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183W nuclear dipole moment determined by gas-phase NMR spectroscopy
Chemical Physics xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Chemical Physics journal homepage: www.elsevier.com/locate/chemphys
183
W nuclear dipole moment determined by gas-phase NMR spectroscopy Piotr Garbacz ⇑, Włodzimierz Makulski Laboratory of NMR Spectroscopy, Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 8 August 2017 In final form 9 October 2017 Available online xxxx Keywords: Nuclear magnetic dipole moment Nuclear magnetic shielding Gas-to-liquid shift Tungsten hexafluoride
a b s t r a c t The magnetic dipole moment of the tungsten-183 nucleus, m(183W), is determined from measurements of gas-phase 183W nuclear magnetic resonance of tungsten hexafluoride dissolved in CF4. The tungsten-183 resonance frequency combined with recently reported computations of the magnetic shielding of the 183 W nucleus in WF6 (Ruud et al., 2014) yields l(183W) = 0.116953(18) lN. Moreover, it is found that the gas-to-liquid shifts of nuclear shielding for WF6 are DrGL(19F) = 6.9 ppm and DrGL(183W) = 18.4 ppm. The spin–spin coupling 1J(183W,19F) is 43.75(24) Hz for liquid WF6. Ó 2017 Published by Elsevier B.V.
1. Introduction The nuclear magnetic resonance (NMR) spectroscopy constitutes a very effective and popular experimental method in physical and chemical sciences. One of the parameters which can be inferred from NMR studies is the nuclear magnetic dipole moment [1–3]. Its precise determination requires corrections for the shift of resonance frequency due to shielding of the external magnetic field applied in the experiment by the electrons of a molecule. For light nuclei, e.g., 1H, 13C, 15N, and 17O, these corrections were studied in depth [4,5]. However, computations of nuclear shielding tensors for heavy nuclei are more difficult than in the case of light nuclei because of pronounced relativistic effects. Consequently, heavy nuclei shielding was only explored by computational methods of quantum chemistry to a small degree. The lack of accurate computational data was a more severe obstacle for determination of heavy nuclei magnetic dipole moments by NMR than for light nuclei, since the shielding of heavy nuclei (e.g. up to 10,000 ppm for 195Pt and 6000 ppm for 183W; 1 ppm = 106) is frequently one or two orders of magnitude larger than for light nuclei (typically 10 ppm for 1H, 200 ppm for 13C). Recently, several reports about computations of heavy nuclei shielding have been published [6–8]. In particular, Ruud, Demissie and Jaszun´ski computed at the level of four-component density functional theory isotropic shielding of tungsten-183 (wolfram) in WF6 [9]. The available experimental data for 183W NMR which ⇑ Corresponding author. E-mail address: [email protected] (P. Garbacz).
could be used for determination of the magnetic moment of tungsten-183 reported by Sahm and Schwenk in 1975 [10,11] was not corrected either for shielding effects or for bulk magnetic susceptibility and intermolecular interactions. Therefore, we decided to reinvestigate 183W NMR of WF6 in order to obtain accurate experiment data and, by combining it with the results given in Ref. [9], find a more reliable value for the 183W magnetic moment. Naturally occurring tungsten (wolfram) consists of five isotopes. Four of which are considered as stable isotopes – 182W (20.50%), 183W (14.31%), 184W (30.64%) and 186W (28.43%) and one unstable isotope – 180W (0.12%), with an extremely long half-life of 1.1 1018 years [12,13]. Only one odd-even isotope of tungsten with a nuclear magnetic spin number of ½, i.e., 183W, is detectable by NMR spectroscopy. The 183W dipole moment is anomalously small compared with other even-odd heavy nuclei, e.g., magnitudes of dipole moments of 129Xe, 195Pt, 199Hg, and 207 Pb are nearly five times larger than for tungsten-183 (see Ref. [14] for details) and tungsten -183 lies clearly outside the Schmidt lines limit for a single neutron p1/2 state (+0.64 ppm). Among the early transition metals, NMR of 183W nuclei is not especially widespread because of its low gyromagnetic ratio and consequently low Larmor frequency often outside the accessible range of standard NMR probes. The receptivity of 183W relative to 1H NMR is only 0.0000107 and relative to 13C is 0.059; therefore, the polarization transfer techniques using high receptive nuclei like 1H, 19F and 31P are usually applied in 183W NMR measurements [15]. Nevertheless, the NMR spectroscopy was often used to study tungsten complexes, among them polyoxide clusters e.g. poloxometalates (POM). The chemical shift range of tungsten is large; thus, 183W NMR
https://doi.org/10.1016/j.chemphys.2017.10.003 0301-0104/Ó 2017 Published by Elsevier B.V.
Please cite this article in press as: P. Garbacz, W. Makulski, Chem. Phys. (2017), https://doi.org/10.1016/j.chemphys.2017.10.003
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
spectroscopy is very sensitive to even small perturbations of the electronic structure of tungsten compounds and anions in solutions. These tungsten structures were also studied at the DFT level involving relativistic effects in the ZORA approximation [16–19].
2. Experimental methods 2.1. Preparation of samples WF6 (ABCR, 99.8%), CF4 (Sigma-Aldrich, 98%), 3He (Chemgas, 99.9%) gases, and other materials were used as supplied. WF6 is an extremely corrosive compound and, upon reaction with humidity, forms hydrofluoric acid. Gas samples were prepared in the glass vacuum line by condensation of WF6 and the gaseous solvent, i.e., CF4 from the calibrated part of the vacuum line to the glass ampoules 4 mm o.d. and 56 mm in length (approx. 0.25 mL volume). Small amounts of 3He, i.e., less than 3.0 103 mol/L, were then added before sealing by a torch. These samples, at total densities in the range 0.7–1.6 mol/L, were fitted into the standard 10 mm o.d. NMR test tubes (Wilmad-Glass Co., 513-3PP) with liquid heavy water D2O in the annular space. The reference samples were 1 M Na2WO4 in D2O for 183W NMR spectra (the line width at half maximum was less than 0.4 Hz; pD 9) and liquid CFCl3 for 19F NMR spectra. The lock system, operating at 76.8464 MHz, allows the stable magnetic field of the strength of B0 = 11.75 T to be preserved. The measurements were performed at a constant temperature of T = 300 K.
2.2. Measurements of NMR spectra High resolution 183W and 19F NMR spectra were recorded on a Varian-INOVA 500 spectrometer equipped with a low-band BB10 probe operating at 20.83 MHz and 471.12 MHz frequencies, respectively. The 3He NMR spectra were recorded at a frequency of approx. 381.36 MHz in the specially adopted helium probe. Line broadening of 1 Hz was used. The insensitive nuclei enhanced by polarization transfer (INEPT) pulse sequence from 19F to 183W was used in order to increase the signal-to-noise ratio. Application of this pulse sequence is especially important for the gas-phase NMR studies of WF6, since for this case the density of observed nuclei is three orders of magnitude lower than in the liquid state. The INEPT spectra of 183W for the gas-phase measurements were decoupled from 19F during acquisition of the NMR signal.
3. Results and discussion 3.1.
183
W and
19
F spectra of WF6
The 183W and 19F spectra of WF6 in the gas and liquid phases are shown in Fig. 1. The liquid-state 183W NMR spectrum of WF6 consists of a septet. The indirect spin-spin coupling between tungsten and fluorine 1J(183W,19F) is 43.75(24) Hz, which gives the reduced spin-spin coupling 1K(183W,19F) = 9.18 1020 N A2 m3. The 19F NMR gas-phase spectrum of WF6 shown in Fig. 1A is decoupled from the fluorine because of substantial broadening of the peaks and loss of signal-to-noise ratio. Only one-seventh of molecules have tungsten nuclei bearing a non-zero spin; thus in the 19F NMR spectra, only this part of the signal is split into a doublet. For 19F NMR signal of WF6, the shift between the central line and the middle of the doublet is less than 0.2 Hz, and therefore, the isotope effects are negligible. The full width at half maximum of the helium-3 peak is much smaller than those of fluorine and tungsten peaks (Fig. 1C).
Fig. 1. 183W and 19F NMR spectra of WF6 (A and B, respectively) for a neat liquid (red curves) and the gaseous mixture with CF4 (blue curves; p = 30 bar) recorded at temperature T = 300 K and the magnetic field of strength B0 = 11.75 T. 3He NMR spectrum of the gaseous mixture sample without line broadening (C). The frequency is given relative to the central line of the multiplet acquired for the liquid sample which is m(183W) = 20 833 943.1 Hz for (A) and m(19F) = 471 117 236.9 MHz for (B). These frequencies correspond to chemical shifts 1115.1 ppm (A; relative to 1 M Na2WO4 in D2O) and 166.2 ppm (B; relative to neat CFCl3). The frequency of the peak of helium is m(3He) = 381 357 449.3 Hz.
3.2. The magnetic dipole moment of
183
W
The spin precession frequency of the
183
W nucleus in WF6 is
mð183 WÞ ¼ cð183 WÞ½1 rð183 WÞB0 ;
ð1Þ
where c(183W) is the gyromagnetic ratio of the tungsten-183 nucleus, r(183W) the isotropic part of the nuclear shielding tensor for that nucleus in WF6, and B0 the strength of the static magnetic
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
Fig. 2. The dependence of
183
W,
19
F, and 3He resonance frequencies on the density of the gas mixture with CF4.
field used in the experiment. In order to obtain the magnetic moment from Eq. (1), one has to determine precisely the strength of the magnetic field B0. The strength of B0 can be obtained measuring the resonance frequency of the second nucleus whose dipole moment is known precisely. In this work, helium-3 has been chosen for this purpose since 3He is highly inert and its resonance frequency is perturbed by intermolecular interactions to a very small extent (<0.1 ppm). The samples consisted of a mixture of 3He gas with WF6 dissolved in CF4 which allows to measure 3He and 183W resonance frequencies at the same strength of the magnetic field B0. Therefore, the dipole moment of the 183W nucleus is
lð183 WÞ ¼
mð183 WÞ ð1 rð3 HeÞÞ 3 lð HeÞ; mð3 HeÞ ð1 rð183 WÞÞ
3
ð2Þ
where l(3He) = 2.127625306(25)lN [20], r0(3He) = 59.96743(10) ppm [21], and the spin number for tungsten-183 is 1/2. In Eq. (2) the strength of the magnetic field B0 is given implicitly. For the 183W nucleus, the major correction to the dipole moment of the nucleus 183W is its magnetic shielding,
r(183W) = 6221.0 ppm [9]. However, in order to obtain accurate experimental results, one has to additionally take into account two effects: (i) the effect of intermolecular interactions on magnetic shielding which is nearly 20 ppm, and (ii) the decrease of the strength of magnetic field due to magnetic susceptibility (a few ppm). These two effects vanish if one extrapolates the 183 W resonance frequency to the zero-density limit. The range of experimentally accessible pressures of a mixture of WF6 and a small amount of 3He is too narrow to obtain sufficiently precise extrapolation to the zero-density limit (WF6 boiling point at the atmospheric pressure is 17 °C), thus an additional gaseous solvent, CF4, was applied. The resonance frequency of a nucleus measured for the gas sample at the moderate pressure (p < 50 bar) depends weakly on the density [22]. Therefore, it is sufficient to limit the power series of the resonance frequency in density to only the two first terms,
mð183 WÞ ¼ m0 ð183 WÞ þ m1 ð183 WÞqCF4 þ . . .
ð3Þ
where m0 is the resonance frequency at the zero-density limit and m1 depends on the intermolecular interactions of WF6 and the bulk
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Table 1 The resonance frequencies extrapolated to the zero density limit (m0), the slope of the resonance frequency dependence of the solvent density (m1), and the gas-to-liquid shifts (DdGL = dL dG) for 183W, 19F, and 3He nuclei. Nucleus
m0/MHz
m1/(Hz mL/mol)
DdGL/ppm
183
20.833612(1) 471.115140(9) 381.357519(3)
16(1) 125(8) 54(3)
15.89 4.45 –
W 19 F 3 He
magnetic susceptibility of the sample. The density dependence of 183 W, 19F, and 3He resonance frequencies are shown in Fig. 2. For densities up to 1.5 mol/L these dependencies are linear; thus, the zero-density limit is determined by finding the best fit parameters of a linear dependence to experimental data. Obtained frequencies are given in Table 1. The magnetic moment of the 183W nucleus obtained from Eq. (2) is l(183W) = 0.116953(18) lN which gives the g-factor, gI = lX/I, 0.233901(18) and the gyromagnetic ratio cI = gIlN/⁄, 1.120249 107 rad s1 T1 (for the ‘‘bare”, i.e., not shielded by electrons) nucleus of tungsten-183. The length of the nuclear magpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi netic dipole moment is 1 þ 1=I times larger than its maximum projection, usually referred to as a magnetic dipole moment of pffiffiffi the nucleus. Thus, for the 183W nucleus, the total length is 3 times larger than its projection reported above, 0.202569(31) lN. The obtained data differs from the magnetic moment of tungsten-183 reported by Stone [14] in his ‘‘Table of nuclear magnetic dipole moments” (Stone used data reported in Ref. [10]), l(183W) = 0.11778476(9) lN, by 0.000834 i.e. 0.71%. The error bars given in the parenthesis for the result from Ref. [14] reflect the precision of the measurements (i.e., spread of data) rather than their accuracy (i.e., proximity to the true value), since the relativistic part of the isotropic shielding of the 183W nucleus in WF6, which is twice the non-relativistic term, was neglected. However, even taking into account the relativistic contribution, the relative uncertainty of the obtained 183W dipole moment is dominated by the uncertainty of r(183W) derived from theory (±200 ppm, estimated as 5% of the relativistic contribution to the isotropic shielding), rather than from the experiment (±2 ppb). 3.3. Gas-to-liquid shift Usually, the resonance frequency of a nucleus in a molecule increases when the sample state passes from a dilute vapour to a liquid (183W and 19F resonance frequencies of WF6 follow this trend, see Fig. 2). Therefore, the gas-to-liquid chemical shift is positive, while the difference between shielding in the liquid state and the gas phase is negative. There are two contributions to this effect: the bulk magnetic susceptibility of the liquid and intermolecular interactions between molecules. For a sample of the shape of a long cylinder, the magnetic susceptibility contribution of the shift equals one third of the volume magnetic susceptibility of a liquid, vV [23]. Taking into account that the molar magnetic susceptibility vM for WF6 is 7.5 ppm (in SI units) [24] and its density is 3.37 g/mL at 300 K, one finds that the bulk magnetic susceptibility changes the 183W and 19F chemical shifts observed in the liquid-state by 2.5 ppm. The differences of chemical shifts between the gas phase and the liquid state found from the experiment for 183W and 19F nuclei are 4.45 ppm and 15.89 ppm, respectively. Thus, the contribution to differences of shielding between the gas phase and the liquid state which characterizes the strength of intermolecular interactions in the liquid phase,
DrGL ¼ rðliquidÞ r0 ðgasÞ þ vm=3;
ð4Þ
Fig. 3. 183W NMR spectrum of WO2 4 in H2O before (A) and after (B) addition of a small amount of hydrochloric acid (the signal to the right) referenced to the signal of 1 M Na2WO4 in D2O (the signal to the left). The spectrum is obtained using a system of two coaxial NMR tubes, which consists of 1 M Na2WO4 solution in D2O placed in the inner 5 mm NMR tube and 1 M Na2WO4 solution in H2O placed between that tube and the outer 10 mm NMR tube.
are DrGL(19F) = 6.9 ppm and DrGL(183W) = 18.4 ppm, which means that 183W and 19F nuclei are deshielded when the state of the sample changes from the gas phase to the liquid state. These differences are much larger than those which are usually observed for light nuclei (e.g., |DrGL| <0.5 ppm for 1H). 3.4. Measurements of WO2 4 One of the references of the tungsten-183 chemical shift is the 1.0 M heavy water solution of Na2WO4 at pD = 9 which is easier to handle then neat WF6. The tungstate oxo-anion WO2 4 is soluble in water above pH = 3 [25] and pH of 0.1–1.0 M solutions of Na2WO4 in water is approx. 9. In this range of concentrations, the 183W signal of WO2 is 3.15 ppm less shielded than that extrapolated to 4 infinite dilution. Moreover, it is found that the 183W shielding of WO2 4 for solution in D2O is 1.32 ppm smaller than if Na2WO4 is dissolved in H2O (see Fig. 3). The ratio of the 183W spin-precession frequency in liquid WF6 to the 2H spin-precession frequency of D2O obtained in the experiment, m(183W)/m(2H) = 0.2711072(18), is in agreement with that reported previously [10], m(183W)/m(2H) = 0.2711106(2). It is found that 183W absolute nuclear magnetic shielding for 1 M WO2 4 in D2O (the primary standard) is 5090 ppm and for neat WF6 is 6205 ppm (the secondary standard). These values are uncorrected for the bulk magnetic susceptibility of the sample; however, since these corrections are at least two orders of magnitude smaller than the uncertainty of the computations, they are negligible. 4. Conclusions It is found that the more reliable value of the nuclear magnetic moment of the 183W nucleus is l(183W) = 0.116953(18) lN (l(183W) = 0.590704(88) 1027 J/T in SI units). For determination of l(183W) from 183W NMR of WF6 corrections originating from the nuclear magnetic shielding, intermolecular interactions and bulk magnetic susceptibility are pronounced and they must be applied in order to obtain an accurate result. The value of the tungsten183 dipole moment might by further improved if a more accurate
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
value of shielding of 183W in WF6 could be known, since its uncertainly mainly determines the error bars of the magnetic moment of 183 W. Obtaining of the accurate value of the magnetic dipole moment for heavy atoms nuclei is still a challenge; thus, the experimentally found magnetic moment of tungsten-183 may be useful for a test of theoretical computational methods. Acknowledgement This work was financed by the National Science Center (Poland) grant according to decision No. DEC-2011/01/B/ST4/06588. References [1] A. Antušek, K. Jackowski, M. Jaszun´ski, W. Makulski, M. Wilczek, Chem. Phys. Lett. 411 (2005) 111–116. [2] M. Jaszun´ski, A. Antušek, P. Garbacz, K. Jackowski, W. Makulski, M. Wilczek, Prog. NMR Spectroscopy 67 (2012) 49–63. [3] K. Jackowski, P. Garbacz, Nuclear magnetic moments and NMR measurements of shielding, in: K. Jackowski, M. Jaszun´ski (Eds.), Gas Phase NMR, The Royal Society of Chemistry, Cambridge, 2006, pp. 95–122. [4] J. Mason (Ed.), Multinuclear NMR, Plenum Press, New York, 1987. [5] K. Jackowski, M. Jaszun´ski, M. Wilczek, J. Phys. Chem. A 114 (2010) 2471–2475. [6] J. Autschbach, T. Ziegler, Encyclopedia of NMR, J. Wiley, Chichester, 2002, pp. 306–323. [7] L.W. Liu, National Sci. Rev. 3 (2016) 204–221.
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[8] B. Adrjan, W. Makulski, K. Jackowski, T.B. Demissie, K. Ruud, A. Antušek, M. Jaszun´ski, Phys. Chem. Chem. Phys. 18 (2016) 16483–16490. [9] K. Ruud, T.B. Demissie, M. Jaszun´ski, J. Chem. Phys. 140 (2014) 194308 (1–7). [10] W. Sahm, A. Schwenk, Z. Naturforsch 29 (1974) 1763–1766. [11] J. Banek, A. Schwenk, Z. Physik B 20 (1975) 75–80. [12] E.M. Baum, M.C. Ernesti, H.D. Knox, T.R. Miller, A.M. Watson, Nuclides and Isotopes. Chart of the Nuclides, 17th Ed., Bechtel, 2010. [13] F.A. Danevich, A.Sh Georgadze, V.V. Kobychev, S.S. Nagorny, A.S. Nikolaiko, O.A. Ponkratenko, V.I. Tretyak, S.Yu Zdesenko, YuG. Zdesenko, P.G. Bizzeti, T.F. Fazzini, P.R. Maurenzig, Phys. Rev. C 67 (2003) (1–16) 014310. [14] N.J. Stone, Atomic Data and Nuclear Data Tables 90 (2005) 75–176. [15] A. Macchioni, P.S. Pregosin, H. Rüegger, G. van Koten, P.A. van der Schaaf, R.A.T. M. Abbenhuis, Mag. Reson. Chem. 32 (1994) 235–241. [16] A. Rodriguez-Fortea, P. Alemany, T. Ziegler, J. Phys. Chem. A 103 (1999) 8288– 8294. [17] J. Gracia, J.M. Poblet, J. Autschbach, L.P. Kazansky, Eur. J. Inorg. Chem. 6 (2006) 1139–1148. [18] A. Bagno, M. Bonchio, J. Autschbach, Chem. Eur.-J. 12 (2006) 8460–8471. [19] M. Filatov, D. Cremer, J. Chem. Phys. 119 (2003) 701–712. [20] P.J. Mohr, D.B. Newell, B.N. Taylor, Rev. Mod. Phys. 88 (2016) (1–63) 035009. [21] A. Rudzin´ski, M. Puchalski, K. Pachucki, J. Chem. Phys. 130 (2009) (1–5) 244102. [22] K. Jackowski, Open Conf. Proc. J. 4 (2013) 54–58. [23] R.K. Harris, E.D. Becker, S.M. Cabral de Menezes, P. Granger, R.E. Hoffman, K.W. Zilm, Pure Appl. Chem. 80 (2008) 59–84. [24] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 81, CRC Press, Boca Raton, 2000. [25] E. Lassner, W.-D. Schubert, Tungsten: Properties, Chemistry, Technology of the Elements, Alloys and Chemical Compounds, Kluwer Academic, New York, 1999, p. 401.
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Contents lists available at ScienceDirect
Chemical Physics journal homepage: www.elsevier.com/locate/chemphys
183
W nuclear dipole moment determined by gas-phase NMR spectroscopy Piotr Garbacz ⇑, Włodzimierz Makulski Laboratory of NMR Spectroscopy, Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 8 August 2017 In final form 9 October 2017 Available online xxxx Keywords: Nuclear magnetic dipole moment Nuclear magnetic shielding Gas-to-liquid shift Tungsten hexafluoride
a b s t r a c t The magnetic dipole moment of the tungsten-183 nucleus, m(183W), is determined from measurements of gas-phase 183W nuclear magnetic resonance of tungsten hexafluoride dissolved in CF4. The tungsten-183 resonance frequency combined with recently reported computations of the magnetic shielding of the 183 W nucleus in WF6 (Ruud et al., 2014) yields l(183W) = 0.116953(18) lN. Moreover, it is found that the gas-to-liquid shifts of nuclear shielding for WF6 are DrGL(19F) = 6.9 ppm and DrGL(183W) = 18.4 ppm. The spin–spin coupling 1J(183W,19F) is 43.75(24) Hz for liquid WF6. Ó 2017 Published by Elsevier B.V.
1. Introduction The nuclear magnetic resonance (NMR) spectroscopy constitutes a very effective and popular experimental method in physical and chemical sciences. One of the parameters which can be inferred from NMR studies is the nuclear magnetic dipole moment [1–3]. Its precise determination requires corrections for the shift of resonance frequency due to shielding of the external magnetic field applied in the experiment by the electrons of a molecule. For light nuclei, e.g., 1H, 13C, 15N, and 17O, these corrections were studied in depth [4,5]. However, computations of nuclear shielding tensors for heavy nuclei are more difficult than in the case of light nuclei because of pronounced relativistic effects. Consequently, heavy nuclei shielding was only explored by computational methods of quantum chemistry to a small degree. The lack of accurate computational data was a more severe obstacle for determination of heavy nuclei magnetic dipole moments by NMR than for light nuclei, since the shielding of heavy nuclei (e.g. up to 10,000 ppm for 195Pt and 6000 ppm for 183W; 1 ppm = 106) is frequently one or two orders of magnitude larger than for light nuclei (typically 10 ppm for 1H, 200 ppm for 13C). Recently, several reports about computations of heavy nuclei shielding have been published [6–8]. In particular, Ruud, Demissie and Jaszun´ski computed at the level of four-component density functional theory isotropic shielding of tungsten-183 (wolfram) in WF6 [9]. The available experimental data for 183W NMR which ⇑ Corresponding author. E-mail address: [email protected] (P. Garbacz).
could be used for determination of the magnetic moment of tungsten-183 reported by Sahm and Schwenk in 1975 [10,11] was not corrected either for shielding effects or for bulk magnetic susceptibility and intermolecular interactions. Therefore, we decided to reinvestigate 183W NMR of WF6 in order to obtain accurate experiment data and, by combining it with the results given in Ref. [9], find a more reliable value for the 183W magnetic moment. Naturally occurring tungsten (wolfram) consists of five isotopes. Four of which are considered as stable isotopes – 182W (20.50%), 183W (14.31%), 184W (30.64%) and 186W (28.43%) and one unstable isotope – 180W (0.12%), with an extremely long half-life of 1.1 1018 years [12,13]. Only one odd-even isotope of tungsten with a nuclear magnetic spin number of ½, i.e., 183W, is detectable by NMR spectroscopy. The 183W dipole moment is anomalously small compared with other even-odd heavy nuclei, e.g., magnitudes of dipole moments of 129Xe, 195Pt, 199Hg, and 207 Pb are nearly five times larger than for tungsten-183 (see Ref. [14] for details) and tungsten -183 lies clearly outside the Schmidt lines limit for a single neutron p1/2 state (+0.64 ppm). Among the early transition metals, NMR of 183W nuclei is not especially widespread because of its low gyromagnetic ratio and consequently low Larmor frequency often outside the accessible range of standard NMR probes. The receptivity of 183W relative to 1H NMR is only 0.0000107 and relative to 13C is 0.059; therefore, the polarization transfer techniques using high receptive nuclei like 1H, 19F and 31P are usually applied in 183W NMR measurements [15]. Nevertheless, the NMR spectroscopy was often used to study tungsten complexes, among them polyoxide clusters e.g. poloxometalates (POM). The chemical shift range of tungsten is large; thus, 183W NMR
https://doi.org/10.1016/j.chemphys.2017.10.003 0301-0104/Ó 2017 Published by Elsevier B.V.
Please cite this article in press as: P. Garbacz, W. Makulski, Chem. Phys. (2017), https://doi.org/10.1016/j.chemphys.2017.10.003
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
spectroscopy is very sensitive to even small perturbations of the electronic structure of tungsten compounds and anions in solutions. These tungsten structures were also studied at the DFT level involving relativistic effects in the ZORA approximation [16–19].
2. Experimental methods 2.1. Preparation of samples WF6 (ABCR, 99.8%), CF4 (Sigma-Aldrich, 98%), 3He (Chemgas, 99.9%) gases, and other materials were used as supplied. WF6 is an extremely corrosive compound and, upon reaction with humidity, forms hydrofluoric acid. Gas samples were prepared in the glass vacuum line by condensation of WF6 and the gaseous solvent, i.e., CF4 from the calibrated part of the vacuum line to the glass ampoules 4 mm o.d. and 56 mm in length (approx. 0.25 mL volume). Small amounts of 3He, i.e., less than 3.0 103 mol/L, were then added before sealing by a torch. These samples, at total densities in the range 0.7–1.6 mol/L, were fitted into the standard 10 mm o.d. NMR test tubes (Wilmad-Glass Co., 513-3PP) with liquid heavy water D2O in the annular space. The reference samples were 1 M Na2WO4 in D2O for 183W NMR spectra (the line width at half maximum was less than 0.4 Hz; pD 9) and liquid CFCl3 for 19F NMR spectra. The lock system, operating at 76.8464 MHz, allows the stable magnetic field of the strength of B0 = 11.75 T to be preserved. The measurements were performed at a constant temperature of T = 300 K.
2.2. Measurements of NMR spectra High resolution 183W and 19F NMR spectra were recorded on a Varian-INOVA 500 spectrometer equipped with a low-band BB10 probe operating at 20.83 MHz and 471.12 MHz frequencies, respectively. The 3He NMR spectra were recorded at a frequency of approx. 381.36 MHz in the specially adopted helium probe. Line broadening of 1 Hz was used. The insensitive nuclei enhanced by polarization transfer (INEPT) pulse sequence from 19F to 183W was used in order to increase the signal-to-noise ratio. Application of this pulse sequence is especially important for the gas-phase NMR studies of WF6, since for this case the density of observed nuclei is three orders of magnitude lower than in the liquid state. The INEPT spectra of 183W for the gas-phase measurements were decoupled from 19F during acquisition of the NMR signal.
3. Results and discussion 3.1.
183
W and
19
F spectra of WF6
The 183W and 19F spectra of WF6 in the gas and liquid phases are shown in Fig. 1. The liquid-state 183W NMR spectrum of WF6 consists of a septet. The indirect spin-spin coupling between tungsten and fluorine 1J(183W,19F) is 43.75(24) Hz, which gives the reduced spin-spin coupling 1K(183W,19F) = 9.18 1020 N A2 m3. The 19F NMR gas-phase spectrum of WF6 shown in Fig. 1A is decoupled from the fluorine because of substantial broadening of the peaks and loss of signal-to-noise ratio. Only one-seventh of molecules have tungsten nuclei bearing a non-zero spin; thus in the 19F NMR spectra, only this part of the signal is split into a doublet. For 19F NMR signal of WF6, the shift between the central line and the middle of the doublet is less than 0.2 Hz, and therefore, the isotope effects are negligible. The full width at half maximum of the helium-3 peak is much smaller than those of fluorine and tungsten peaks (Fig. 1C).
Fig. 1. 183W and 19F NMR spectra of WF6 (A and B, respectively) for a neat liquid (red curves) and the gaseous mixture with CF4 (blue curves; p = 30 bar) recorded at temperature T = 300 K and the magnetic field of strength B0 = 11.75 T. 3He NMR spectrum of the gaseous mixture sample without line broadening (C). The frequency is given relative to the central line of the multiplet acquired for the liquid sample which is m(183W) = 20 833 943.1 Hz for (A) and m(19F) = 471 117 236.9 MHz for (B). These frequencies correspond to chemical shifts 1115.1 ppm (A; relative to 1 M Na2WO4 in D2O) and 166.2 ppm (B; relative to neat CFCl3). The frequency of the peak of helium is m(3He) = 381 357 449.3 Hz.
3.2. The magnetic dipole moment of
183
W
The spin precession frequency of the
183
W nucleus in WF6 is
mð183 WÞ ¼ cð183 WÞ½1 rð183 WÞB0 ;
ð1Þ
where c(183W) is the gyromagnetic ratio of the tungsten-183 nucleus, r(183W) the isotropic part of the nuclear shielding tensor for that nucleus in WF6, and B0 the strength of the static magnetic
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
Fig. 2. The dependence of
183
W,
19
F, and 3He resonance frequencies on the density of the gas mixture with CF4.
field used in the experiment. In order to obtain the magnetic moment from Eq. (1), one has to determine precisely the strength of the magnetic field B0. The strength of B0 can be obtained measuring the resonance frequency of the second nucleus whose dipole moment is known precisely. In this work, helium-3 has been chosen for this purpose since 3He is highly inert and its resonance frequency is perturbed by intermolecular interactions to a very small extent (<0.1 ppm). The samples consisted of a mixture of 3He gas with WF6 dissolved in CF4 which allows to measure 3He and 183W resonance frequencies at the same strength of the magnetic field B0. Therefore, the dipole moment of the 183W nucleus is
lð183 WÞ ¼
mð183 WÞ ð1 rð3 HeÞÞ 3 lð HeÞ; mð3 HeÞ ð1 rð183 WÞÞ
3
ð2Þ
where l(3He) = 2.127625306(25)lN [20], r0(3He) = 59.96743(10) ppm [21], and the spin number for tungsten-183 is 1/2. In Eq. (2) the strength of the magnetic field B0 is given implicitly. For the 183W nucleus, the major correction to the dipole moment of the nucleus 183W is its magnetic shielding,
r(183W) = 6221.0 ppm [9]. However, in order to obtain accurate experimental results, one has to additionally take into account two effects: (i) the effect of intermolecular interactions on magnetic shielding which is nearly 20 ppm, and (ii) the decrease of the strength of magnetic field due to magnetic susceptibility (a few ppm). These two effects vanish if one extrapolates the 183 W resonance frequency to the zero-density limit. The range of experimentally accessible pressures of a mixture of WF6 and a small amount of 3He is too narrow to obtain sufficiently precise extrapolation to the zero-density limit (WF6 boiling point at the atmospheric pressure is 17 °C), thus an additional gaseous solvent, CF4, was applied. The resonance frequency of a nucleus measured for the gas sample at the moderate pressure (p < 50 bar) depends weakly on the density [22]. Therefore, it is sufficient to limit the power series of the resonance frequency in density to only the two first terms,
mð183 WÞ ¼ m0 ð183 WÞ þ m1 ð183 WÞqCF4 þ . . .
ð3Þ
where m0 is the resonance frequency at the zero-density limit and m1 depends on the intermolecular interactions of WF6 and the bulk
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
Table 1 The resonance frequencies extrapolated to the zero density limit (m0), the slope of the resonance frequency dependence of the solvent density (m1), and the gas-to-liquid shifts (DdGL = dL dG) for 183W, 19F, and 3He nuclei. Nucleus
m0/MHz
m1/(Hz mL/mol)
DdGL/ppm
183
20.833612(1) 471.115140(9) 381.357519(3)
16(1) 125(8) 54(3)
15.89 4.45 –
W 19 F 3 He
magnetic susceptibility of the sample. The density dependence of 183 W, 19F, and 3He resonance frequencies are shown in Fig. 2. For densities up to 1.5 mol/L these dependencies are linear; thus, the zero-density limit is determined by finding the best fit parameters of a linear dependence to experimental data. Obtained frequencies are given in Table 1. The magnetic moment of the 183W nucleus obtained from Eq. (2) is l(183W) = 0.116953(18) lN which gives the g-factor, gI = lX/I, 0.233901(18) and the gyromagnetic ratio cI = gIlN/⁄, 1.120249 107 rad s1 T1 (for the ‘‘bare”, i.e., not shielded by electrons) nucleus of tungsten-183. The length of the nuclear magpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi netic dipole moment is 1 þ 1=I times larger than its maximum projection, usually referred to as a magnetic dipole moment of pffiffiffi the nucleus. Thus, for the 183W nucleus, the total length is 3 times larger than its projection reported above, 0.202569(31) lN. The obtained data differs from the magnetic moment of tungsten-183 reported by Stone [14] in his ‘‘Table of nuclear magnetic dipole moments” (Stone used data reported in Ref. [10]), l(183W) = 0.11778476(9) lN, by 0.000834 i.e. 0.71%. The error bars given in the parenthesis for the result from Ref. [14] reflect the precision of the measurements (i.e., spread of data) rather than their accuracy (i.e., proximity to the true value), since the relativistic part of the isotropic shielding of the 183W nucleus in WF6, which is twice the non-relativistic term, was neglected. However, even taking into account the relativistic contribution, the relative uncertainty of the obtained 183W dipole moment is dominated by the uncertainty of r(183W) derived from theory (±200 ppm, estimated as 5% of the relativistic contribution to the isotropic shielding), rather than from the experiment (±2 ppb). 3.3. Gas-to-liquid shift Usually, the resonance frequency of a nucleus in a molecule increases when the sample state passes from a dilute vapour to a liquid (183W and 19F resonance frequencies of WF6 follow this trend, see Fig. 2). Therefore, the gas-to-liquid chemical shift is positive, while the difference between shielding in the liquid state and the gas phase is negative. There are two contributions to this effect: the bulk magnetic susceptibility of the liquid and intermolecular interactions between molecules. For a sample of the shape of a long cylinder, the magnetic susceptibility contribution of the shift equals one third of the volume magnetic susceptibility of a liquid, vV [23]. Taking into account that the molar magnetic susceptibility vM for WF6 is 7.5 ppm (in SI units) [24] and its density is 3.37 g/mL at 300 K, one finds that the bulk magnetic susceptibility changes the 183W and 19F chemical shifts observed in the liquid-state by 2.5 ppm. The differences of chemical shifts between the gas phase and the liquid state found from the experiment for 183W and 19F nuclei are 4.45 ppm and 15.89 ppm, respectively. Thus, the contribution to differences of shielding between the gas phase and the liquid state which characterizes the strength of intermolecular interactions in the liquid phase,
DrGL ¼ rðliquidÞ r0 ðgasÞ þ vm=3;
ð4Þ
Fig. 3. 183W NMR spectrum of WO2 4 in H2O before (A) and after (B) addition of a small amount of hydrochloric acid (the signal to the right) referenced to the signal of 1 M Na2WO4 in D2O (the signal to the left). The spectrum is obtained using a system of two coaxial NMR tubes, which consists of 1 M Na2WO4 solution in D2O placed in the inner 5 mm NMR tube and 1 M Na2WO4 solution in H2O placed between that tube and the outer 10 mm NMR tube.
are DrGL(19F) = 6.9 ppm and DrGL(183W) = 18.4 ppm, which means that 183W and 19F nuclei are deshielded when the state of the sample changes from the gas phase to the liquid state. These differences are much larger than those which are usually observed for light nuclei (e.g., |DrGL| <0.5 ppm for 1H). 3.4. Measurements of WO2 4 One of the references of the tungsten-183 chemical shift is the 1.0 M heavy water solution of Na2WO4 at pD = 9 which is easier to handle then neat WF6. The tungstate oxo-anion WO2 4 is soluble in water above pH = 3 [25] and pH of 0.1–1.0 M solutions of Na2WO4 in water is approx. 9. In this range of concentrations, the 183W signal of WO2 is 3.15 ppm less shielded than that extrapolated to 4 infinite dilution. Moreover, it is found that the 183W shielding of WO2 4 for solution in D2O is 1.32 ppm smaller than if Na2WO4 is dissolved in H2O (see Fig. 3). The ratio of the 183W spin-precession frequency in liquid WF6 to the 2H spin-precession frequency of D2O obtained in the experiment, m(183W)/m(2H) = 0.2711072(18), is in agreement with that reported previously [10], m(183W)/m(2H) = 0.2711106(2). It is found that 183W absolute nuclear magnetic shielding for 1 M WO2 4 in D2O (the primary standard) is 5090 ppm and for neat WF6 is 6205 ppm (the secondary standard). These values are uncorrected for the bulk magnetic susceptibility of the sample; however, since these corrections are at least two orders of magnitude smaller than the uncertainty of the computations, they are negligible. 4. Conclusions It is found that the more reliable value of the nuclear magnetic moment of the 183W nucleus is l(183W) = 0.116953(18) lN (l(183W) = 0.590704(88) 1027 J/T in SI units). For determination of l(183W) from 183W NMR of WF6 corrections originating from the nuclear magnetic shielding, intermolecular interactions and bulk magnetic susceptibility are pronounced and they must be applied in order to obtain an accurate result. The value of the tungsten183 dipole moment might by further improved if a more accurate
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P. Garbacz, W. Makulski / Chemical Physics xxx (2017) xxx–xxx
value of shielding of 183W in WF6 could be known, since its uncertainly mainly determines the error bars of the magnetic moment of 183 W. Obtaining of the accurate value of the magnetic dipole moment for heavy atoms nuclei is still a challenge; thus, the experimentally found magnetic moment of tungsten-183 may be useful for a test of theoretical computational methods. Acknowledgement This work was financed by the National Science Center (Poland) grant according to decision No. DEC-2011/01/B/ST4/06588. References [1] A. Antušek, K. Jackowski, M. Jaszun´ski, W. Makulski, M. Wilczek, Chem. Phys. Lett. 411 (2005) 111–116. [2] M. Jaszun´ski, A. Antušek, P. Garbacz, K. Jackowski, W. Makulski, M. Wilczek, Prog. NMR Spectroscopy 67 (2012) 49–63. [3] K. Jackowski, P. Garbacz, Nuclear magnetic moments and NMR measurements of shielding, in: K. Jackowski, M. Jaszun´ski (Eds.), Gas Phase NMR, The Royal Society of Chemistry, Cambridge, 2006, pp. 95–122. [4] J. Mason (Ed.), Multinuclear NMR, Plenum Press, New York, 1987. [5] K. Jackowski, M. Jaszun´ski, M. Wilczek, J. Phys. Chem. A 114 (2010) 2471–2475. [6] J. Autschbach, T. Ziegler, Encyclopedia of NMR, J. Wiley, Chichester, 2002, pp. 306–323. [7] L.W. Liu, National Sci. Rev. 3 (2016) 204–221.
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