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Alternative Approach to the Standardization of NMR Spectra. Direct Measurement of Nuclear Magnetic Shielding in Molecules Karol Jackowski,*,† Michał Jaszun´ski,‡ and Marcin Wilczek† Laboratory of NMR Spectroscopy, Faculty of Chemistry, UniVersity of Warsaw, Pasteura 1, 02-093 Warszawa, Poland, and Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01-224 Warszawa, Poland ReceiVed: October 7, 2009; ReVised Manuscript ReceiVed: January 8, 2010
Exploring the relation between shielding constants, resonance frequencies and magnetic moments of the nuclei we demonstrate that nuclear magnetic shielding can be directly observed from NMR spectra. In this approach, the absolute shielding constants of all the nuclei can be related to a single reference scale, with atomic 3He as the primary standard. The accuracy of the data obtained using our method is confirmed comparing the 1H and 13C shielding constants for a series of deuterated compounds with those determined analyzing the traditional chemical shifts. Since the use of helium-3 is not in general a practical alternative, we next transfer the reference standard to the 2H signals of external lock solvents, in this way making the method easy and ready for application with most NMR spectrometers. Finally, we illustrate our new method with the measurements of the 2/1H primary isotope effects in several liquid deuterated solvents. δi ) (σref - σi)/(1 - σref) ≈ σref - σi
Introduction
(1)
1,2
Since its discovery in 1950, the chemical shift became the most important single parameter to be derived from the NMR spectrum. In most NMR studies the resonance frequencies (νi, νref) of sample (i) and reference (ref) nuclei are observed and the chemical shift is determined according to the formula: δi ) (νi - νref)/νref. It is well-known that the resonance frequencies can be precisely measured, but the problem of referencing of chemical shifts is complex and requires specific conventions described in detail by IUPAC.3-6 In particular, for each magnetic nucleus one chemical compound is assigned, which can be applied as the internal or external reference standard. The external referencing seems to be much better for applications in multinuclear magnetic resonance as it is always free from the errors due to intermolecular effects. It requires a bulk susceptibility correction, because the investigated and reference compounds are in different compartments, but this difficulty can be solved in NMR spectroscopy.7,8 Stable superconducting magnets allow for the valuable modification of external referencing when the sample and reference compounds are measured separately. The latter approach, known as the substitution method of referencing5 is fairly universal and can be easily applied for gases, liquids and solids. We focus in this work on the fundamental problems that appear when the chemical shifts are used for the determination of nuclear shielding parameters. At this point we shall limit our discussion exclusively to the isotropic medium, where nuclear magnetic shielding can be described by scalars known as shielding constants (σref, σi) but the present method may be easily extended for any case of more general application. The chemical shift is related to the appropriate shielding constants as follows: * Corresponding author. E-mail:
[email protected]. † University of Warsaw. ‡ Polish Academy of Sciences.
The latter approximation is reasonably accurate for small shielding constants (σ < 10-3), so for light nuclei the chemical shift is almost equal to the shielding difference with the opposite sign.3,4 Equation 1 enables bypassing the problems related to the measurement of the shielding as originally defined, that is with respect to the bare nucleus. However, it means that each magnetic nucleus has its own absolute shielding scale. To establish this scale, accurate data taken from quantum chemical calculations and/or microwave spectra are used, and the shielding is determined following the analysis of an isolated molecule of a reference compound: H2 for protons,9,10 CO for 13C11 and 17 12 O, NH3 for 15N,13 HF for 19F,14 COS for 33S,15,16 etc. Appropriate NMR measurements of shielding for these reference compounds must be performed in the gas phase, and the results should be extrapolated to the zero-density point. Once the first value on the absolute scale is fixed, absolute shielding constants for the nucleus of interest in other compounds can be easily determined by using chemical shifts. Although often the use of chemical shifts allows us to forget about all these problems, the introduction of a separate scale for each isotopic species requires that reference compounds are defined using specific conventions.5 The latter problem can be bypassed by applying a unified scale of chemical shifts (Ξ),17,5 which is defined as the ratio of observed frequency of a sample containing any X nuclide to the proton frequency of tetramethylsilane (TMS) in a dilute solution, below 1% of volume fraction, in CDCl3 when both experiments are carried out in the same magnetic field: Ξ ) νX(sample)/νH(TMS, 1% in CDCl3). The determination of shielding constants in molecules is complex and it would be much better if the absolute value of shielding (σi) instead of the chemical shift (δi) could be directly read from the NMR spectrum and if the same reference standard of shielding could be used for different nuclei. We present below such a procedure with the application of helium-3 gas as the universal reference standard of nuclear magnetic shielding. To obtain accurate results, we use the best recently calculated value
10.1021/jp9096056 2010 American Chemical Society Published on Web 01/29/2010
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TABLE 1: Direct Measurements of Proton Shielding (σH*/ppm) for Residual Hydrogen Atoms in Deuterated Solvents Using Helium-3 Gas as the Universal Reference Standarda no.
solvent
lock signal
observed protonsb
νH(TMS)c
νHc
νHec
δHd
σHe
σH *
σ H - σH *
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
cyclohexane-d12 acetone-d6 methanol-d4 methanol-d4 water-d2 benzene-d6 chloroform-d DMSO-d6 toluene-d8 toluene-d8 toluene-d8 toluene-d8 acetonitrile-d3 nitromethane-d3 ethanol-d6 ethanol-d6
C6D12 -CD3 -CD3 -CD3 D2 O C6 D 6 CDCl3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3
CH CH CH OH OH CH CH CH CH (methyl) CH (ortho) CH (meta) CH (para) CH CH CH (methyl) CH (methylene)
500.6076211 500.6069912 500.6065000 500.6065000 500.6061205 500.6049219 500.6048968 500.6069914 500.6074684 500.6074684 500.6074684 500.6074684 500.6071350 500.6057243 500.6077127 500.6077127
500.6081904 500.6081833 500.6081847 500.6089486 500.6081703 500.6081654 500.6081916 500.6081777 500.6081876 500.6106343 500.6106944 500.6106536 500.6081884 500.6081825 500.6081833 500.6094084
381.3586331 381.3581518 381.3577809 381.3577809 381.3574902 381.3565765 381.3565562 381.3581531 381.3585162 381.3585162 381.3585162 381.3585162 381.3582635 381.3571883 381.3587056 381.3587056
1.137 2.381 3.365 4.891 4.095 6.479 6.582 2.370 1.437 6.324 6.444 6.363 2.104 4.910 0.940 3.387
31.736 30.492 29.508 27.982 28.778 26.394 26.291 30.503 31.436 26.549 26.429 26.510 30.769 27.963 31.933 29.486
31.686 30.438 29.463 27.937 28.729 26.343 26.238 30.453 31.385 26.498 26.379 26.459 30.721 27.914 31.890 29.443
0.050 0.053 0.045 0.045 0.049 0.050 0.054 0.050 0.051 0.051 0.051 0.051 0.048 0.049 0.043 0.043
a According to eq 2, using µH ) 2.792 847 356 µN,20 µHe ) -2.127 625 306 µN, and the tabulated measured frequencies (νH, νHe). Gaseous sample of helium-3 in SF6 described in the text. b Residual 1H peaks from deuterated solvents. c NMR frequencies (MHz) for external liquid TMS, residual hydrogen atoms in deuterated solvents, and the reference sample of 3He, respectively. d δH ) [νH - νH(TMS)]/νH(TMS) (ppm) when pure liquid TMS is used as the external reference standard. e Applying eq 1 and σH(TMSliq, 300 K) ) 32.873 ppm (see the text).
of magnetic shielding in an isolated helium-3 atom18 and we refer to our previous investigation of resonance frequency for the same atom.19 The proposed method starts with the exact measurement of resonance frequencies, similarly as is done for the unified scale of chemical shifts, but it aims to give the absolute nuclear shielding in molecules instead of the frequency ratio (Ξ).17,5 Actually, it permits direct reading of shielding constants from 1H NMR spectra and can be extended to many other nuclei (as shown for 13C and 2H in this work) when accurate values of their magnetic moments are known. We have selected on purpose a group of popular deuterated solvents as samples to demonstrate the performance of the proposed method. We show that the parametrization of absolute shielding can be transferred from helium-3 atoms to the shielding of deuterons in solvents, which are commonly used in routine NMR measurements for the stabilization of external magnetic field (deuterium lock). Thus, it follows that such deuterated solvent can be used as the secondary reference standard of nuclear magnetic shielding. We verify the latter approach to the standardization of magnetic resonance spectra presenting the measurements of shielding constants from 13C NMR experiments as an example. Finally, we compare the shielding of 1H and 2H nuclei in the same molecules and estimate the primary isotope effects on the basis of the described new method of measurements. Experimental Section A reference gas sample (3He in SF6) was prepared by condensing SF6 from the calibrated part of the vacuum line to a 4 mm o.d. cylindrical glass ampule (∼5.5 cm long), adding a small amount of helium-3 and sealed. Final concentrations of gaseous components in the reference sample were 0.3783 mol · L-1 of SF6 and 0.0086 mol · L-1 of helium-3. Its shielding, σHe(3He in SF6, 300 K) ) 60.0431 ppm, was determined by comparing the observed resonance frequency with the zerodensity point in our previous 3He NMR measurements19 and using the new calculated value of nuclear magnetic shielding in an isolated helium atom (59.967 43 ppm).18 Pure liquid TMS (Aldrich, 99.99+%) was placed in a similar 4 mm o.d. cylindrical glass tube, degassed when TMS was frozen in liquid nitrogen, and sealed. The sealed samples (reference helium-3
and liquid TMS) were fitted into the standard 5 mm o.d. NMR tubes (Wilmad 528-PP), and liquid deuterated solvent was placed in the annular space. All deuterated solvents were the highest grade chemicals available from Aldrich, used without further purification, and they were observed also as pure liquids in 5 mm o.d. tubes (Wilmad 528-PP). NMR measurements of 1H (or 13C) shielding constants for each sample solvent were performed as follows: · First the TMS sample was observed and the 1H (or 13C) resonance frequency of liquid TMS, νH(TMS) (or νC(TMS)), and the frequency of lock signal (νD) were recorded. · Then the same deuterated solvent was observed in 5 mm o.d. tube, locked to the same deuterium signal, and the resonance frequencies of residual protons (νH) (or 13C (νC)) and lock signal (νD) were measured. · Next the reference helium-3 sample was measured with the same deuterated solvent in the annular space and the 3 He and 2H frequencies were collected, νHe and νD. · The cycle was completed observing again the TMS sample and all the above measurements were confirmed when the frequencies of TMS (νH or νC) and deuterium lock (νD) were unchanged. One-dimensional spectra were acquired for all NMR measurements and proton decoupled spectra in the 13C NMR case. All the experiments were carried out for locked samples, spinning sample tubes and at a constant temperature of 300 K, on a Varian INOVA-500 FT spectrometer operating at 500.61, 76.84, and 381.36 MHz for 1H, 2H, and 3He, respectively, and using our homemade three-channel probehead.19 For the same set of samples 13C, 1H, and 2H NMR resonance frequencies were also observed with a Varian switchable-5 BB VT probehead. The lock frequency (2H) was practically constant for all our measurements and all samples, νD ) 76.846 401 5(2) MHz. Results and Discussion Direct Measurements of Proton and Carbon Shielding. Table 1 displays the observed frequencies of (1) protons in pure liquid TMS, (2) the residual protons in selected deuterated solvents, and (3) helium-3 nuclei in our standard gaseous sample. All measurements were performed using the same probe and
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in exactly the same external conditions. From the proton frequencies we have determined the 1H chemical shifts (δH) of residual hydrogen nuclei in deuterated solvents relative to external liquid TMS; cf. Table 1. No corrections for bulk susceptibility effects were applied as the 1H signal of TMS serves only for the transfer of proton shielding scale from the primary reference, H2. Assuming that the absolute shielding of protons in an isolated H2 molecule at 300 K is equal to 26.288 ppm9,10 the shielding parametrization has been transferred from the hydrogen molecule to the cylindrical sample of pure liquid TMS, leading to σH(TMSliq, 300 K) ) 32.873 ppm when the axis of a sample tube is parallel to the external magnetic field.19 This permits the determination of shielding constants (σH) for the residual protons in deuterated solvents according to eq 1 and these values are given in the next column of Table 1. Measuring two resonance frequencies (νX, νY) for molecules X and Y in the same external magnetic field, one can determine any unknown shielding constant σX when the other shielding parameter σY is known and the relevant nuclear magnetic moments (µX, µY) are available with satisfactory accuracy:20-22
νX |µY | IX σX ) 1 · · (1 - σY) νY |µX | IY
(2)
where IX and IY are the spin numbers of X and Y nuclei. (It is worth noting that in eq 2 nuclear magnetic moments can be used instead of their absolute values if one accepts the convention of positive and negative frequencies for magnetic nuclei in NMR experiments.23) As mentioned above, for any application of eq 2, accurate values of nuclear magnetic moments are crucial, and for proton, deuteron, and helium-3 they are discussed in literature. A measurement of the ratio µe/µH in the hydrogen atom leads to the bare proton magnetic moment, µH ) 2.792 847 356(23)µN,20 where µN is the nuclear magneton. A similar experiment for deuterium yields µD ) 0.857 438 230 8(72)µN.20 On the other hand, for helium-3 the experiment provides the magnetic moment of shielded helion, µHe′ ) -2.127 497 719(25)µN.20 Taking into account σHe ) 59.967 43 ppm,18 the most recent value of shielding of an isolated helium-3 atom, we obtain for 3He bare nucleus µHe ) -2.127 625 306(25) µN. Using eq 2, measured frequencies (νH and νHe), the shielding of our reference helium-3 sample (σHe(3He in SF6, 300 K) ) 60.0431 ppm), and the described values of the magnetic moments of bare nuclei (µH and µHe), we have determined all the 1H shielding constants of residual protons in deuterated solvents (σH*). These values are in Table 1 compared with the σH shielding constants obtained in the usual way as described earlier, with the last column of Table 1 showing the difference between σH and σH* parameters. As seen, all the σH - σH* values are in the range 0.043-0.054 ppm and it suggests that some of the parameters used in eq 2 are not yet accurately determined or consistent with the accepted shielding scale for protons.9,10 The σH values are always larger than the σH* parameters; these systematic differences may be due to either inaccuracy of the absolute scale for 1H (for instance in the studies of H2, which provide the primary source of the shielding scale for 1H), or inaccuracy in some value used to obtain σH* (for instance, in the value of the magnetic moment of 3He, a change of 10-7 µN in this magnetic moment leads to a change of 0.05 ppm in the resulting σH*). However, a discrepancy of 0.05 ppm is not critical even for 1H NMR spectra. In general, quantum-chemical calculations of the shielding can reach such
Figure 1. Schematic relations between magnetic shielding of different nuclei explored and described in the present study: (a), (b) direct reading of proton and carbon shielding constants when helium-3 is used as the reference standard, (c) proton and carbon shielding determined with the application of deuterated solvents as the secondary reference standards, (d) verification of the primary isotope effects (0∆H(2/1H)), (e) other possible applications of this method for different nuclei.
accuracy only for the smallest atoms and molecules. At this moment we can assume that the proton shielding scale is known with sufficient accuracy and use the proposed method for the determination of shielding constants instead of chemical shifts. It is sufficient to measure required 1H resonance frequencies and compare them with the frequency of a standard helium-3 sample. Future investigations of nuclear magnetic moments (µH, µHe) and shielding constants (σH, σHe) for standard molecules will certainly minimize all the inaccuracies shown in Table 1. All the measurements presented in Table 1 and described in the previous section were performed with one NMR probe and exactly the same conditions of measurements, except of course different resonance frequencies for protons and helium-3 nuclei. This approach is marked by (a) on the diagram presented in Figure 1. In the next step we have performed similar observations of 13C shielding at the same spectrometer but with two different NMR probes: one for 3He NMR and the other for 13C NMR experiments; the sample units and lock solvents were unchanged. Table 2 gives the details and summarizes the results at this stage, corresponding to approach (b) in Figure 1. As shown, the results are very satisfying and prove that there is no need to use one probe for the exact measurement of shielding. However, in fact, the accuracy of 13C shielding constants in Table 2 is temporarily reduced to (0.9 ppm, the present error bar of the existing absolute scale of shielding for carbon-13 given by σC(CO, isolated molecule) ) 0.6 ( 0.9 ppm,11 since this error is introduced into σC* via magnetic moment of 13C nucleus.21,22 The same problem arises for all the nuclei, for which the most accurate magnetic moments are determined from NMR data and thus depend on the absolute shielding scale. Here we have to add that the proposed new method of shielding measurements neither removes nor solves the problem of bulk susceptibility correction when the helium-3 sample is used as the external standard. The susceptibility correction is simply included in the final result exactly in the same way as it occurs for chemical shifts, and as it is carefully described by Harris et al.6 On the other hand any NMR experiment performed for a gaseous compound with the extrapolation of results to the zero-density point gives immediately the exact value of the shielding constant. Simplified Procedure of Shielding Measurements. As shown in the previous sections, the use of helium-3 as the reference standard of magnetic shielding gives satisfying results. However, the measurement of 3He frequency can be somewhat difficult for common use, because this frequency belongs to the
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TABLE 2: Direct Measurements of 13C Shielding (σC*/ppm) in Deuterated Solvents Using Helium-3 Gas as the Universal Reference Standarda no.
solvent
Lock signal
observed carbons
νC(TMS)b
νCb
νHeb
δCc
σCd
σC*
σ C - σ C*
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
cyclohexane-d12 acetone-d6 methanol-d4 benzene-d6 chloroform-d DMSO-d6 toluene-d8 toluene-d8 toluene-d8 toluene-d8 toluene-d8 acetonitrile-d3 acetonitrile-d3 nitromethane-d3 ethanol-d6 ethanol-d6
C6D12 -CD3 -CD3 C6 D6 CDCl3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3 -CD3
C6D12 -CD3 -CD3 C 6D 6 CDCl3 -CD3 -CD3 dC(1)-CD- (ortho) -CD- (meta) -CD- (para) -CD3 -CN -CD3 -CD3 -CH2-
125.8778041 125.8776438 125.8775211 125.8771252 125.8771169 125.8776457 125.8777644 125.8777644 125.8777644 125.8777644 125.8777644 125.8776805 125.8776805 125.8773266 125.8778259 125.8778259
125.8810593 125.8814089 125.8835993 125.8931957 125.8868075 125.8827476 125.8802827 125.8950196 125.8939353 125.8938209 125.8934643 125.8778203 125.8925493 125.8852045 125.8799276 125.8849185
381.3586333 381.3581482 381.3577752 381.3565784 381.3565522 381.3581534 381.3585135 381.3585135 381.3585135 381.3585135 381.3585135 381.3582592 381.3582592 381.3571872 381.3587006 381.3587006
25.860 29.911 48.286 127.668 76.984 40.530 20.005 137.079 128.465 127.556 124.723 1.111 118.121 62.584 16.696 56.345
160.510 156.459 138.084 58.702 109.386 145.840 166.365 49.291 57.905 58.814 61.647 185.259 68.249 123.786 169.674 130.025
160.513 156.464 138.089 58.724 109.400 145.845 166.367 49.316 57.928 58.837 61.669 185.259 68.270 123.797 169.678 130.037
-0.003 -0.005 -0.005 -0.022 -0.014 -0.005 -0.002 -0.025 -0.023 -0.023 -0.022 0.000 -0.021 -0.011 -0.004 -0.011
a According to eq 2, using µC ) 0.702 369 417 µN,21,22 µHe ) -2.127 625 306 µN and the tabulated measured frequencies (νC, νHe). Gaseous sample of helium-3 in SF6 described in the text. b NMR frequencies (MHz) for external liquid TMS, observed carbon atoms in deuterated solvents and the reference sample of 3He, respectively. c δC ) [νC - νC(TMS)]/νC(TMS) when pure liquid TMS is used as the external reference standard. d Applying eq 1 and σC(TMSliq, 300 K) ) 186.37 ppm.24
TABLE 3: 2H Shielding Constants Determined from Helium-3 (σD*)a, 1H and 13C Shielding Constants Measured Directly from NMR Spectra When the Lock Solvents are Accepted as External Reference Standards of Shielding (σH**, σC**)b, and the Primary Isotope Effects (0∆H(2/1H))c Found for the Selected Functional Groups of the Lock Solventsd no.
solvent
observed nuclei
νHe(MHz)
σ D*
σH**
σH* - σH**
σC**
1 2 3 4 5 6 7 8 9 10 11
cyclohexane-d12 acetone-d6 methanol-d4 water-d2 benzene-d6 chloroform-d DMSO-d6 toluene-d8 acetonitrile-d3 nitromethane-d3 ethanol-d6
-CD2-CD3 -CD3 -OD dCD-CD -CD3 -CD3 -CD3 -CD3 -CD3
381.3586331 381.3581518 381.3577809 381.3574902 381.3565765 381.3565562 381.3581531 381.3585162 381.3582635 381.3571883 381.3587056
31.834 30.570 29.593 28.837 26.441 26.389 30.574 31.525 30.864 28.041 32.020
31.687 30.439 29.464 28.730 26.344 26.239 30.454 31.387 30.722 27.914 31.891
-0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.002 -0.001 -0.000 -0.001
160.522 156.479 138.108 58.731 109.421 145.852 166.390 185.274 123.807 169.692
σC* - σC**
0
-0.009 -0.015 -0.019 -0.007 -0.021 -0.007 -0.023 -0.016 -0.010 -0.014
-0.148 -0.142 -0.130 -0.108 -0.098 -0.151 -0.121 -0.140 -0.143 -0.127 -0.130
∆H(2/1H)
a According to eq 2 with µD ) 0.857 438 230 8 µN20 and measured frequencies: νHe as shown in this table and νD ) 76.846 401 5 MHz. Using eq 2, the actual σD* parameter and appropriate resonance frequencies presented in Tables 1 and 2. c 0∆H(2/1H) ) σH* - σD*, the values of σH* are given in Table 1. d All the shielding constants are given in ppm.
b
uninteresting region, which is usually omitted in standard NMR spectrometers. Harris et al.5 have already noted that gaseous helium-3 could be a good primary reference of chemical shifts “... but this is not practicable”. In the next step marked (c) in Figure 1, we show that for the measurement of shielding it is not necessary to have the 3He NMR capability, it is sufficient to have a deuterium lock, which is available almost in every spectrometer. As shown in Table 3, we have determined the shielding constants of deuterated solvents (σD*); therefore, we can use the 2H lock signal as the secondary reference standard of nuclear magnetic shielding. Applying again eq 2 with all the previous parameters for magnetic moments and shielding, we have obtained a new set of shielding constants for 1H and 13C NMR spectra, σH** and σC**, respectively. The new values are also shown in Table 3, together with the appropriate parameters determined directly with the use of frequency and shielding of gaseous helium-3; cf. Tables 1 and 2. We observe that there is practically no difference between two approaches: the strict application of the primary reference standard of shielding (helium-3) and its simplified for practical use version, based on the deuterated solvents as the secondary reference standards. We summarize this paragraph with a recipe for quick measurements of 1H and 13C magnetic shielding constants. In such a procedure one should:
· use any NMR spectrometer with a superconducting magnet and 4 mm o.d. cylindrical glass tube for a sample of gaseous or liquid compound, e.g., Wilmad 406-PP, · insert the sample tube into a standard 5 mm o.d. tube with deuterated solvent in the annular space (it is important to select the deuterated solvent from Table 3 and use the appropriate signal for locking), · obtain the standard 1H (or 13C) NMR spectrum reading absolute resonance frequencies of sample νH (or νC) and the frequency of lock signal νD, · calculate the shielding constants as follows: σH ) 1 - (νH /νD) · 0.153506104 · (1 - σ* D) σC ) 1 - (νC /νD) · 0.610389782 · (1 - σ* D)
for protons and for 13C nuclei
where σD* values (ppm) are given in Table 3 and the numerical coefficients account for the nuclear magnetic moment and spin ratios. In the present study we have limited the investigations to isotropic shielding constants of 1H, 2H, and 13C nuclei but eq 2 can be also applied to other nuclides and for the determination of suitable secondary standards of shielding for NMR in the
Nuclear Magnetic Shielding in Molecules solid state. It implies that the new method of the determination of nuclear magnetic shielding can be successfully used in the wide range of NMR spectroscopy. Primary Isotope Effects in 2H/1H Shielding. The proposed method of shielding measurements can be applied to solve many new problems in NMR spectroscopy. In particular, it allows for the first direct observation of primary isotope effects in nuclear magnetic shielding of hydrogen; cf. the comparison (d) in Figure 1. Table 3 presents the shielding constants of protons (σH*) and deuterons (σD*) determined for our selected deuterated solvents. It is possible to monitor the primary isotope effects (0∆H(2/1H) ) σH* - σD*) because usually some molecules of deuterated solvents still contain one proton per molecule. Thus, we can observe this isotope effect between two different molecules (isotopomers) immersed in the same solution, e.g., C6D6 and C6D5H for benzene-d6 or C6D12 and C6D11H for cyclohexane-d12. The last column of Table 3 gives the values of 0∆H(2/1H), which show the change of the shielding when heavier deuterons are replaced by protons. These effects are fairly distinct and vary from -0.098 to -0.151 ppm for investigated solvents. We can compare our measurements with the predictions of shielding change in a hydrogen molecule at 296 K given by Sundholm and Gauss:10 the proton shielding in a H2 molecule is 26.288 6(15) ppm while the deuteron shielding in a HD molecule is 26.343 6(48) ppm. The difference gives the primary isotope effect in a hydrogen molecule, 0∆H(2/1H) ) σH - σD ) -0.055(6) ppm. The isotope effects in Table 3 are all in the same direction and of similar magnitude, but they are more significant. Let us note that the present primary effects are measured for different molecules, so their values have to differ. Moreover, we report the values for liquid solvents, not for isolated molecules. The appropriate 2H and 1H NMR signals in our experiments come from the same medium and consequently no bulk susceptibility correction is needed here, but the primary isotope effects can still be significantly modified by molecular interactions. In addition, the results of the present measurements depend on the accuracy of nuclear magnetic moments (µH, µD, and µHe) used in eq 2 and at present it is difficult to estimate the error bars up to the fraction of ppm. Nevertheless, the existing general agreement implies that the proposed method is already suitable for further applications. Conclusion We have presented a new general method of shielding measurements available for isotropic species on a standard NMR spectrometer whenever the spectrometer allows the reading of resonance frequencies of the studied nuclei. As shown, the chemical shifts can be successfully replaced by absolute shielding constants assuming that NMR measurements are simultaneously carried out for the investigated and reference (3He or 2H) nuclei and the final results are evaluated according to eq 2. In addition, the experimental shielding constants determined in this way are suitable for direct comparison with theoretical results obtained for the same molecular objects. The new method allows one to study the primary isotope effects, 0 ∆H(2/1H) as the nuclear magnetic shielding can be precisely measured for the observed nuclei in different isotopomers. In summary, we propose a new alternative approach to the standardization of NMR spectra. The underlying relation
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2475 between the shielding constants, resonance frequencies and magnetic moments is valid for any pair of nuclei in any pair of molecules and thus eliminates the need to define a specific scale for each isotopic species. From the theoretical point of view, it is undoubtedly best to relate all the results to 3Hesfor atomic helium the shielding constant and the magnetic dipole moment are well-known. However, we have verified that pure deuterated solvents can be also applied as the secondary reference standards of magnetic shielding. On the basis of the present results, with a modest modification the operational software program can already be used to print the 1H and 13C shielding constants in NMR spectrum if the sample is in a cylindrical tube, fixed parallel to the external magnetic field and locked to the external deuterated solvent. This configuration is certainly available in most standard NMR spectrometers. It makes the measurements of shielding constants very simple, easily available for everyone and always ready for comparison with other results. In near future it may even be possible to eliminate the use of chemical shifts from NMR spectra of the most popular nuclei. Acknowledgment. We are indebted to Prof. Robin K. Harris for many helpful discussions, and we acknowledge financial support from the Ministry of Science and Higher Education, research grant N N204 244134 (2008-2011). References and Notes (1) Proctor, W. G.; Yu, F. C. Phys. ReV. 1950, 77, 717. (2) Dickinson, W. C. Phys. ReV. 1950, 77, 736. (3) Recommendation for the Presentation of NMR Data for Publication in Chemical Journals. Pure Appl. Chem. 1972, 29, 625. (4) Presentation of NMR Data for Publication in Chemical Journals B. Conventions Relating to Spectra from Nuclei Other than Protons. Pure Appl. Chem. 1976, 45, 217. (5) Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Goodfellow, R.; Granger, P. Pure Appl. Chem. 2001, 73, 1795. Reprinted in Magn. Reson. Chem. 2002, 40, 489. (6) Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Granger, P.; Hoffman, R. E.; Zilm, K. W. Pure Appl. Chem. 2008, 80, 5. Reprinted in Magn. Reson. Chem. 2008, 46, 582. (7) Zimmerman, J. R.; Foster, M. R. J. Phys. Chem. 1957, 61, 282. (8) Smith, A.; Raynes, W. T. J. Cryst. Spectrosc. Res. 1983, 13, 77. (9) Sundholm, D.; Gauss, J.; Scha¨fer, A. J. Chem. Phys. 1996, 105, 11051. (10) Sundholm, D.; Gauss, J. Mol. Phys. 1997, 92, 1007. (11) Raynes, W. T.; McVay, R.; Wright, S. J. J. Chem. Soc., Faraday Trans. 2 1989, 85, 759. (12) Wasylishen, R. E.; Bryce, D. L. J. Chem. Phys. 2002, 117, 10061. (13) Jameson, C. J.; Jameson, A. K.; Oppusunggu, D.; Wille, S.; Burell, P. M.; Mason, J. J. Chem. Phys. 1981, 74, 81. (14) Hindermann, D. K.; Cornwell, C. D. J. Chem. Phys. 1968, 48, 4148. (15) Wasylishen, R. E.; Connor, C.; Friedrich, J. O. Can. J. Chem. 1984, 62, 981. (16) Jackowski, K.; Makulski, W.; Koz´min´ski, W. Magn. Reson. Chem. 2002, 40, 563. (17) McFarlane, W. Proc. R. Soc. London, Ser. A 1968, 306, 185. (18) Rudzin´ski, A.; Puchalski, M.; Pachucki, K. J. Chem. Phys. 2009, 130, 244102. (19) Jackowski, K.; Jaszun´ski, M.; Kamien´ski, B.; Wilczek, M. J. Magn. Reson. 2008, 193, 147. (20) Mohr, P. J.; Taylor, B. N.; Newell, D. B. ReV. Mod. Phys. 2008, 80, 633. (21) Jackowski, K.; Jaszun´ski, M. Concepts Magn. Reson. A 2007, 30, 246. (22) Antusˇek, A.; Jackowski, K.; Jaszun´ski, M.; Makulski, W.; Wilczek, M. Chem. Phys. Lett. 2005, 411, 111. (23) Levitt, M. H. J. Magn. Reson. 1997, 126, 164. (24) Jackowski, K.; Wilczek, M.; Pecul, M.; Sadlej, J. J. Phys. Chem. A 2000, 104, 5955. Erratum. J. Phys. Chem. A 2000, 104, 9806.
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