Christ Church 3 rd Year: Magnetic Resonance. Reading. Topics

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1 Christ Church 3 rd Year: Magnetic Resonance Reading The following sources are recommended for this tutorial: Nuclear Magnetic Resonance by P. J. Hore (Oxford Chemistry Primers). This text contains the basics that you need to know. It s packed with useful marginal notes, correlates closely with the lecture course and might well be a source for exam questions. NMR Spectroscopy by H. Günther provides a more in-depth treatment of many topics. NMR: The Toolkit by P. J. Hore, J. Jones and S Wimperis provides a logical extension to actually calculating quantites of interest in magnetic resonance. Spin Dynamics: Basics of Nuclear Magnetic Resonance by M. H. Levitt is another useful extension to actual calculations. Finally, for the interpretative aspects of NMR (and especially for practice with inorganic NMR nearer to Part IB), I recommend Modern NMR Spectroscopy: A Workbook of Chemical Problems by Sanders, Constable, Hunter and Pearce. This workbook accompanies another textbook on NMR by Sanders and Hunter. You may also find material from the following lecture courses useful: Dr C Timmel (MT 3rd year), Dr T D W Claridge & Dr N J Oldham (MT 3rd year), Dr R G Denning & Prof A J Downs (HT 3rd year) and Dr L J Smith (HT 2nd year). Topics Please cover the following topics in your reading, making notes as appropriate. The physics of magnetic resonance: the magnetic moment, the spin quantum number, the gyromagnetic ratio, space quantization, the resonance condition, the vector model, populations and bulk magnetization. Nuclei suitable for use in NMR, isotopomers and enrichment. Selection rules, chemical shift, the origin of shielding, diamagnetic and paramagnetic shielding, neighbouring group anisotropy, ring current effects, electronic effects, intermolecular interactions. Spin-Spin Coupling, energy level considerations, labeling of spin systems. Energy levels, labelling and splittings in AMX systems, AX 2 systems, AX 3 systems, AX n systems. Coupling to spins with I > 1 2, limits of the simple splitting rules, magnetic equivalence, the origin of the roof effect, strong coupling effects, discussion of Fermi contact interaction and dipole-dipole interactions. Experimental methods: continuous wave and pulsed NMR, introduction of Free Induction Decay (FID) and Fourier Transformation for simple FIDs. The rotating frame, linear and circularly polarized fields, NMR as a coherence phenomenon. Spin relaxation, spin lattice and spin-spin relaxation, the rotational correlation time and the spectral density function, spin relaxation and the vector model, measurement of relaxation times, linewidths, the inversion recovery experiment, the spin echo experiment. Quadrupolar coupling and relaxation. Chemical Exchange, symmetrical exchange, slow and fast exchange limits (quantitatively), intermediate exchange, unsymmetrical two-site exchange.

2 Briefly, two-dimensional NMR: Correlated Spectroscopy (COSY), Exchange Spectroscopy (EXSY) and Nuclear Overhauser Spectroscopy (NOESY). EPR: comparison with NMR, g-values, hyperfine couplings, derivative spectra. Use of hyperfine couplings to probe molecular orbitals via spin densities. Questions Please submit a complete set of answers to following problems. Answers should be sent to me via the R pigeon hole in the PTCL by 2pm Wednesday 10/Nov/ The most powerful NMR spectrometers currently available operate at a Larmor frequency of 900 MHz for protons. (i) How does the energy of one quantum at 900 MHz compare with kt at 298 K? (ii) What are the relative populations of the proton energy levels? (iii) What is the Larmor frequency of 2 H on this spectrometer? (Gyromagnetic ratios, γ: 1 H = T 1 s 1, 2 H = T 1 s 1 ) O has spin magnetic quantum number I = 5 2. Compute the magnitude of the spin angular momentum of this spin and hence draw a diagram illustrating the spin quantization of this spin- 5 2 nucleus (indicating clearly the angles of precession). 3. (i) Is it possible to obtain EPR spectra with NMR equipment? (ii) Assuming g = , what magnetic field would be required to observe EPR in a 400 MHz NMR spectrometer? 4. In Oxford, the Earth s magnetic field strength is approximately 47 mt; in Kursk (Russia) it reaches 190 mt. What will be the Larmor frequency of protons in the Earth s field in the two places? Why is NMR in the Earth s field of limited use, even in Kursk? 5. An NMR spectrometer operating at 100 MHz was used to record the proton spectrum of acetaldehyde, CH 3 CHO. The frequency difference between the resonances of the methyl and the aldehydic protons was 760 Hz. (i) What is the chemical shift difference in parts per million (ppm) between the two resonances? The 1 H spectrum of the same molecule was recorded on another spectrometer which used a magnetic field of T. On this new spectrometer, what is: (ii) the frequency difference in Hz? (iii) the chemical shift difference in ppm, between the two resonances? The splitting of the methyl proton doublet in the MHz spectrum is 2.9 Hz. (iv) What will be the values of the spin-spin coupling constant on the T spectrometer?

3 6. Comment on the difference in 1 H chemical shifts of the indicated protons in these two phenanthrene derivatives. 8.65ppm H 10.35ppm H H C C 7. Comment on the chemical shift values in this molecule: H B +8.9 ppm H A -1.8 ppm 8. The 59 Co chemical shifts of a number if octahdedral cobalt complexes in aqueous solution were found to depend linearly on the wavelength of the first electronic absorption band of the complex. Comment on this observation. 9. The one-bond 13 C- 1 H spin-spin coupling constants in ethane, ethane and ethyne are 125 Hz, 167 Hz and 250 Hz, respectively. Comment on these values in the light of the mechanism of spin-spin coupling. 10. The frequencies of the NMR transition of a nucleus in an AX 3 spin system (X is spin- 1 2 ) are given by: ν A = γ A B 0 (1 σ A )/2π J AX (m X1 + m X2 + m X3 ). (i) Explain the significance of the symbols and the physical origin of the term that contains J AX. (ii) Show that the spectrum of A is a 1:3:3:1 quartet if X is a spin- 1 2 nucleus. (iii) Using the same method, predict the appearance of the multiplet if X is a spin-1 nucleus. 11. Scalar couplings between magnetically equivalent spins do not produce multiplet splittings. Discuss. 12. (i) The 1 H NMR spectrum of CH 4 consists of a single line and it is not possible to measure 2J H H from the spectrum. Explain why this is so.

4 (ii) The 1 H NMR spectrum of dideuteromethane (CD 2 H 2 ) is given below. Rationalise the splitting pattern and explain how you could estimate 2J H H using this spectrum. 13. Cis-decalin (C 10 H 18, below) undergoes flips between two degenerate conformations by chairto-chair inversions in both rings at high temperatures. 13 C spectra taken below 240 K consist of five lines of equal intensity but when the temperature is elevated to 320 K, only three lines appear in the spectrum with one of the lines unaffected by the temperature rise. The 13 C spectra were recorded in a proton-decoupled mode so that the splittings due to the protons are not observed. (i) Account for the fact that only five lines are observed at low temperatures and that three are observed at higher temperatures. (ii) Predict how the line positions and linewidths observed in the NMR spectrum vary over this temperature range? (iii) How would the chemical shifts, transition frequencies and the temperature dependence be affected as the spectrometer frequency is increased by a factor of ten?

5 14. Consider the 1 H NMR spectrum of the borohydride ion (BH 4 ). Noting that the element boron has two isotopes, both of which are NMR active : 10 B (I=3, 20%) and 11 B (I=3/2, 80%), rationalise the appearance of the observed 1 H spectrum. 15. The following data give the observed 31 P chemical shift of phosphate ions involved in the reaction H 2 PO 4(aq) H+ (aq) + HPO2 4(aq) ph δ/ppm Determine the acid dissociation constant of H 2 PO, assuming that all activity coefficients are equal to unity. You may wish to know that δ(h 2 PO ) = 3.41ppm and that 4(aq) 4(aq) δ(hpo 2 4(aq) ) = 5.82ppm.

6 16. Consider the spectra of N-methyl-2,4,6-trinitroaniline recorded at a number of different temperatures: Discuss the appearance of the spectra in terms of an exchange process in this molecule. 17. (i) Explain why the NMR lines of 13 C atoms bonded to the halogen atoms, Cl, Br and I are affected in frequency but not split by spin-spin coupling although all common isotopes of these halogens have non-zero nuclear spin. (ii) Explain why the 1 H spectrum of the NH + 4 ion in solution shows splitting into three lines by the 14 N nucleus but spectra of primary amines show no such splitting for protons bonded to the nitrogen atoms. 18. Discuss the processes that allow nuclear spins to return to equilibrium after disturbance. Name experiments that allow the measurement of the longitudinal relaxation time, T 1 and the transverse relaxation time T 2, respectively. Explain in detail how each of these experiments is performed. 19. Why does the 1 H spin lattice relaxation time of liquid water increases with increasing temperature? 20. Predict the appearance of the 1 H NMR spectrum and the COSY spectrum of ethyl acrylate: H x H b 3 1 O 1' CH 3 2 CH2 2' H a O

7 21. This is a schematic 1 H COSY spectrum of a fragrant substance found in cucumber and melon. The relative intensities of the nine multiplets (a i) in the one-dimensional spectrum (not shown) are 1:1:1:1:1:2:2:2:3 in alphabetical order. It contains only C, H and O. What is its structure? Given the following spin-spin coupling constants, J de = 10.5 Hz, J de = 15.5 Hz, what can be said about the stereochemistry?

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