and isotropic chemical shifts obtained via exact modeling of the quadrupole interactiona

n2(185Re)/MHz

n1(187Re)/MHz

n2(187Re)/MHz

|CQ(185Re)|b/MHz

|CQ(187Re)|/MHz

ZQ

disoc/ppm

— 56.754(0.015) 79.621(0.004)

— 26.860(0.010) 37.674(0.004)

— 53.718(0.015) 75.347(0.007)

— 189.18(0.06) 265.40(0.03)

— 179.06(0.06) 251.16(0.03)

— o0.003e o0.005

2940(8)d 0(50) 175(50)

40.508(0.030) 53.341(0.025) 39.876(0.012)

26.038(0.013) 32.915(0.018) 27.718(0.012)g

38.348(0.020) 50.481(0.023) 37.742(0.012)g

142.23(0.10) 185.94(0.09) 142.06(0.04)

134.65(0.07) 175.96(0.09) 134.46(0.04)

0.553(0.002) 0.506(0.002) 0.6425(0.0008)

150(75) 225(75) 4400(75)

a Measurement errors are within parentheses and parameter definitions are as follows: CQ = eQV33/h; ZQ = (V11 V22)/V33, where |V11| r |V22| r |V33|; diso = (d11 + d22 + d33)/3, where d33 r d22 r d11. The frequencies n1 and n2 correspond to the doubly-degenerate single-quantum NQR resonance frequencies, which for I = 5/2 and ZQ = 0 can be defined as: n1 = nQ = 3CQ/20 and n2 = 2nQ = 3CQ/10. When ZQ a 0, the relationships between the measured NQR frequencies and the EFG tensor parameters are more complex, but EFG tensor parameters using NQR data were determined using the procedure outlined by Semin.92 Unless noted otherwise, SSNMR measurements were carried out at T = 291.8(0.2) K, and SSNMR line shape simulations were performed using QUEST.90 b While CQ may take any real value, |CQ| is typically measured experimentally using NQR/SSNMR. c Rhenium chemical shifts are relative to 0.1 mol dm 3 NaReO4 in D2O (diso(185/187Re) = 0 ppm). d The measured shift position is strongly influenced by the Knight shift and T = 295 K. e Value determined as a result of modeling a low-frequency mI = 1/2 2 3/2 ST. f The 185/187Re overtone NQR (mI = 1/2 2 5/2) transitions were measured at 65.466(0.010) and 69.162(0.010) MHz, allowing for enhanced precision in the determinations of |CQ(185/187Re)| and ZQ. Chemical shift tensor data: O = 150(75) ppm; k o 0.5; b = 70(20)1. g From ref. 90.

pseudopotentials to represent the core electrons.100 For the rhenium and calcium atoms, as we desired NMR property calculations at these sites, ‘on-the-fly generation’ ultrasoft pseudopotentials were used, as detailed in the ESI† (footnotes to Table S3), while all other atoms were represented using the standard ultrasoft pseudopotentials that come bundled with the CASTEP software. All GIPAW DFT calculations used the generalized gradient approximation (GGA) with the exchange– correlation (XC) functional of Perdew, Burke, and Ernzerhof (i.e., PBE).101,102 Input structures are based upon various literature sources, as provided in Table 2. For most systems, NMR

Table 2

(GI)PAW DFT-calculated

tensor calculations were performed on the reported crystal structures without any structural optimization; however, in certain instances optimization of the atomic positions was carried out. In all cases, the unit cell dimensions were fixed. Further details, including the detailed specification of input coordinates and cell dimensions, k-point sampling, and basis set kinetic energy cutoffs, may be found in the ESI,† Tables S2, S3, and S6. Euler angles were determined using EFGShield (v. 4.1).103 For molecular calculations on Re2(CO)10, the Amsterdam Density Functional (ADF) DFT software suite104,105 (version 2012.01), distributed by Scientific Computing & Modelling, was used.

187

Re EFG tensor parameters and isotropic chemical shiftsa

Compound

|CQ(187Re)|b/MHz

ZQ

NaReO4 KReO4 AgReO4 RbReO4 ND4ReO4 (1993) ND4ReO4 (1997-A)d ND4ReO4 (1997-B)d NH4ReO4 (refined)e Ca(ReO4)2
2H2O (1988)f – site I Ca(ReO4)2
2H2O (1988)f – site II Ca(ReO4)2
2H2O (1988)g – site I Ca(ReO4)2
2H2O (1988)g – site II Ca(ReO4)2
2H2O (1992)f – site I Ca(ReO4)2
2H2O (1992)f – site II Ca(ReO4)2
2H2O (1992)g – site I Ca(ReO4)2
2H2O (1992)g – site II Re2(CO)10 Re2(CO)10h

328.5 185.3 254.2 187.2 78.8 187.7 228.3 116.5 466.0 323.4 208.3 233.8 401.0 423.1 209.0 215.8 695.0 651.5

0 0 0 0 0 0 0 0 0.334 0.318 0.630 0.433 0.497 0.457 0.680 0.434 0.409 0.166

disoc/ppm 51.7 68.6 73.8 194.9 89.9 43.1 25.9 — 228.6 295.8 73.9 8.0 319.7 360.1 70.6 11.8 4400.9 4174.0

O/ppm 63.9 40.5 68.0 41.2 6.7 30.1 55.5 — 380.7 238.0 248.1 111.0 220.3 404.4 247.8 99.9 123.5 140.5

k 1 1 1 1 1 1 1 — 0.15 0.21 0.13 0.50 0.62 0.87 0.12 0.46 0.80 0.23

a, b, g/1

Original structure

90, 90, 180 90, 90, 180 90, 90, 180 90, 90, 180 90, 90, 180 90, 90, 180 90, 90, 180 — 3.0, 49.1, 69.3 5.7, 68.1, 338.9 111.9, 89.3, 189.5 75.1, 87.2, 203.3 73.0, 48.1, 75.5 317.8, 84.0, 253.4 67.6, 89.2, 170.6 73.7, 87.4, 207.0 112.0, 15.9, 163.0 101.9, 20.9, 282.6

Atzesdorfer and Range173 Brown et al.153 Naumov et al.174 ¨gner and Range175 Ro Powell et al.164 Swainson and Brown152 Swainson and Brown152 Swainson and Brown152 Picard et al.149,150 Picard et al.149,150 Baur and Kassner151 Baur and Kassner151 Churchill et al.169 Churchill et al.169

a A more complete disclosure of the calculated rhenium EFG and magnetic shielding tensor eigenvalues can be found in the ESI, Table S4. Additional parameter definitions: O = d11 d33 and k = 3(d22 diso)/O. Euler angles are specified by a, b, and g and define the orientation between the EFG tensor principal axis system (PAS) and the chemical shift tensor PAS. Further discussion on Euler angles can be found in ref. 176. b While CQ may take any real value, |CQ| is typically measured experimentally using NQR/SSNMR and hence the calculated values are reported as |CQ|. c Calculated rhenium chemical shifts have been determined from computed rhenium magnetic shielding values (i.e., diso/ppm = 0.9884siso/ppm 410.7), as detailed in the ESI, Fig. S9. d Labels of ‘A’ and ‘B’ denote the two disordered forms (disorder in ND4+) proposed to be present in the structure of Swainson and Brown. e Structure was refined as specified in the main text, starting from the structure of ND4ReO4 (1997-A) specified by Swainson and Brown. f Prior to calculation of the NMR tensor parameters, the H atoms were optimized computationally. To map calculated siso values to diso values for Ca(ReO4)2
2H2O, experimental ‘site 1’ is assigned to computational ‘site I’, and analogously, ‘site 2’ is assigned to ‘site II’. g Prior to calculation of the NMR tensor parameters, the O and H atoms were optimized computationally. h Prior to calculation of the NMR tensor parameters, the O and C atoms were optimized computationally.

This journal is © the Owner Societies 2015

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10121

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

Relativistic effects (including spin-orbit106) were included under the zeroth-order regular approximation (ZORA).107–109 All-electron basis sets were used, which were quadruple-z in the valence (triple-z in the core) with polarization functions (i.e., ‘QZ4P’ according to the ADF software).110 A variety of commonlyavailable XC functionals were tested (PBE,101,102 TPSS,111,112 and PBE0113,114), with further details provided in the ESI,† Tables S7 and S8.

Results and discussion 1. Rhenium-185/187 solid-state NMR i. ReO3: suggested rhenium chemical shift reference compound. One of the first challenges encountered when performing 185/187Re SSNMR experiments is the poor sensitivity associated with the accepted chemical shift reference material. The IUPAC recommends that a 0.1 mol dm 3 solution containing the ReO4 group in D2O may be taken as the primary chemical shift reference.115 It is unfortunate that the observation of this NMR reference signal is somewhat time-consuming (often needing several thousands of transients to be collected to obtain a modest S/N ratio). A search was thus initiated to find a convenient secondary reference material for 185/187Re NMR experiments. For reasons we outline below, ReO3 is suggested as a suitable secondary 185/187Re NMR reference compound. To begin, this material packs in a cubic lattice71 and therefore the EFG at the 185/187Re nuclei is expected to be very small. As line shape broadening effects due to the quadrupolar interaction are minimized, a sharp signal should be obtained. Due to the high amount of rhenium

Paper

by mass, relative to the accepted reference material, it is also expected that fewer transients would need to be acquired. As well, 185/187Re T1 values are necessarily very small116 due to the large Q value associated with each Re nuclide (although not to the extent that lifetime broadening effects are of paramount significance). By coupling these advantages (i.e., fewer scans and short recycle delays), high-quality 185/187Re SSNMR spectra using ReO3 should be obtained very rapidly, thereby minimizing the amount of NMR spectrometer time dedicated to experiments on the reference sample. Our 185/187Re SSNMR observations using ReO3 live up to the above expectations (see Fig. 1(a), (b), and Fig. S1 in the ESI†). A high S/N (ca. 150 : 1) NMR spectrum can be obtained using 256 scans at B0 = 21.1 T, which corresponds to roughly 30 seconds of spectrometer time. The measured rhenium isotropic chemical shifts of both NMR-active rhenium nuclides at B0 = 11.75 and at 21.1 T have been calibrated relative to the accepted primary standard as 2940(8) ppm (Table 1). The diso value therefore appears to be field independent within the magnetic fields associated with most NMR experiments (ca. 9.4–21.1 T), and we were unable to discern any significant isotope-dependence in the measured rhenium chemical shift values. Due to the presence of delocalized conduction band electrons, we note that the measured diso for ReO3 is necessarily strongly shifted due to the Knight mechanism.117 Prior measurements of the Knight shift for ReO3 at liquid helium temperatures establish a value of 2500(200) ppm,71 consistent with the conduction band electrons having 5d character. Presently, experiments were also conducted to probe the temperature-dependence of the diso(187Re) value for ReO3, and it was found to be very

Fig. 1 Experimental static Bloch decay 185Re (a) and 187Re (b) SSNMR spectra of powdered ReO3 acquired at B0 = 21.1 T. For each, a recycle delay of 0.1 s was used, 256 transients were collected, and T = 295 K. In (c), variable-temperature 187Re SSNMR measurements at B0 = 21.1 T highlight the modest temperature dependence of the rhenium chemical shift of ReO3. Over the range of temperatures considered (i.e., T = 276.5–306.5 K), the data were fit to the following linear equation (black solid line): diso(187Re)/ppm = 0.2414T/K 3010, with R2 = 0.9927.

10122 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

modest for temperatures ranging from T = 276.5 to 306.5 K (Fig. 1c). Although the measurement errors in the position of the 187Re SSNMR signal are somewhat large compared to the total shift in the signal over the temperature range considered, we find that the temperature-dependence of the diso value is +0.24 ppm K 1 for near ambient temperatures. This slight sensitivity could potentially offer the side benefit of temperature calibration, as demonstrated using the halogen nuclei in K79Br and Cs127I.118,119 Finally, measurements performed on the same sample of ReO3 over the course of a 1 year period produced the same chemical shift value (i.e., within the errors reported above). It is therefore believed that ReO3 represents a reliable secondary chemical shift reference material that may be used in lieu of the suggested IUPAC reference material. ii. KReO4: new (and useful) high-order quadrupole-induced effects. The local rhenium environment in KReO4 is a distorted tetrahedron, and as such it is similar to that of NH4ReO4 and NaReO4, both of which have been successfully studied using rhenium SSNMR experiments.66,67 Prior rhenium NQR experiments have been performed upon KReO4, and establish the following EFG tensor parameters near room temperature: |CQ(185Re)| = 188.68 MHz; |CQ(187Re)| = 178.76 MHz; and ZQ o 0.02.120 The present 185/187Re NQR measurements confirm these findings (Fig. S2, ESI† and Table 1), with the slight discrepancy between the two datasets being attributed to differences in the respective measurement temperatures. After precisely measuring the 185/187Re EFG tensor parameters, rhenium SSNMR experiments were performed at B0 = 11.75 and 21.1 T (Fig. 2) to establish the isotropic rhenium chemical shift value for this compound, and to comment upon the presence of any rhenium CSA effects (something which has never been measured for 185/187 Re using a powdered sample). The 185/187Re CT SSNMR spectra at both 11.75 and 21.1 T are modeled using QUEST exact QI simulation software90 with the EFG tensor parameters in Table 1, and diso = 0(50) ppm. While there is little evidence of HOQIE in the 185/187Re SSNMR spectrum acquired at 21.1 T, a striking observation is made at the lower applied field (i.e., B0 = 11.75 T) if one includes SSNMR observations of one of the STs. Typically, for cases where the ZQ value is nearly zero, it is well known that the CT discontinuities are of significantly higher intensity than the individual ST discontinuities. Hence, it was rather surprising to find that the discontinuities associated with the low-frequency mI = 1/2 2 3/2 STs were of comparable intensity to the CT discontinuities at 11.75 T. At 21.1 T, partial observation of the same ST discontinuities led to the expected result (i.e., much lower relative intensity for the ST) and hence is not discussed further. Due to this effect only being present at the lower applied field, it can be reasonably stated to be due to HOQIE. This observation is verified by QUEST simulations, and validates earlier literature predictions.68 Hence, while it is often assumed to be impractical to measure the STs for half-integer quadrupolar nuclei, in the case of a sufficiently strong QI, the critical discontinuities from the STs possess very similar intensity as the more commonly-measured CT discontinuities. With more discontinuities available for line shape fitting, it is expected that

This journal is © the Owner Societies 2015

PCCP

Fig. 2 Numerical QUEST simulations (a, c, e), experimental static 185/187Re VOCS Solomon echo SSNMR spectrum (b), and 185/187Re VOCS Hahn echo spectra (d, f) of KReO4 at T = 291.8 K. For the spectra in (a, b), B0 = 21.1 T, while for the spectra in (c–f), B0 = 11.75 T. Below (b, d, and f), deconvolutions of the two NMR-active rhenium isotopes is provided: 187Re (long dashed traces); 185Re (dotted traces).

the accuracy of the extracted EFG tensor parameters could be increased. We emphasize that this finding is not limited to the 185/187Re nuclides, but would apply to any half-integer quadrupolar nucleus experiencing a strong QI (e.g., 33S, 35/37Cl, 69/71 Ga, 73Ge, 79/81Br, 91Zr, 127I, etc.). It is also noted that the above-mentioned ST discontinuities in this rather strong QI regime are exceptionally sensitive to even small deviations in the ZQ value from zero (Fig. 3). This allowed for a very precise determination of ZQ(185/187Re) for KReO4 (i.e., ZQ o 0.003). It is also established that SSNMR observations allow for the ZQ value to be determined even more precisely than if only 185/187Re NQR experimental data were used (assuming a powdered sample): when using only the 185/187 Re NQR data for KReO4, the ZQ value can only be constrained to o0.02. Proper line shape modeling of the 185/187 Re ST SSNMR spectrum for KReO4 under these conditions thus offers nearly an order of magnitude gain in the measurement precision for ZQ relative to analogous NQR measurements. As the ZQ value can offer insight into the local nuclear site symmetry,121 methods by which one can precisely measure

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10123

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

Paper

Fig. 3 Numerical QUEST simulations (a–f), and experimental static VOCS Hahn echo SSNMR spectrum (low-frequency mI = 1/2 2 3/2) of powdered KReO4 acquired at B0 = 11.75 T and T = 291.8 K (g), which highlight the effects of ZQ variation upon the 185/187Re SSNMR line shape. The following values are used for ZQ, while all other parameters remain as given in Table 1: (a) ZQ = 0.015; (b) ZQ = 0.012; (c) ZQ = 0.009; (d) ZQ = 0.006; (e) ZQ = 0.003; (f) ZQ = 0.

its value are of interest in any area of chemical science where solid state structures are of importance. iii. AgReO4: the role of cation identity in determining rhenium chemical shifts. Unsurprisingly, silver perrhenate possesses a very similar local rhenium environment compared to the other systems containing the ReO4 group. Prior NQR measurements at 296 K established the following QI parameters: |CQ(185Re)| = 265.1 MHz; |CQ(187Re)| = 250.9 MHz; and ZQ = 0.027.122 This material was chosen for study to see if there was a measurable difference in the rhenium chemical shift values resulting from a change in the cationic species. While a definitive difference between the rhenium chemical shifts of NaReO4 and KReO4 could not be established (the former was measured in ref. 67), a silver ion might be expected to meaningfully change the SSNMR observables, as Ag+ is significantly more polarizable than the alkali metal ions studied earlier. Precise measurements of the |CQ(185/187Re)| and ZQ values using NQR experiments (ESI,† Fig. S3) largely confirm earlier NQR accounts (again after taking into consideration the slight changes in the EFG as a result of the differences in temperature between the present account and those in the literature). With the EFG tensor information established, 185/187Re SSNMR experiments at B0 = 21.1 T were used to additionally establish the isotropic rhenium chemical shift value for this compound, and we find that diso(185/187Re) = 175(50) ppm (Fig. 4). This small positive chemical shift is in contrast with the chemical shifts which have been measured previously for NH4ReO4, NaReO4, and KReO4, all of which are indistinguishable from 0 ppm.67 While subtle, the accuracy of this measurement is supported by

10124 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

Fig. 4 Numerical QUEST simulations (a, c) and experimental static 185/187 Re VOCS Solomon echo SSNMR spectra (b, d) of AgReO4 at B0 = 21.1 T and T = 291.8 K. (a, b) depict the high frequency CT discontinuities, while (c, d) depict the low-frequency CT discontinuities. The daggers denote minute signals or distortions of unknown origin.

several points. First, the rhenium EFG tensor parameters for AgReO4 are known very precisely through NQR measurements and second, in the NMR regime we have employed simulation software which includes the effects of the QI exactly (as compared to perturbation theory approaches). In addition, although we have attempted to include rhenium CSA in our line shape modeling for all the perrhenates we have studied to date, we have yet to see any striking evidence of its presence in the highsymmetry ReO4 group. The measured shift is consistent with what one would predict when replacing a given Na+/K+ counter-ion with a more polarizable Ag+ counter-ion. Following the model of magnetic shielding of nuclei outlined by Ramsey,123–125 and assuming that any differences in the relativistic portion of the magnetic shielding interaction as one goes from (Na/K)ReO4 to AgReO4 are small (as might be expected since the Fermi contact mechanism from the cationic species at the Re should be suppressed), it can be qualitatively understood that there exists an increased opportunity for ion–ion overlap in the latter case. As ion–ion overlap would be expected to lead to increased paramagnetic shielding contributions to the magnetic shielding tensor,126,127 and as the paramagnetic shielding mechanism nearly always leads to decreased shielding (and hence a corresponding

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

increase in diso), it appears that the observed differences in the chemical shifts between (Na/K)ReO4 and AgReO4 are consistent with the Ramsey model. In addition, GIPAW DFT quantum chemical calculations are complementary as they predict decreased magnetic shielding at the rhenium nucleus in AgReO4 relative to (Na/K)ReO4 (vide infra). We believe that this represents the first measurement of a rhenium chemical shift in the solid state within a set of rhenium(VII) compounds, although limited information exists from solution NMR.128 iv. Ca(ReO4)2
2H2O: deconvolution of multiple sites in complex 185/187Re SSNMR spectra. Calcium perrhenate dihydrate presents additional aspects which should be important in future 185/187 Re SSNMR studies of rhenium-containing materials. To begin, unlike the perrhenate systems above, it does not pack in the I41/a space group, and it possesses two unique local rhenium environments. As well, it should be interesting to probe the effect that hydration has upon the rhenium SSNMR parameters, something which to the best of our knowledge has not been discussed previously. Prior NQR measurements have been performed on Ca(ReO4)2
2H2O, but they were carried out at liquid nitrogen temperatures and hence room temperature EFG tensor data do not exist for this compound.129 The 185/187Re SSNMR spectrum that was recorded at B0 = 21.1 T is complex, possessing many discontinuities and interesting spectral features (Fig. 5). This may be expected, since the 185Re and 187 Re NMR signals are overlapping in the spectrum, and in addition there are two crystallographically distinct Re environments.

Fig. 5 Numerical QUEST simulation (a) and experimental static 185/187Re VOCS Solomon echo SSNMR spectrum (b) of Ca(ReO4)2
2H2O at B0 = 21.1 T and T = 291.8 K. Inset below spectrum (b) is a deconvolution of the four contributing signals to the total observed powder pattern in (b): red traces correspond to the 187Re signals, while purple traces are due to 185Re signals. Long dashed traces are due to site 2, while dotted traces are due to site 1. Inset: Analytical WSolids1 simulation (red trace) and experimental MAS 43Ca Bloch decay SSNMR spectrum (black trace, MAS frequency of 5 kHz) at room temperature and B0 = 21.1 T.

This journal is © the Owner Societies 2015

PCCP

When taken together this would mean that the complex line shape measured by SSNMR is actually composed of four overlapped powder patterns. Attempts to fit the SSNMR data using the EFG tensor parameters measured earlier with NQR at T = 77 K were not fruitful, and it became clear that there was significant variation in the rhenium EFG tensor parameters between T = 77 K and room temperature (potentially due to the onset of H2O dynamics in addition to the usual changes in lattice parameters). As such, 185/187Re NQR data were measured at room temperature for Ca(ReO4)2
2H2O (Fig. S4 and S5, ESI†). All eight of the expected (i.e., allowed single-quantum) NQR signals were observed; however, unless additional information is known beforehand (e.g., that ZQ = 0), it is not always possible to unambiguously determine the EFG tensor parameters for multiple-site systems when I = 5/2 and making use of these single-quantum NQR transitions. If it is known a priori that ZQ a 0, one could venture into overtone NQR measurements to arrive at unambiguous EFG tensor parameters for each site, but such experiments are exceedingly insensitive or otherwise time consuming.90,130–133 Although the solution space is not extensive, to rapidly establish the set of 185/187Re EFG tensor parameters for Ca(ReO4)2
2H2O, we undertook the intuitive, although novel, approach for a system with multiple sites,134 which simultaneously fits all the SSNMR/NQR data. In essence, the NQR data were used to begin the process with several ‘test’ solutions as to what the expected 185/187Re SSNMR spectrum would look like under the assumption that the NQR data had been assigned correctly. Predictably, all trial solutions except one yielded SSNMR spectra which did not match the experimentally observed spectrum even remotely. Only one assignment of the NQR data (Table 1) produced a simulated (via QUEST) 185/187Re SSNMR spectrum at B0 = 21.1 T that was in modest agreement with the experimental spectrum. At this point, a further iterative fitting process was carried out on the NMR data alone, which allowed us to establish a final solution for both the EFG tensor parameters, as well as the isotropic chemical shifts for the two rhenium sites in Ca(ReO4)2
2H2O. We believe that this process holds sufficient promise to analyze any multiple-site SSNMR spectrum where the QI is sufficiently strong (e.g., 79/81Br, 127I, 209Bi, etc.). The measured isotropic chemical shift values for Ca(ReO4)2
2H2O are rather shielded (diso = 150(75) and 225(75) ppm for the two sites) relative to the other perrhenate systems studied earlier, which typically had chemical shifts equal to or greater than 0 ppm. Although we are cautious to not over-interpret this data, it is highly interesting that the direction of the shift is diamagnetic, which is analogous to that which has been observed before in the halogen SSNMR spectra of numerous halidecontaining systems.135 The rationale behind this trend in the chemical shifts was noted earlier as being due to decreasing ion–ion overlap (i.e., exactly the opposite effect observed for AgReO4) as a result of the water molecules being incorporated into the lattice structure of the compound. Analogous 43Ca SSNMR measurements were performed for Ca(ReO4)2
2H2O (Fig. 5, inset). We briefly note that the measured diso(43Ca) value of 32.6(0.4) ppm is shielded when compared against the

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10125

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

typical calcium chemical shift range.136–139 Even at the high B0 of 21.1 T, clear second-order quadrupolar broadening is present in the observed line shape, affording the ability to extract values for the 43Ca EFG tensor parameters: |CQ| = 1.75(0.08) MHz; ZQ = 0.71(0.06). v. Re2(CO)10: a compound containing metal–metal bonds – 185/187 Re SSNMR, overtone NQR, and chemical shift anisotropy. Even allowing for the fact that the rhenium diso value for ReO3 is strongly influenced by the Knight shift, the above examples demonstrate the probable existence of a relationship between the rhenium diso value and the Re oxidation state. A finding of this sort is expected based on similar findings for other transition metals, with increasing oxidation states correlating with deshielding (i.e., positive chemical shifts).140 To further this discussion, a Re(0) compound was chosen, which interestingly also possesses a Re–Re bond. As with most of the compounds in this study, 185/187Re NQR measurements have been performed previously on Re2(CO)10,141,142 and the rhenium NQR parameters isolated here are complementary to these earlier reports. Using only the single-quantum NQR data, we arrive at: |CQ(185Re)| = 142.06(0.06) MHz, |CQ(187Re)| = 134.46(0.06) MHz, and ZQ = 0.642(0.02), (see Fig. S6 in the ESI,† and Table 1). In addition, we performed 185/187Re overtone NQR measurements (Fig. 6e). Briefly, for I = 5/2, these experiments involve observing the strictly forbidden 1/2 2 5/2 NQR transitions that become weakly allowed when ZQ a 0.143,144 Hence, while overtone NQR experiments are very insensitive relative to standard NQR experiments using the allowed single-quantum transitions, this data enabled us to decrease the uncertainty in the measurements of |CQ(185/187Re)| (from 0.06 MHz to 0.04 MHz) and

Paper

ZQ (0.002 to 0.0008). The enhanced precision will become relevant in our attempts to measure rhenium CSA for this compound (vide infra). Rhenium-185/187 SSNMR data have been acquired at B0 = 21.1 T and modeled with exact theory using the EFG tensor parameters arrived at from the NQR measurements (Fig. 6f–h). To begin, the best-fit exact QI simulation requires the inclusion of a substantially negative chemical shift value, leading to the very low observed diso value of 4400(75) ppm. Our finding is somewhat in accord with the ambitious (but relatively imprecise) work of Sheline and co-workers over 40 years ago using a single crystal of Re2(CO)10.82 The presently observed rhenium diso value is also over 1400 ppm more shielded than that of ReO3, where rhenium is in the +6 oxidation state (keeping in mind that for ReO3 there is necessarily a non-zero Knight shift term). Even if we consider only the Re(VII) and Re(0) compounds, there appears to be a relationship between the rhenium isotropic chemical shift value and the oxidation state of the Re atom. Initial line shape models which included only the EFG tensor and isotropic chemical shift parameters, while in good agreement with the experimental spectrum, did not yield a calculated 185/187 Re SSNMR spectrum that exactly matched the experimental observations (Fig. S7, ESI†). Inclusion of a modest amount of rhenium CSA (O = 150(75) ppm; k o 0.5) improved the agreement for essentially all the observed spectral features. Although subtle, this represents the first measurement of rhenium CSA in a powdered sample to the best of our knowledge. Earlier single crystal NMR work from Sheline and co-workers indicated a rhenium O value of ca. 300–500 ppm,82 but these measurements were somewhat imprecise and clearly inconsistent

Fig. 6 Numerical QUEST simulations (a–d, and green trace in (e)), and experimental Hahn echo 187Re (e) overtone (mI = 1/2 2 5/2) NQR spectrum of powdered Re2(CO)10 acquired at T = 291.8(2) K. Best fit simulation to the experimental data (e) yields |CQ(187Re)| and ZQ values that are within experimental error of the expected positions from single-quantum NQR. The traces in (a, b) highlight the effect of small variations in the CQ value (with ZQ = 0.6425), while the traces in (c, d) highlight the effect of small variations in the ZQ value (with |CQ| = 134.46 MHz). Likewise, numerical QUEST simulation (f) and experimental static 185/187Re VOCS Solomon echo SSNMR spectrum (g) of Re2(CO)10 at B0 = 21.1 T and T = 291.8 K. In (h), a deconvolution of the two contributing signals to the total observed powder pattern in (f) is provided: the red trace corresponds to the 187Re signal, while the purple trace is due to the 185Re signal.

10126 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

PCCP

with our present data (in Fig. S8, ESI† we include a QUEST simulation using their NMR tensor parameters). We note that O = 150 ppm is consistent with GIPAW DFT computations. Finally, we note that the best agreement was found when including b = 70(20)1. This infers that the magnetic shielding and EFG tensor frames are non-coincident. To arrive at this value, we tracked one of the ‘horn’ discontinuities (as shown before for 79/81Br SSNMR of CaBr2),145 which is particularly sensitive to b variation. While Re2(CO)10 should be isostructural with Mn2(CO)10, when attempting to fit the rhenium data using analogous parameters from Mn2(CO)10 (i.e., k = 0.95; a = b = 901; g = 01 with the O parameter variable)146 we observed slightly worse agreement relative to the parameters denoted earlier. 2. Quantum chemical calculations of rhenium EFG and magnetic shielding tensors i. General trends. Although relativistic effects play a role in determining the magnetic shielding and, to a lesser extent, the EFG tensor parameters probed by 185/187Re SSNMR, we note that qualitative successes of non-relativistic GIPAW DFT calculations of NMR parameters of nuclei as heavy as 209Bi have appeared in the literature.147 We do not expect exact agreement between the calculated and experimental rhenium NMR tensor parameters, but were interested to see if we could arrive at qualitative conclusions using GIPAW DFT by relating the calculated parameter values to structural features. The primary advantage of using this computational method, relative to molecular quantum chemistry approaches, is the inclusion of the translational symmetry that is present in the vast majority of crystal structures. Calculations were performed on all systems considered above in the present study (with the exception of ReO3 which is not insulating), as well as NH4ReO4, NaReO4, and RbReO4, for which high-quality 185/187Re SSNMR and/or NQR data exist.66,67,148 For the perrhenates, using crystal structures from the literature and without performing any geometry optimizations leads to calculated |CQ(187Re)| values which are in very good agreement in some cases (e.g., NaReO4, KReO4, and AgReO4), in fair agreement in others (RbReO4), but sometimes also in relatively poor agreement (Ca(ReO4)2
2H2O and NH4ReO4) (Table 2 and Fig. 7). With this in mind, a partial geometry optimization (H and O atoms) of Ca(ReO4)2
2H2O leads to |CQ(187Re)| values which are in fair agreement with experiment. We note in passing that two crystal structures have been presented for Ca(ReO4)2
2H2O which appear at first glance to be dissimilar despite being derived from the same diffraction data (heavy atom rmsd = 0.164 Å).149–151 However, we note that after performing a quantum chemical geometry optimization of the H and O atoms, the structures were nearly identical (all atom atomic rmsd = 0.012 Å). The enhanced structural agreement between this pair of geometry optimized structures is reflected in the increased similarity of the associated rhenium NMR tensor parameters with one another (Table 2). Likewise, when compared to the experimental 43Ca SSNMR EFG tensor and diso values, the (GI)PAW DFT calculated 43Ca SSNMR parameters for each of the original structures do not compare overly well (Table S5, ESI†).

This journal is © the Owner Societies 2015

Fig. 7 Comparison between experimentally measured and PAW DFT calculated |CQ(187Re)| values for various perrhenate systems. Line of best linear fit and Pearson product R value is arrived at by fitting data from the ’ series: |CQ(187Re, exp.)|/MHz = 1.0165|CQ(187Re, calc.)|/MHz 40.44, R2 = 0.801. Data points from the series correspond to values for the structures of ND4ReO4, as published in ref. 152 and were not used in the fitting process.

However, very good agreement between experiment and calculation is realized after optimizing the O and H positions. Returning to our earlier discussion, while the lack of quantitative agreement is not surprising, it is unexpected that use of the same structural building block (i.e., the ReO4 group) could lead to such disparity when comparing the agreement between experiment and calculation across all perrhenate systems considered above. One might be tempted to state that dynamic processes which partially average the rhenium EFG tensor magnitudes in Ca(ReO4)2
2H2O and NH4ReO4 are responsible for the disparity, but we will subsequently outline that this contribution is secondary relative to tetrahedral distortions of the perrhenate group. When required by symmetry, it is seen that the experimentally observed ZQ values are reproduced by PAW DFT calculations: all of the AReO4 systems which belong to the Scheelite class (A = Na, K, Rb, NH4, Ag) are calculated to have ZQ = 0, in agreement with experiment. Calculated rhenium diso values are consistent with the observed chemical shift difference of ca. 4400 ppm between the Re(VII) and Re(0) systems (Fig. S9, ESI†); however, due to the errors associated with both the experimental measurements and computational limitations (as outlined above), the calculations are not reliable for distinguishing between members of the perrhenate group. As shown below, very slight structural changes (order of 0.01 Å) lead to very large changes in calculated diso values. This is important to note, as structural displacements of this sort would be very near to the precision of the reported diffraction crystal structures. ii. Impact of average Re–O bond distance and shear strain on rhenium NMR parameters in perrhenates. To understand the somewhat erratic behavior of the calculated rhenium EFG tensor values based on similar input structures for the ReO4 systems, we sought to establish the sensitivities of the CQ(187Re),

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10127

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

diso (via siso), and O parameters to slight changes in the ReO4 group geometry. We chose KReO4 to represent the other AReO4 systems (i.e., A = Na, Rb, Ag, NH4) as its structure is known from relatively recent neutron powder diffraction results.153 Changes in the perrhenate anion geometry were effected by modifying the average Re–O bond distances and O–Re–O bond angles about their accepted values. To begin, we note that exceptionally slight alterations in the average Re–O distance on the order of 0.01 Å produced dramatically different calculated values, especially for the value of siso, which changes by ca. 120 ppm per 0.01 Å (Fig. 8a). While the calculated changes in the CQ values are modest relative to the chemical shift changes, it would be expected that they could serve as useful restraints for NMR crystallography approaches where structural refinements were carried out (Fig. 8b). We will return to this aspect of NMR crystallography using the rhenium NMR tensor parameters in subsequent discussions. It is also calculated that the rhenium O value would be relatively insensitive to changes in the average Re–O distance (Fig. S10, ESI†).

Paper

Deviations of the O–Re–O bond angles from their Platonic solid values are nicely parameterized using the shear parameter, |c|.154,155 In contrast to the moderate augmentations in |CQ(187Re)| with variations in the Re–O internuclear distance, when modifying |c| about the accepted crystal structure value for KReO4, we find that |CQ(187Re)| is very sensitive to |c| (Fig. 8c). Altering |c| while retaining the unit cell parameters and rhenium site symmetry necessarily introduces a slight change in the average Re–O bond distances (+0.011 to 0.007 Å over the entire data range presented in Fig. 8c). Fortunately, as shown in Fig. 8b and noted above, the 187Re CQ value is not particularly sensitive to Re–O variations in this range and hence much of the CQ variation comes from the alterations in the O–Re–O bond angles. While perhaps it is not surprising that the calculated |CQ(187Re)| reaches a minimum absolute value when |c| reaches 0 (as K+ ions are present at other lattice sites, |CQ(187Re)| should not be exactly 0), what is striking is the drastic sensitivity of the |CQ(187Re)| parameter to slight changes in |c|. Over the range of values reported in Fig. 8c, it is important

Fig. 8 (GI)PAW DFT calculations which illustrate the sensitivity of 187Re NMR tensor parameters to various changes in the local ReO4 geometry. Changes were brought about by taking the known crystal structure for KReO4 (NMR tensor parameters associated with the reference structure are indicated using red data points) and slightly modifying the position of the single unique oxygen atom. In (a, b) the sensitivity of the rhenium siso (a) and |CQ(187Re)| to changes in the average Re–O distance is shown, while in (c, d) the effects of altering the shear strain, |c|, on |CQ(187Re)| (c) and O (d) are displayed. Lines of best linear fit and Pearson product R values: siso/ppm = 12 120(DrRe–O)/Å 347.6, R2 = 0.9998 in (a); |CQ(187Re)|/MHz = 209.5(DrRe–O)/Å + 185.3, R2 = 1 in (b); |CQ(187Re)|/MHz = 2099|c| + 30.42, R2 = 0.9998 in (c); and O/ppm = 381.6|c| + 12.16, R2 = 0.9959 in (d). The shear strain parameter, |c|, is calculated by determining the sum of the absolute deviations between the O–Re–O angles in ReO4 relative to that of an idealized tetrahedron: P |c| = |tan(ya yi)|, where ya and yi parameterize the actual and idealized O–Re–O angles, respectively (and where yi E 109.471).

10128 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

to note that the unique oxygen position has only been changed by ca. 0.03 Å (+0.01 to 0.02 Å) from the accepted value, but the calculated 187Re CQ value changes by a full order of magnitude. We also find some sensitivity in the rhenium O value over this range (Fig. 8d), but realize that its measurement would be very challenging and hence would not envision this parameter to be overly useful in structural refinement endeavors. However, due to the relationship between |CQ(187Re)| and |c|, coupled with the high precision that the EFG tensor can be measured for rhenium, CQ(187Re) could be used to refine chemical structures determined by diffraction measurements (vide infra). iii. Refinement of the oxygen position in NH4ReO4. Recall that for the majority of the AReO4 group members in the present study (A = Na, K, Rb, Ag), we found fair to good agreement between the calculated and experimental 185/187Re EFG tensor parameters. However, using the most recent neutron diffraction structure152 of ND4ReO4 leads to calculated |CQ(187Re)| values that were too high by a factor of about 2 (ranging from 188 to 228 MHz) relative to experiment (110.62 MHz).67 While the topic of ammonium dynamics and its influence on both the lattice156 and the 185/187Re NQR parameters157,158 is well documented for both NH4ReO4 and ND4ReO4, the reported rhenium NQR signals as functions of temperature159–162 make it clear that this alone cannot reconcile our presently calculated EFG tensor values with those measured by NMR. Likewise, effects due to deuteration (i.e., going from NH4ReO4 to ND4ReO4) upon the CQ(185/187Re) values have been shown to be very minor (ca. 1.3% at 297 K).163 In light of the profound sensitivity of the |CQ(187Re)| value to small distortions in the ReO4 tetrahedron (captured above in |c|), it is relevant to note the small but significant variation in the reported O–Re–O angle as a function of temperature for ND4ReO4 (from 110.0(1)1 to 110.9(1)1)152,164 would be expected to yield dramatic (i.e., order of magnitude) changes in |CQ(187Re)| rather than the modest (ca. 10–20% over the temperature range from 100 to 400 K) and continuous changes that are actually observed via NQR. Importantly, recent crystal structure accounts that used the same room temperature neutron diffraction data, and arrive at essentially the same agreement for the model fits to the data (i.e., reported Rwp values were 5.73% and 5.97%), yield O–Re–O angles of 110.1(2)1 and 110.8(2)1.152,164 Clearly, there is somewhat greater uncertainty in this parameter than the diffractionbased models would lead one to believe. Recent literature reports have also found that R values from powder diffraction methods above 5% are correlated with parameter uncertainties that are larger than would be expected.165 Hence, while there is not a large variation between structures, the |CQ(185/187Re)| values, in tandem with GIPAW DFT calculations, could be used to refine the earlier structural models. Using an adapted version of a procedure recently outlined by some of us,166 we allowed the oxygen atom coordinates to vary with the calculated |CQ(187Re)| value being the convergence parameter (Fig. 9). As a condition of the refinement, we did not allow the oxygen atom position to stray beyond the range of locations defined by the prior structure determinations using neutron diffraction data.152,164 As the GIPAW DFT calculations did not include relativistic effects, strict convergence criteria

This journal is © the Owner Societies 2015

PCCP

Fig. 9 Plot showing the rapid convergence of the w2 parameter (determined by evaluating the variance between the calculated and experimental |CQ(187Re)| values) with respect to the refinement step. Values of w2 are indicated in text next to each datum. Inset: ReO4 units in the refined and original structures, with one of the structures being colored fully in yellow to highlight that there is essentially no discernable difference between the two structures (displacement of the O atoms is 0.007 Å), although the calculated |CQ(187Re)| value differs by over 50% between these two structures.

were not applied (i.e., once the calculated |CQ| value was within 10% of the experimental value, we considered the system wellconverged for the present purposes). The main goal of this endeavor was to see if it was possible to arrive at an alternate set of oxygen coordinates which simultaneously satisfy the diffraction results and reproduce the experimental |CQ(187Re)|. Due to the sensitivity of the rhenium EFG tensor to small perturbations in the oxygen position, convergence was rapidly achieved (after three refinement steps), and all conditions outlined above were satisfied. The refined oxygen coordinates are given in the ESI,† Table S6, and we note that although the position of the oxygen atom only changed by 0.007 Å, the calculated |CQ(187Re)| was reduced from 188 to 116 MHz. Additionally, we note that the DFT calculated system energy is lower for the presently refined structure (ESI,† Table S3), relative to any of the diffraction structures, even though we did not include the system energy as a restraint in the refinement. This finding again highlights the complementary nature of diffraction, quantum chemistry, and SSNMR experiments in structure determination and refinement. iv. Re2(CO)10: influence of Re–Re bond distance and modeling Re–Re interactions. As noted earlier, the presence of a Re–Re single bond in Re2(CO)10 allows for us to potentially comment on the influence of metal–metal interactions upon the rhenium NMR tensor parameters. Of course, probing metal– metal bonding via SSNMR, while not commonplace, is not unknown,167,168 but to our knowledge this is the first time such an interaction has been probed by 185/187Re NMR methods on a powdered sample. To begin, we note that while the GIPAW DFT calculations were able to roughly reproduce the experimental chemical shift of Re2(CO)10, the calculated |CQ(187Re)| value of 695.0 MHz is in such spectacular error when compared to the experimental measurements (|CQ(187Re)| = 134.46 MHz) that we

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10129

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

thought additional discussion was warranted. As with the perrhenate species, to gain further insight we considered small structural changes about the accepted crystal structure values.169 One of the most obvious parameters to change would be the Re–Re bond distance. Indeed, while we find the calculated |CQ(187Re)| value to be sensitive to the Re–Re distance (Fig. 10), this alone does not account for the majority of the difference between the calculated and experimental values. In addition, due to most of the electron density in Re2(CO)10 being associated with the Re atoms, the Re–Re distance is expected to be precisely known, while the oxygen and carbon positions perhaps are known less precisely. This is borne out by observing the reported estimated standard deviations for the O and C atoms, which are typically about 50 times larger than for the rhenium position.169 The positions of the lighter atoms in Re2(CO)10 have also been noted in other studies as possessing ‘‘irregularities of an obviously random nature’’.170 As such, we carried out PAW DFT geometry optimizations of the C and O atoms in Re2(CO)10, while holding the Re positions fixed to their experimentally determined values. However, the agreement between experiment and calculation is not greatly enhanced (i.e., the calculated |CQ(187Re)| value is reduced only from 695.0 MHz to 651.5 MHz). As an additional test to determine the source of the discrepancy between the experimental and calculated |CQ(187Re)| values for Re2(CO)10, we carried out relativistic molecular DFT calculations using several XC functionals which are known to perform reasonably well at describing the geometries and singlet–triplet energy gaps for systems which exhibit single metal–metal bonds.171 By using this particular computational approach the translational symmetry of the crystal structure is lost, but as the intramolecular contributions to the EFG tensor should greatly exceed the intermolecular contributions, we do not expect this simplification to create any critical errors in understanding or

Fig. 10 Plot illustrating the sensitivity of the PAW DFT calculated |CQ(187Re)| value to small changes in the Re–Re distance in Re2(CO)10. Line of best linear fit and Pearson product R value: |CQ(187Re)|/MHz = 2083(DrRe–Re)/Å + 693.5, R2 = 0.9998. The |CQ(187Re)| value calculated using the reference structure is indicated by the red datum point.

10130 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

Paper

interpreting the results. Unfortunately, while the calculated results using the molecular model (Table S7, ESI†) within the relativistic framework are such that the calculated |CQ(187Re)| values are significantly reduced (Table S8, ESI†), it is not to the extent that the agreement between calculation and experiment could be considered anything other than poor. Even the use of large quadruple-z valence basis sets, the inclusion of spin–orbit effects, and using XC functionals beyond the GGA (i.e., meta-GGA and hybrid-GGA) did not dramatically improve the calculated rhenium EFG tensor. It is therefore clear that many commonly used DFT approaches are unable to reproduce the |CQ(187Re)| value for Re2(CO)10. This very well may be due to the presence of a metal–metal bond and inherent difficulties that modern DFT methods have when dealing with this feature, but we postulate again that this may also come from small deficiencies in the reported crystal structure. As the crystal structure of Re2(CO)10 has too many adjustable parameters to justify a refinement using only three NMR parameters (CQ, ZQ, and diso), we do not attempt a refinement at present but note that reconciling this discrepancy will be of ongoing interest.

Conclusions The combination of both standard as well as high-field (B0 = 21.1 T) solid-state NMR experiments with gauge-including projector augmented-wave (GIPAW) DFT calculations on a variety of rhenium-containing systems highlights the information that may be garnered by using the 185Re and 187Re nuclei as probes. As the 185/187Re NMR signals of dilute ReO4 solutions are relatively weak, we suggest that solid ReO3 may be used as a secondary chemical shift standard since it presents narrow, stable, and strong solid-state rhenium NMR signals. By performing experiments on KReO4 at both high and standard applied fields, we have been able to ‘tune’ the highorder quadrupole-induced effects in such a manner that they can yield EFG tensor information to unprecedented levels of precision using powdered samples. This finding is of course not limited to 185/187Re nuclei, and can be applied whenever the quadrupolar interaction is sufficiently large. Assuming a powdered sample, the measured error in the ZQ value for KReO4 (using one of the satellite transitions) is nearly one order of magnitude smaller than competing methods such as centraltransition SSNMR and nuclear quadrupole resonance (NQR). Samples of AgReO4 and Ca(ReO4)2
2H2O have allowed us to measure for the first time chemical shift effects between Re(VII) species in the solid state. Additionally, we have shown that NQR and SSNMR experiments may yield spectra that can be fit simultaneously to accurately measure rhenium EFG and chemical shift information for the very spectrally dense Ca(ReO4)2
2H2O system (8 single-quantum NQR signals and 4 overlapping powder patterns in the solid-state 185/187Re NMR spectrum). Rhenium-185/187 SSNMR, and in particular overtone 185/187Re NQR experiments, on Re2(CO)10 allow us to measure rhenium chemical shift anisotropy for the first time

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

using a powdered sample (and to greater precision than earlier studies using a single crystal sample). GIPAW DFT calculations, despite not including relativistic effects, were found to reasonably reproduce many of the solidstate NMR observables, such as diso, |CQ(187Re)|, and ZQ. In the perrhenate systems, the extreme sensitivity of the |CQ(187Re)| value to the tetrahedral shear strain parameter, |c|, has allowed us to refine the structure of NH4ReO4 so that it not only agrees well with the diffraction crystal structures established earlier, but also so that the rhenium EFG tensor parameters are well reproduced. Importantly, we find that the |CQ(187Re)| parameter was much more sensitive to the refinement process than the diffraction metrics. Lastly, we have found that the EFG tensor parameters for Re2(CO)10 cannot be reproduced using several common DFT methods. This finding is not fully unexpected, as DFT sometimes struggles when calculating properties of systems containing d orbitals which are involved in metal–metal bonds.172 Hence, the Re2(CO)10 system may provide experimental observables which can be used in future DFT calibration and benchmarking tests.

Acknowledgements D.L.B. thanks the Natural Sciences and Engineering Research Council (NSERC) of Canada for funding. C.M.W. acknowledges NSERC for an Alexander Graham Bell CGS D2 scholarship and a postdoctoral fellowship. F. A. Perras acknowledges NSERC for a graduate scholarship. We are grateful to Dr Victor Terskikh and Dr Eric Ye for technical support, and the High-Performance Computing Virtual Laboratory (HPCVL) for computational resources. Access to the 21.1 T NMR spectrometer was provided by the National Ultrahigh-Field NMR Facility for Solids (Ottawa, Canada), a national research facility funded by a consortium of Canadian Universities, supported by the National Research Council Canada and Bruker Biospin, and managed by the University of Ottawa (http://nmr900.ca).

References 1 2 3 4 5 6 7 8 9

E. Scerri, Nat. Chem., 2010, 2, 598. F. A. Cotton, Acc. Chem. Res., 1969, 2, 240–247. A. V. Naumov, Russ. J. Non-Ferr. Met., 2007, 48, 418–423. ˜o, F. E. Ku ¨hn and W. A. Herrmann, Chem. Rev., C. C. Roma 1997, 97, 3197–3246. A. T. Herrmann, T. Saito, C. E. Stivala, J. Tom and A. Zakarian, J. Am. Chem. Soc., 2010, 132, 5962–5963. I. Ahmad, G. Chapman and K. M. Nicholas, Organometallics, 2011, 30, 2810–2818. B. Dudle, K. Rajesh, O. Blacque and H. Berke, J. Am. Chem. Soc., 2011, 133, 8168–8178. Y. Kuninobu and K. Takai, Chem. Rev., 2011, 111, 1938–1953. Y. Kuninobu, K. Ohta and K. Takai, Chem. Commun., 2011, 47, 10791–10793.

This journal is © the Owner Societies 2015

PCCP

10 B. C. Vicente, R. C. Nelson, A. W. Moses, S. Chattopadhyay and S. L. Scott, J. Phys. Chem. C, 2011, 115, 9012–9024. 11 N. M. West, J. A. Labinger and J. E. Bercaw, Organometallics, 2011, 30, 2690–2700. ´, A. Susset, A. Tougerti, D. Gallego, S. V. Ramani, 12 A. Yoboue M. Kalyanikar, D. S. Dolzhnikov, S. G. Wubshet, Y. Wang, S. Cristol, V. Briois, C. La Fontaine, R. M. Gauvin, J.-F. Paul and E. Berrier, Chem. Commun., 2011, 47, 4285–4287. 13 Y. Fukumoto, M. Daijo and N. Chatani, J. Am. Chem. Soc., 2012, 134, 8762–8765. 14 M. J. McKay and H. M. Nguyen, ACS Catal., 2012, 2, 1563–1595. 15 M. Shiramizu and F. D. Toste, Angew. Chem., Int. Ed., 2012, 51, 8082–8086. 16 S. C. A. Sousa, I. Cabrita and A. C. Fernandes, Chem. Soc. Rev., 2012, 41, 5641–5653. 17 Y. Wang, L. Zhang, Y. Yang, P. Zhang, Z. Du and C. Wang, J. Am. Chem. Soc., 2013, 135, 18048–18051. 18 S. Raju, M.-E. Moret and R. J. M. K. Gebbink, ACS Catal., 2015, 5, 281–300. 19 C. L. Anfuso, R. C. Snoeberger III, A. M. Ricks, W. Liu, D. Xiao, V. S. Batista and T. Lian, J. Am. Chem. Soc., 2011, 133, 6922–6925. 20 J. Agarwal, E. Fujita, H. F. Schaefer III and J. T. Muckerman, J. Am. Chem. Soc., 2012, 134, 5180–5186. 21 J. A. Keith, K. A. Grice, C. P. Kubiak and E. A. Carter, J. Am. Chem. Soc., 2013, 135, 15823–15829. 22 L. T.-L. Lo, S.-W. Lai, S.-M. Yiu and C.-C. Ko, Chem. Commun., 2013, 49, 2311–2313. 23 E.-G. Ha, J.-A. Chang, S.-M. Byun, C. Pac, D.-M. Jang, J. Park and S. O. Kang, Chem. Commun., 2014, 50, 4462–4464. 24 M. Mauro, C.-H. Yang, C.-Y. Shin, M. Panigati, C.-H. Chang, G. D’Alfonso and L. De Cola, Adv. Mater., 2012, 24, 2054–2058. 25 Y. Jia, L. Duan, D. Zhang, J. Qiao, G. Dong, L. Wang and Y. Qiu, J. Phys. Chem. C, 2013, 117, 13763–13769. 26 B. Happ, A. Winter, M. D. Hager and U. S. Schubert, Chem. Soc. Rev., 2012, 41, 2222–2255. 27 J. Martı´nez-Lillo, T. F. Mastropietro, R. Lappano, A. Madeo, M. E. Alberto, N. Russo, M. Maggiolini and G. De Munno, Chem. Commun., 2011, 47, 5283–5285. 28 D. Can, B. Spingler, P. Schmutz, F. Mendes, P. Raposinho, C. Fernandes, F. Carta, A. Innocenti, I. Santos, C. T. Supuran and R. Alberto, Angew. Chem., Int. Ed., 2012, 51, 3354–3357. 29 A. Leonidova, V. Pierroz, R. Rubbiani, Y. Lan, A. G. Schmitz, A. Kaech, R. K. O. Sigel, S. Ferrari and G. Gasser, Chem. Sci., 2014, 5, 4044–4056. `de, F. Lambert, C. Sandt, Z. Gueroui, M. Re ´fre ´giers, 30 S. Cle `res and C. Policar, M.-A. Plamont, P. Dumas, A. Vessie Chem. Commun., 2012, 48, 7729–7731. 31 C. Mari, M. Panigati, L. D’Alfonso, I. Zanoni, D. Donghi, L. Sironi, M. Collini, S. Maiorana, C. Baldoli, G. D’Alfonso and E. Licandro, Organometallics, 2012, 31, 5918–5928. 32 G. R. Morais, A. Paulo and I. Santos, Organometallics, 2012, 31, 5693–5714.

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10131

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

33 M.-W. Louie, H.-W. Liu, M. H.-C. Lam, Y.-W. Lam and K. K.-W. Lo, Chem. – Eur. J., 2011, 17, 8304–8308. ´rac and J. R. Long, J. Am. 34 T. D. Harris, M. V. Bennett, R. Cle Chem. Soc., 2010, 132, 3980–3988. 35 J. Martı´nez-Lillo, T. F. Mastropietro, E. Lhotel, C. Paulsen, J. Cano, G. De Munno, J. Faus, F. Lloret, M. Julve, S. Nellutla and J. Krzystek, J. Am. Chem. Soc., 2013, 135, 13737–13748. 36 K. S. Pedersen, M. Sigrist, M. A. Sørensen, A.-L. Barra, ¨ller, S. Piligkos, C. Aa. Thuesen, M. G. Vinum, T. Weyhermu ´rac and J. Bendix, Angew. Chem., H. Mutka, H. Weihe, R. Cle Int. Ed., 2014, 53, 1351–1354. 37 S. Muhammad, S. Moncho, E. N. Brothers and A. A. Bengali, Chem. Commun., 2014, 50, 5874–5877. 38 S. E. Ashbrook and S. Sneddon, J. Am. Chem. Soc., 2014, 136, 15440–15456. 39 S. E. Ashbrook and M. J. Duer, Concepts Magn. Reson., Part A, 2006, 28, 183–248. ¨ster, N. M. Trease, J. Se ´galini, P.-L. 40 H. Wang, T. K.-J. Ko Taberna, P. Simon, Y. Gogotsi and C. P. Grey, J. Am. Chem. Soc., 2011, 133, 19270–19273. ¨hlich, G. Kehr, 41 T. Wiegand, H. Eckert, O. Ekkert, R. Fro G. Erker and S. Grimme, J. Am. Chem. Soc., 2012, 134, 4236–4249. 42 I. Hung, L. Zhou, F. Pourpoint, C. P. Grey and Z. Gan, J. Am. Chem. Soc., 2012, 134, 1898–1901. 43 N. H. M. Hogg, P. J. T. Boulton, V. E. Zorin, R. K. Harris and P. Hodgkinson, Chem. Phys. Lett., 2009, 475, 58–63. 44 L. A. O’Dell and C. I. Ratcliffe, Chem. Commun., 2010, 46, 6774–6776. 45 A. E. Aliev, S. E. Mann, A. S. Rahman, P. F. McMillan, `, D. Iuga, C. E. Hughes and K. D. M. Harris, J. Phys. F. Cora Chem. A, 2011, 115, 12201–12211. 46 L. A. O’Dell, Prog. Nucl. Magn. Reson. Spectrosc., 2011, 59, 295–318. 47 S. E. Ashbrook, A. J. Berry, D. J. Frost, A. Gregorovic, C. J. Pickard, J. E. Readman and S. Wimperis, J. Am. Chem. Soc., 2007, 129, 13213–13224. 48 D. H. Brouwer, J. Am. Chem. Soc., 2008, 130, 6306–6307. 49 D. Laurencin, C. Gervais, A. Wong, C. Coelho, F. Mauri, D. Massiot, M. E. Smith and C. Bonhomme, J. Am. Chem. Soc., 2009, 131, 13430–13440. 50 J. V. Hanna, K. J. Pike, T. Charpentier, T. F. Kemp, M. E. Smith, B. E. G. Lucier, R. W. Schurko and L. S. Cahill, Chem. – Eur. J., 2010, 16, 3222–3239. 51 K. E. Johnston, C. C. Tang, J. E. Parker, K. S. Knight, P. Lightfoot and S. E. Ashbrook, J. Am. Chem. Soc., 2010, 132, 8732–8746. 52 C. Martineau, A. Cadiau, B. Bouchevreau, J. Senker, F. Taulelle and K. Adil, Dalton Trans., 2012, 41, 6232–6241. 53 A.-L. Rollet, M. Allix, E. Veron, M. Deschamps, V. Montouillout, M. R. Suchomel, E. Suard, M. Barre, ˜a, A. Sadoc, F. Boucher, C. Bessada, D. Massiot M. Ocan and F. Fayon, Inorg. Chem., 2012, 51, 2272–2282. 54 D. V. Dudenko, P. A. Williams, C. E. Hughes, O. N. Antzutkin, S. P. Velaga, S. P. Brown and K. D. M. Harris, J. Phys. Chem. C, 2013, 117, 12258–12265.

10132 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

Paper

55 F. A. Perras, I. Korobkov and D. L. Bryce, CrystEngComm, 2013, 15, 8727–8738. 56 C. Martineau, Solid State Nucl. Magn. Reson., 2014, 63–64, 1–12. 57 M. H. Cohen and F. Reif, Solid State Physics, Academic Press, New York, 1957, vol. 5, pp. 321–438. 58 E. A. C. Lucken, Nuclear Quadrupole Coupling Constants, Academic Press, London, 1969. 59 K. J. D. MacKenzie and M. E. Smith, Multinuclear SolidState NMR of Inorganic Materials, Pergamon, Amsterdam, 2002. 60 C. M. Widdifield and D. L. Bryce, J. Phys. Chem. A, 2010, 114, 10810–10823. 61 F. A. Perras and D. L. Bryce, Angew. Chem., Int. Ed., 2012, 51, 4227–4230. 62 A. Bhattacharya, Nature, 2010, 463, 605–606. 63 R. Siegel, T. T. Nakashima and R. E. Wasylishen, Concepts Magn. Reson., Part A, 2005, 26, 47–61. 64 R. Siegel, T. T. Nakashima and R. E. Wasylishen, Concepts Magn. Reson., Part A, 2005, 26, 62–77. 65 F. A. Perras, J. Viger-Gravel, K. M. N. Burgess and D. L. Bryce, Solid State Nucl. Magn. Reson., 2013, 51–52, 1–15. 66 R. W. Schurko, S. Wi and L. Frydman, J. Phys. Chem. A, 2002, 106, 51–62. 67 C. M. Widdifield, A. D. Bain and D. L. Bryce, Phys. Chem. Chem. Phys., 2011, 13, 12413–12420. ´, W. Socher and J. Voitla ¨nder, J. Chem. 68 J. Abart, E. Palangie Phys., 1983, 78, 5468–5473. `vre, J. W. Gramlich, 69 I. L. Barnes, T. L. Chang, P. De Bie R. J. Ch. Hageman, N. E. Holden, T. J. Murphy, K. J. R. Rosman and M. Shima, Pure Appl. Chem., 1991, 63, 991–1002. 70 R. K. Harris, E. D. Becker, S. M. Cabral de Menezes, R. Goodfellow and P. Granger, Pure Appl. Chem., 2001, 73, 1795–1818. 71 A. Narath and D. C. Barham, Phys. Rev., 1968, 176, 479–483. 72 M. Bernasson, P. Descouts and G. A. Styles, Helv. Phys. Acta, 1970, 43, 393–401. 73 S. Wada and K. Asayama, J. Phys. Soc. Jpn., 1973, 34, 1163–1167. 74 J. E. Schirber, L. J. Azevedo and A. Narath, Phys. Rev. B: Condens. Matter Mater. Phys., 1979, 20, 4746–4747. 75 Y. Nishihara, Y. Yamaguchi, S. Waki and T. Kohara, J. Phys. Soc. Jpn., 1983, 52, 2301–2303. 76 D. G. Klobasa and P. K. Burkert, Magn. Reson. Chem., 1987, 25, 154–157. 77 M. Grommelt and P. K. Burkert, Z. Naturforsch., B: J. Chem. Sci., 1989, 44, 1053–1059. 78 C. Dimitropoulos, J. P. Bucher, F. Borsa and M. Corti, Phys. Rev. B: Condens. Matter Mater. Phys., 1989, 39, 7232–7235. 79 P. K. Burkert, M. Grommelt, T. Pietraß, J. Lachmann and ¨ller, Z. Naturforsch., B: J. Chem. Sci., 1990, 45, G. Mu 725–730. 80 J. A. Davies and S. Dutremez, Coord. Chem. Rev., 1992, 114, 201–247.

This journal is © the Owner Societies 2015

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

Paper

¨, Mol. Phys., 2008, 106, 1965–1974. 81 P. Pyykko 82 E. S. Mooberry, H. W. Spiess and R. K. Sheline, J. Chem. Phys., 1972, 57, 813–821. 83 I. Solomon, Phys. Rev., 1958, 110, 61–65. 84 I. D. Weisman and L. H. Bennett, Phys. Rev., 1969, 181, 1341–1350. 85 A. C. Kunwar, G. L. Turner and E. Oldfield, J. Magn. Reson., 1986, 69, 124–127. 86 E. L. Hahn, Phys. Rev., 1950, 80, 580–594. 87 D. Massiot, I. Farnan, N. Gautier, D. Trumeau, A. Trokiner and J. P. Coutures, Solid State Nucl. Magn. Reson., 1995, 4, 241–248. 88 A. Medek, V. Frydman and L. Frydman, J. Phys. Chem. A, 1999, 103, 4830–4835. 89 L. A. O’Dell, R. He and J. Pandohee, CrystEngComm, 2013, 15, 8657–8667. 90 F. A. Perras, C. M. Widdifield and D. L. Bryce, Solid State Nucl. Magn. Reson., 2012, 45–46, 36–44. 91 K. Eichele and R. E. Wasylishen, WSolids1, version 1.19.11, ¨t Tu ¨bingen, Tu ¨bingen, Germany. Universita 92 G. K. Semin, Russ. J. Phys. Chem. A, 2007, 81, 38–46. 93 T. Charpentier, Solid State Nucl. Magn. Reson., 2011, 40, 1–20. 94 C. Bonhomme, C. Gervais, F. Babonneau, C. Coelho, F. Pourpoint, T. Azaı¨s, S. E. Ashbrook, J. M. Griffin, J. R. Yates, F. Mauri and C. J. Pickard, Chem. Rev., 2012, 112, 5733–5779. 95 C. J. Pickard and F. Mauri, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 245101. 96 M. Profeta, F. Mauri and C. J. Pickard, J. Am. Chem. Soc., 2003, 125, 541–548. 97 S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson and M. C. Payne, Z. Kristallogr., 2005, 220, 567–570. 98 J. R. Yates, C. J. Pickard and F. Mauri, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 024401. ¨rkman, Comput. Phys. Commun., 2011, 182, 1183–1186. 99 T. Bjo 100 D. Vanderbilt, Phys. Rev. B: Condens. Matter Mater. Phys., 1990, 41, 7892–7895. 101 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 102 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1997, 78, 1396. 103 S. Adiga, D. Aebi and D. L. Bryce, Can. J. Chem., 2007, 85, 496–505. 104 C. Fonseca Guerra, J. G. Snijders, G. te Velde and E. J. Baerends, Theor. Chem. Acc., 1998, 99, 391–403. 105 G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fonseca Guerra, S. J. A. van Gisbergen, J. G. Snijders and T. Ziegler, J. Comput. Chem., 2001, 22, 931–967. 106 E. van Lenthe, J. G. Snijders and E. J. Baerends, J. Chem. Phys., 1996, 105, 6505–6516. 107 E. van Lenthe, E. J. Baerends and J. G. Snijders, J. Chem. Phys., 1993, 99, 4597–4610. 108 E. van Lenthe, E. J. Baerends and J. G. Snijders, J. Chem. Phys., 1994, 101, 9783–9792.

This journal is © the Owner Societies 2015

PCCP

109 E. van Lenthe, A. Ehlers and E. J. Baerends, J. Chem. Phys., 1999, 110, 8943–8953. 110 E. van Lenthe and E. J. Baerends, J. Comput. Chem., 2003, 24, 1142–1156. 111 V. N. Staroverov, G. E. Scuseria, J. Tao and J. P. Perdew, J. Chem. Phys., 2003, 119, 12129–12137. 112 J. Tao, J. P. Perdew, V. N. Staroverov and G. E. Scuseria, Phys. Rev. Lett., 2003, 91, 146401. 113 M. Ernzerhof and G. E. Scuseria, J. Chem. Phys., 1999, 110, 5029–5036. 114 C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158–6170. 115 R. K. Harris, E. D. Becker, S. M. Cabral de Menezes, P. Granger, R. E. Hoffman and K. W. Zilm, Pure Appl. Chem., 2008, 80, 59–84. 116 R. J. C. Brown, M. E. Shortreed, A. J. Szabo, B. M. Powell and S. N. Stuart, Z. Naturforsch., A: Phys. Sci., 1992, 47, 308–312. 117 W. D. Knight, Phys. Rev., 1949, 76, 1259–1260. 118 K. R. Thurber and R. Tycko, J. Magn. Reson., 2009, 196, 84–87. `, O. G. Johannessen, P. Beckett, 119 R. Sarkar, M. Concistre M. Denning, M. Carravetta, M. al-Mosawi, C. Beduz, Y. Yang and M. H. Levitt, J. Magn. Reson., 2011, 212, 460–463. 120 M. T. Rogers and K. V. S. Rama Rao, J. Chem. Phys., 1968, 49, 1229–1231. 121 O. H. Han and E. Oldfield, Inorg. Chem., 1990, 29, 3666–3669. 122 M. T. Rogers and K. V. S. Rama Rao, J. Chem. Phys., 1973, 58, 3233–3235. 123 N. F. Ramsey, Phys. Rev., 1950, 78, 699–703. 124 N. F. Ramsey, Phys. Rev., 1951, 83, 540–541. 125 N. F. Ramsey, Physica, 1951, 17, 303–307. 126 J. Kondo and J. Yamashita, J. Phys. Chem. Solids, 1959, 10, 245–253. 127 D. W. Hafemeister and W. H. Flygare, J. Chem. Phys., 1966, 44, 3584–3590. ¨gge, M. Penk and ¨ller, E. Krickemeyer, H. Bo 128 A. Mu D. Rehder, Chimia, 1986, 40, 50–52. 129 A. A. Boguslavskii, M. B. Varfolomeev, N. B. Shamrai and S. K. Shcherbakova, Izv. Akad. Nauk SSSR, Ser. Fiz., 1981, 45, 1780–1783. 130 A. Ramamoorthy, Mol. Phys., 1991, 72, 1425–1429. 131 S. Z. Ageev and B. C. Sanctuary, Mol. Phys., 1996, 87, 1423–1438. 132 M.-Y. Liao and G. S. Harbison, J. Chem. Phys., 1999, 111, 3077–3082. 133 E. Harel and H. Cho, J. Magn. Reson., 2006, 183, 308–314. 134 B. Peric´, R. Gautier, C. J. Pickard, M. Bosiocˇic´, M. S. Grbic´ and M. Pozˇek, Solid State Nucl. Magn. Reson., 2014, 59–60, 20–30. 135 R. P. Chapman, C. M. Widdifield and D. L. Bryce, Prog. Nucl. Magn. Reson. Spectrosc., 2009, 55, 215–237. 136 D. L. Bryce, Dalton Trans., 2010, 39, 8593–8602. 137 D. Laurencin and M. E. Smith, Prog. Nucl. Magn. Reson. Spectrosc., 2013, 68, 1–40.

Phys. Chem. Chem. Phys., 2015, 17, 10118--10134 | 10133

View Article Online

Published on 11 March 2015. Downloaded by Durham University Careers Centre on 08/04/2015 10:42:14.

PCCP

138 I. L. Moudrakovski, Annu. Rep. NMR Spectrosc., 2013, 79, 129–240. 139 C. M. Widdifield, I. Moudrakovski and D. L. Bryce, Phys. Chem. Chem. Phys., 2014, 16, 13340–13359. 140 J. Mason, Chem. Rev., 1987, 87, 1299–1312. 141 S. L. Segel and R. G. Barnes, Phys. Rev., 1957, 107, 638. 142 C. B. Harris, Inorg. Chem., 1968, 7, 1691–1692. 143 S. L. Segel and L. A. Anderson, J. Chem. Phys., 1968, 49, 1407–1410. 144 A. N. Nesmeyanov, G. K. Semin, E. V. Bryukhova, T. A. Babushkina, K. N. Anisimov, N. E. Kolobova and Yu. V. Makarov, Izv. Akad. Nauk SSSR, Ser. Khim., 1968, 9, 1953–1958. 145 C. M. Widdifield and D. L. Bryce, J. Phys. Chem. A, 2010, 114, 2102–2116. 146 K. J. Ooms, K. W. Feindel, V. V. Terskikh and R. E. Wasylishen, Inorg. Chem., 2006, 45, 8492–8499. 147 H. Hamaed, M. W. Laschuk, V. V. Terskikh and R. W. Schurko, J. Am. Chem. Soc., 2009, 131, 8271–8279. 148 P. K. Burkert, F. Hutter and D. Koth, Z. Naturforsch., B: J. Chem. Sci., 1975, 30, 198–201. 149 J. P. Picard, J. P. Besse, R. Chevalier and M. Gasperin, J. Solid State Chem., 1987, 69, 380–384. 150 J. P. Picard, J. P. Besse, R. Chevalier and M. Gasperin, J. Solid State Chem., 1988, 75, 205–206. 151 W. H. Baur and D. Kassner, J. Solid State Chem., 1992, 100, 166–169. 152 I. P. Swainson and R. J. C. Brown, Acta Crystallogr., Sect. B: Struct. Sci., 1997, 53, 76–81. 153 R. J. C. Brown, B. M. Powell and S. N. Stuart, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1993, 49, 214–216. 154 K. Robinson, G. V. Gibbs and P. H. Ribbe, Science, 1971, 172, 567–570. 155 S. Ghose and T. Tsang, Am. Mineral., 1973, 58, 748–755. 156 E. C. Reynhardt and G. J. Kruger, J. Magn. Reson., 1978, 29, 159–162. 157 K. Negita, N. Nakamura and H. Chihara, Chem. Phys. Lett., 1979, 63, 187–189.

10134 | Phys. Chem. Chem. Phys., 2015, 17, 10118--10134

Paper

158 H. Chihara, K. Negita, Y. Yoshioka and N. Nakamura, J. Mol. Struct., 1980, 58, 155–160. 159 P. K. Burkert and M. F. Eckel, Z. Naturforsch., B: J. Chem. Sci., 1973, 28, 379–382. 160 R. A. Johnson and M. T. Rogers, J. Magn. Reson., 1974, 15, 584–589. 161 S. K. Shcherbakova, A. A. Boguslavskii, V. M. Burbelo and R. Sh. Lotfullin, Izv. Akad. Nauk SSSR, Ser. Fiz., 1975, 39, 2505–2512. 162 R. J. C. Brown and S. L. Segel, J. Chem. Phys., 1977, 67, 3163–3169. 163 P. K. Burkert and M. F. Eckel, Z. Naturforsch., B: J. Chem. Sci., 1973, 28, 5–7. 164 B. M. Powell, R. J. C. Brown, A. M. C. Harnden and J. K. Reid, Acta Crystallogr., Sect. B: Struct. Sci., 1993, 49, 463–468. 165 B. H. Toby, Powder Diffr., 2006, 21, 67–70. 166 F. A. Perras and D. L. Bryce, J. Phys. Chem. C, 2012, 116, 19472–19482. 167 S. Wi and L. Frydman, J. Chem. Phys., 2000, 112, 3248–3261. 168 F. A. Perras and D. L. Bryce, J. Phys. Chem. Lett., 2014, 5, 4049–4054. 169 M. R. Churchill, K. N. Amoh and H. J. Wasserman, Inorg. Chem., 1981, 20, 1609–1611. 170 J. Bacsa and J. C. A. Boeyens, J. Organomet. Chem., 2000, 596, 159–164. 171 S. I. Gorelsky, J. Chem. Theory Comput., 2012, 8, 908–914. 172 C. J. Cramer and D. G. Truhlar, Phys. Chem. Chem. Phys., 2009, 11, 10757–10816. 173 A. Atzesdorfer and K.-J. Range, Z. Naturforsch., B: J. Chem. Sci., 1995, 50, 1417–1418. 174 D. Yu. Naumov, A. V. Virovets, S. V. Korenev and A. I. Gubanov, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1999, 55, IUC9900097. ¨gner and K.-J. Range, Z. Naturforsch., B: J. Chem. Sci., 175 P. Ro 1993, 48, 233–234. 176 D. L. Bryce, in NMR Crystallography, ed. R. K. Harris, R. E. Wasylishen and M. J. Duer, John Wiley & Sons, West Sussex, United Kingdom, 2009, ch. 20, pp. 289–301.

This journal is © the Owner Societies 2015