1. Lecture Date: February 11 th, 2008 Nuclear Magnetic Resonance 1

2. Nuclear Magnetic Resonance  Reading for NMR: –Chapter 19 of Skoog, et al. –Handout: “What SSNMR can offer to organic chemists”  Nuclear Magnetic Resonance (NMR) –Nuclear spin transitions, in the 5-900 MHz range –Magnetic resonance imaging (MRI)

3. The Electromagnetic Spectrum  NMR, MRI  EPR/ESR

4. What is NMR?  NMR is an experiment in which the resonance frequencies of nuclear magnetic systems are investigated.  NMR always employs some form of magnetic field (usually a strong externally applied field B 0 )  NMR is a form of both absorption and emission spectroscopy, in which resonant radiation is absorbed by an ensemble of nuclei in a sample, a process causing detectable emissions via a magnetically induced electromotive force. A. Abragam, The Principles of Nuclear Magnetism, 1961, Oxford: Clarendon Press.

5. Things that can be learned from NMR data…  Covalent chemical structure (“2D structure”) –Which atoms/functional groups are present in a molecule –How the atoms are connected (covalently bonded)  3D Structure –Conformation –Stereochemistry  Molecular motion  Chemical dynamics and exchange  Diffusion rate  3D Distribution of NMR spins in a medium – an image! –(Better known as MRI)  Plus many more things of interest to chemists…

6. History of NMR  1920-1930: physics begins to grasp the concepts of electron and nuclear spin  1936: C. J. Gorter (Netherlands) attempts to study 1 H and 7 Li NMR with a resonance method, but fails because of relaxation  1945-6: E. M. Purcell (Harvard) and F. Bloch (Stanford) observe 1 H NMR in 1 kg of parafin at 30 MHz and in water at 8 MHz, respectively  1952: Nobel Prize in Physics to Purcell and Bloch  1957: P. C. Lauterbur and Holm independently record 13 C spectra  1991: Nobel Prize in Chemistry to R. R. Ernst (ETH) for FT and 2D NMR  2002: Nobel Prize in Chemistry to K. Wuthrich  2003: Nobel Prize in Medicine to P. C. Lauterbur and P. Mansfield for MRI P. C. LauterburF. Bloch E. M. PurcellR. R. Ernst Photographs from www.nobelprize.org

7. Nuclear Magnetism  A nuclear electromagnet is created by the nucleons (protons and neutrons) inside the atomic nucleus.  This little electromagnet has a magnetic moment (J T -1 ) –The magnetic moment is proportional to the current flow through the “nuclear loop”  The nucleus looks like a dipole to a distant charge center N S From http://education.jlab.org

8. Basic NMR Theory  In a strong applied magnetic field (B 0 ), certain atomic nuclei will align or oppose this field.  This alignment is caused by the magnetic moments of the nuclei, which themselves are caused by the internal structure of the nucleus. Two nuclear properties stand out: –Spin (1/2 for 1 H, 13 C, etc…) –Gyromagnetic ratio  An excess of alignments is found in the lower energy state (determined by a Boltzmann distribution).  At room temperature, this excess is very small, typically only 1 part per trillion!

9. Nuclear Spin  In a classical sense the bulk nuclear magnetization is observed to “precess” at the Larmor frequency (usually several hundred MHz):  The constant  is the magnetogyric ratio. angular (rad/s)linear (Hz, cycles/s) B0B0

10. Elements Accessible by NMR Figure from UCSB MRL website White = only spin ½ Pink = spin 1 or greater (quadrupolar) Yellow = spin ½ or greater

11. Pulsed vs. Continuous-Wave NMR  NMR effects are most commonly detected by resonant radio-frequency experiments  Continuous-wave NMR: frequency is swept over a range (e.g. several kilohertz), absorption of RF by sample is monitored –Historically first method for NMR –Poor sensitivity –Still used in lock circuits  Pulsed NMR – short pulses (at a specific frequency) are applied to the sample, and the response is monitored. –Much more flexible (pulse sequences followed from this…) –Short pulses can excited a range of frequencies

12. NMR Theory: The Rotating Frame  The magnetization precesses at the Larmor frequency, the RF field(s) oscillate at or near this same frequency  The “rotating frame” rotates at this frequency, simplifies the picture for analysis and understanding Frame rotating at the Larmor frequency (hundreds of MHz) Frame is now still eye zz x y

13. Spin Systems  The reason NMR is so applicable to structural problems is that the governing interactions can be separated and treated individually –Experimentally, this results in spectral simplification (in that transitions are not hopelessly entangled) and also allows for detailed manipulations (pulse sequences) to extract information  This involves separation of electronic Hamiltonian from the nuclear spin Hamiltonians  NMR is thus “simplified” in that its data can be linked back to “spin systems”. Examples of spin systems: –Several 1 H nuclei (i.e. hydrogen) within 2 or 3 covalent bonds of each other –A 1 H nucleus attached to a 13 C nucleus

14. NMR Theory: RF Pulses z x y Drawing depicts a 90 o pulse z x y  RF pulses are used to drive the bulk magnetization to the desired position  The action of an RF pulse is determined by its frequency, amplitude, length and phase  For an on-resonant pulse, the right hand rule predicts its action Drawing depicts a 180 o pulse

15. NMR Theory: RF Pulses and Spin Echoes An RF pulse: Two pulses: echo (delays and extra pulse) Actually not “solid”, contains RF frequencies

16. Selection Rules  Single-quantum transitions (  m = +/- 1) are allowed by angular momentum rules (which govern spins in NMR).  Single-quantum states are directly detected in NMR experiments  However, it is possible to excite double-quantum states (or zero- quantum, triple-quantum, etc…), let them evolve with time, then convert them back to SQ states for observation    Energy levels for two coupled spins showing SQ (single quantum) transitions in green and forbidden ZQ (zero quantum) and DQ (double quantum) transitions in red SQ X X

17. NMR Theory: T 1 Relaxation  T 1 relaxation: longitudinal relaxation (re-establishment of Boltzmann equilibrium) by spins interacting with the “lattice”  In practice, T 1 controls how quickly FT experiments can be repeated for signal averaging  Measurements of T 1 can provide useful data on molecular motions x z y

18. NMR Theory: T 2 Relaxation  T 2 relaxation transverse relaxation (dephasing of coherence) by spins interacting with each other  Controls how long magnetization can be kept in the x-y plane  Controls the linewidth (FWHH) of the NMR signals: x z y

19. NMR Theory: The Chemical Shift  The electrons around a nucleus shield are circulated by the big magnetic field, inducing smaller fields.  Anisotropy:  Units – ppm:  Shift-structure correlations – the basis of NMR as an analytical tool.  Shift-structure correlations are available for 1 H, 13 C, 15 N, 29 Si, 31 P and many other nuclei TPPO PbSO 4 x y z Above: the chemical shift in solids is not a single peak!

20. Typical 1 H NMR Chemical Shielding

21. Typical 13 C NMR Chemical Shielding

22. Other Nuclei: 17 O NMR Note – 17 O NMR requires labeling or concentrated solutions, and suffers from large solution-state linewidths (caused by quadrupolar relaxation)

23. NMR Theory: The Chemical Shift  Contributions from electronegativity and ring current effects: Dailey et. al., J. Am. Chem. Soc., 77, 3977 (1955).

24. NMR Theory: The Chemical Shift  Contributions from ring current effects  Above center of ring (z-axis): shielding  In plane of ring (  axis): deshielding Figure from http://www.chemlab.chem.usyd.edu.au/thirdyear/organic/field/nmr/ans02.htm

25. NMR J-Coupling  The J-coupling is an effect in which nuclear magnetic dipoles couple to each other via the surrounding electrons.  The effect is tiny but detectable!  Typical J-values – 2-4 J HH can range from –15 to +15 Hz and depends on the number of bonds, bond angles, and torsion angles – 1 J CH can range from 120 to 280 Hz, but typically is ~150 Hz in most organics – 2-4 J CH ranges from –15 to +15 Hz and depends on effects similar to the 2-4 J HH  The narrow ranges that certain 1 H and 13 C J-coupling values fall into make spectral editing and heteronuclear correlation experiments possible!!!

26. J-Coupling: Effects on NMR Spectra  Two basic types of coupling –Homonuclear (e.g. 1 H- 1 H) –Heteronuclear (e.g. 1 H- 19 F)  Weak coupling –Large difference in frequency  >> J  #Lines = 2 n I + 1  All heteronuclear coupling is “weak”  More complex splitting patterns can be visualized using Pascal’s triangle (see text)  Strong coupling –Small difference in frequency  ~ J  Complex patterns Figure simulated in Bruker Topspin 2.0 DAISY module Inspired by S. W. Homans, A Dictionary of Concepts in NMR, Oxford 1989, p297.

27. J-Coupling: Effects on NMR Spectra  Example: monofluorobenzene  Homonuclear coupling between 1 H: –ortho-coupling –meta-coupling –para-coupling  Heteronuclear coupling between 1 H and 19 F: –As above (ortho, meta, and para). –Observed from the 19 F, appears as a doublet of triplets of triplets (ttd)  Fluorine can be decoupled from the 1 H spectrum (not shown) para ortho meta

28. Structural and Conformational Analysis  J-coupling is widely used (in conjunction with 2D NMR) to assemble portions of a molecule –In this case, the J-coupling is simply detected in a certain range and its magnitude is not examined closely  J-coupling is also used to study conformation and stereochemistry of organic/organometallic/biochemical systems in solution –In this case, the J-coupling is measured e.g. to the nearest 0.1 Hz and analyzed more closely W. A. Thomas, Prog. NMR Spectros., 30 (1997) 183-207.

29. J-Coupling: Angle Effects  Karplus relationships – the effects of bond and torsion angles on J-coupling  Bond angles, dihedral (torsion) angles, 4 and 5- bond angles Dihedral angle (radians) Coupling constant (Hz)

30. Dipolar Coupling  The magnetic dipolar interaction between the moments of two spin-1/2 nuclei –One spin senses the other’s orientation directly through space  The dipolar coupling is simply related to the internuclear distance between the spins:  The truncated (secular) dipolar Hamiltonians (relevant to NMR) have the form:

31. Dipolar Coupling  Example – what’s the dipolar coupling between a 13 C and a 15 N nucleus 1.32 angstroms apart?

32. The Nuclear Overhauser Effect  The idea: detect the “cross-relaxation” caused by instantaneous dipolar coupling in an NMR or EPR experiment.  This was conceived by A. W. Overhauser, while a graduate student at UC Berkeley in 1953  Overhauser predicted that saturation of the conduction electron spin resonance in a metal, the nuclear spins would be polarized 1000 times more than normal!!!

33. The Nuclear Overhauser Effect  Dipolar coupling is a direct magnetic interaction between the moments of two spin-1/2 nuclei.  The coherent effects of dipolar coupling are averaged away in solution-state NMR by rapid molecular tumbling.  However, the dipolar interaction can still play a role via in solution-state NMR via dipolar cross- relaxation mechanisms, better known as the nuclear Overhauser effect (NOE).

34. NMR Spectrometer Design  The basic idea:

35. NMR Magnets  Superconducting magnets:

36. Resonance  The natural frequency of a inductive-capacitive circuit:  The NMR system requires a resonant circuit to detect nuclear spin transitions – this circuit is part of the probe

37. Resonant Circuits in Probes  Figure from Bruker Instruments

38. NMR Probe Design  The NMR probe – designed to efficiently produce an inductance (~W) and detect the result (< mW)

39. NMR Electronics  NMR transmitter and receiver designs

40. Further Reading  A. E. Derome, “Modern NMR Techniques for Chemistry Research”, Pergamon 1987.  P. W. Atkins and R. S. Friedman, “Molecular Quantum Mechanics, 3 rd Ed.”, Oxford 1997.  A. Abragam, “Principles of Nuclear Magnetism”, Oxford, 1961.  R. R. Ernst, G. Bodenhausen, and A. Wokaun, “Principles of Nuclear Magnetic Resonance in One and Two Dimensions”, Oxford, 1987.  C. P. Slichter, “Principles of Nuclear Magnetic Resonance”, Springer-Verlag, 1996.