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Basic principles of NMR NMR signal origin, properties, detection, and processing

Basic principles of NMR NMR signal origin, properties, detection, and processing. Nils Nyberg NPR, Department of Drug Design and Pharmacology. Outline. 10 00 – 10 45 Establishing current knowledge level Nuclear Magnetic Resonance phenomenon Vector model, in and out of the rotating frame

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Basic principles of NMR NMR signal origin, properties, detection, and processing

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  1. NTDR, 2014 Basic principles of NMRNMR signal origin, properties, detection, and processing Nils Nyberg NPR, Department of Drug Design and Pharmacology

  2. NTDR, 2014 Outline • 1000 – 1045 • Establishing current knowledge level • Nuclear Magnetic Resonance phenomenon • Vector model, in and out of the rotating frame • 1045 – 1100 • Short break • 1100 – 1130 • The phase of pulses and signals • Effect of different chemical shifts in the vector model • Effect of homonuclear coupling in the vector model • The spin-echo sequence (homonuclear case) • The spin-echo sequence (heteronuclear case) • 1130 – 1200 • Spin-echo exercise • 1215 – 1315 • Lunch

  3. NTDR, 2014 Outline • 1215 – 1315 • Lunch • 1315 – 1415 • Signal processing • Window functions • Fourier transform • Real and imaginary parts • Phasing • Topspin starter

  4. NTDR, 2014 Establishing current knowledge level • Build (sketch) a NMR-instrument! • Magnet • Probes • Amplifiers • Receiver • ADC • Gradients • Temperature control • Lock • Shimming

  5. NTDR, 2014 Establishing current knowledge level • Draw a spectrum! • Chemical shifts • Integrals • Phases • Coupling constants • Line widths • life time of signals, shimming, exchange, dynamics

  6. NTDR, 2014 Nuclear Magnetic Resonance phenomenon • Nuclear: concerns the nuclei of atoms. • Magnetic: uses the magnetic properties of the nuclei. • Resonance: physics term describing oscillations.

  7. NTDR, 2014 Resonance • A system prefers some frequencies over others… • A small energy input at the right frequency will give large oscillations…

  8. NTDR, 2014 The magnetic properties of atomic nuclei • Atoms has a spin quantum number, I, and a magnetic quantum number, m = 2×I +1. • The magnetic quantum number = the number of different energy levels when the atom is placed in an external magnetic field. • Spin I = 0: 12C, 16O • Spin I = ½: 1H, 13C, 15N, 19F, 31P, 77Se • Spin I = 1: 2H, 14N • Spin I = 1½: 33S, 35Cl, 37Cl

  9. NTDR, 2014 Chemical shifts • The energy for a spin ½ nuclei can take two different levels in a magnetic field. • The population of the two states is almost equal. A small surplus in the low energy α spin state and slightly fewer atoms in the higher β spin state. • Stronger magnetic field = larger energy differences between the states.

  10. NTDR, 2014 Chemical shifts • A magnet provides the static field (B0) in the NMR instrument. • The rest of the molecule provides a ’local magnetic field’, which is dependent on structure.

  11. NTDR, 2014 Chemical shifts • The chemical shifts are expressed on a frequency scale (by convention plotted in reverse direction). • To make spectra comparable between instruments, the frequencies are expressed in parts per million [ppm] relative to a reference frequency. • Early instruments with electromagnets worked by slowly change the magnetic field. Hence the terms ‘Downfield’ and ‘Upfield’. • Less shielded • More deshielded • Downfield • Higher frequency • More shielded • Less deshielded • Upfield • Lower frequency

  12. NTDR, 2014 Vector model (a statistical abstraction…) • Unordered collection of½-spin nuclei, with a magnetic moment (μ).

  13. NTDR, 2014 Vector model • Unordered collection of½-spin nuclei, with a magnetic moment (μ). • In an external magnetic field, the magnetic moment starts to precess…

  14. NTDR, 2014 Vector model • Unordered collection of½-spin nuclei, with a magnetic moment (μ). • In an external magnetic field, the magnetic moment starts to precess… • …and aligns, at an angle of 54.7°, with the external field…

  15. NTDR, 2014 Vector model • Unordered collection of½-spin nuclei, with a magnetic moment (μ). • In an external magnetic field, the magnetic moment starts to precess… • …and aligns, at an angle of 54.7°, with the external field… • …either up (along the field, slightly lower energy) or down (opposite the field, slightly higher energy) according to the Boltzmann distribution.

  16. NTDR, 2014 Boltzmann distribution • The distribution of spins in a-state relative those in the b-state is described by the Boltzmann distribution. • The number of spins in each state is almost equal. There is a small surplus in the lower state. • Calculate how many spins in total you need to get one extra spin in the low energy state![1H, 600 MHz, 298 K]

  17. NTDR, 2014 Boltzmann distribution • One spin extra in the low energy state![1H, 600 MHz, 298 K] • Nβ = 12 922 • Nα = 12 923 • Σ = 25 845

  18. NTDR, 2014 Vector model • The ordered collection of spins can be handled from a common origin. • The Boltzmann distribution of up- and down-spins, makes a net magnetic vector along the external field (green). • An external magnetic field (radio frequency pulse, B1) perpendicular to the first (B0) have two effects:

  19. NTDR, 2014 Vector model • The ordered collection of spins can be handled from a common origin. • The Boltzmann distribution of up- and down-spins, makes a net magnetic vector along the external field (green). • An external magnetic field (radio frequency pulse, B1) perpendicular to the first (B0) have two effects: • Creation of phase coherence (‘bunching of spins’)

  20. NTDR, 2014 Vector model • The ordered collection of spins can be handled from a common origin. • The Boltzmann distribution of up- and down-spins, makes a net magnetic vector along the external field (green). • An external magnetic field (radio frequency pulse, B1) perpendicular to the first (B0) have two effects: • Creation of phase coherence (‘bunching of spins’) • Switch from up- to down-spin (or down- to up- !)

  21. NTDR, 2014 Vector model • The resultant magnetic vector is spinning at the precession frequency, which is the same as the frequency of the external magnetic field. • The spinning magnetic vector induces a current in the detector coil around the sample. The alternating current is recorded. • The detector senses the absolute length of the magnetic vector in the horizontal plane (XY-plane). • Cosine curve along y-axis. • Sine curve along x-axis.

  22. NTDR, 2014 Vector model • The resultant magnetic vector is spinning at the precession frequency, which is the same as the frequency of the external magnetic field. • The ‘rotating frame’ reference is used to simplify the model. • The coordinate system is spun at the same speed as the vectors  the vectors appear as fixed.

  23. NTDR, 2014 Relaxation • T1-relaxation • Exponential recovery of magnetization along B0-axis • Back to equilibrium populations of up- and down-spin

  24. NTDR, 2014 Relaxation • T1-relaxation • Exponential recovery of magnetization along B0-axis • Back to equilibrium populations of up- and down-spin • T2-relaxation • Gradual ‘fanning’ out of individual magnetic vector. • emission-absorption among spins (changes phase) • bad homogeneity of magnetic field

  25. NTDR, 2014 Relaxation • T1-relaxation • Exponential recovery of magnetization along B0-axis • Back to equilibrium populations of up- and down-spin • T2-relaxation • Gradual ‘fanning’ out of individual magnetic vector. • emission-absorption among spins (changes phase) • bad homogeneity of magnetic field

  26. NTDR, 2014 Pulsed experiments • The basic 1D-FT NMR experiment • Pulse (μseconds) • Broadband (covers a wide range of frequencies) • Acquisition (seconds) • Records all frequencies within a preset frequency width • Relaxation delay (seconds) • To return the magnetization vector close to equilibrium • Repeat and add results • signals increases linearly with n, while the noise partly cancels out and increases with n½.

  27. NTDR, 2014 Phase of pulses and signals • Basic 1D NMR-experiment: With a 90°-pulse along the x-axis

  28. NTDR, 2014 Phase of pulses and signals • Basic 1D NMR-experiment: With a 90°-pulse along the y-axis

  29. NTDR, 2014 Phase of pulses and signals • The phase of the pulse gives the phase of the signal…

  30. NTDR, 2014 Phase of pulses and signals Y X Y X

  31. NTDR, 2014 Phase of pulses and signals Y X Y X

  32. NTDR, 2014 Different chemical shifts in the vector model • Two signals with different chemical shifts rotates with different speed in the vector model • Interpreted as two different frequencies in the spectrum Y X

  33. NTDR, 2014 Different chemical shifts in the vector model • Two signals with different chemical shifts rotates with different speed in the vector model • Interpreted as two different frequencies in the spectrum Y X

  34. NTDR, 2014 Different chemical shifts in the vector model • One of the signals right on the carrier frequency • The other resonance will have a different speed Y X

  35. NTDR, 2014 Different chemical shifts in the vector model • One of the signals right on the carrier frequency • The other resonance will have a different speed Y X

  36. NTDR, 2014 Coupling in the vector model • A doublet with two signals • The same effect as two different chemical shifts, but usually depicted with the carrier frequency in the middle of the doublet. • J = Coupling constant in Hz (Hz = rounds per seconds)

  37. NTDR, 2014 Spin-echoes in pulse sequences • Chemical shifts are refocused

  38. NTDR, 2014 Spin-echoes in pulse sequences • Chemical shifts are refocused

  39. NTDR, 2014 Spin-echoes in pulse sequences • Chemical shifts are refocused

  40. NTDR, 2014 Spin-echoes in pulse sequences • Couplings evolve (if both of the coupled nuclei are inverted)

  41. NTDR, 2014 Spin-echoes in pulse sequences • Couplings evolve • (if both of the coupled nuclei are inverted)

  42. NTDR, 2014 Spin-echoes in pulse sequences • Couplings evolve (if both of the coupled nuclei are inverted)

  43. NTDR, 2014 Spin-echo example • Explain the appearance of the normal 1H spectrum of the hypothetical molecule.

  44. NTDR, 2014 Spin-echo exercise I • Explain the appearance of the spin-echo spectrum… • Use vector model • What delay was used around the 180-degree pulse?

  45. NTDR, 2014 Spin-echo exercise II • Explain the appearance of the spin-echo spectrum with simultaneous 180-pulses at both proton and carbon… • Use vector model • What delay was used around the 180-degree pulse?

  46. NTDR, 2014 Spin-echo exercise I

  47. NTDR, 2014 Spin-echo exercise II

  48. NTDR, 2014 LUNCH • The lunch is served in the cafeteria in building 22 • 1215-1315

  49. NTDR, 2014 Outline • 1215 – 1315 • Lunch • 1315 – 1415 • Signal processing • Window functions • Fourier transform • Real and imaginary parts • Phasing • Topspin starter

  50. NTDR, 2014 Acquisition time • The acquisition time is usually ~100 ms – 10 sec depending of type of experiment. • The best theoretical resolution in the spectrum is the inverse of the acquisition time (ta). • ta = 10 seconds  Δν= 0.1 Hz • ta. = 0.1 seconds  Δν= 10 Hz

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