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The Basic 1D NMR Experiment

The Basic 1D NMR Experiment. Experimental details will effect the NMR spectra and the corresponding interpretation. NMR Pulse. NMR pulse length or Tip angle (t p ). z. z. q t. M o. t p. x. x. B 1. M xy. y. y. q t = g * t p * B 1.

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The Basic 1D NMR Experiment

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  1. The Basic 1D NMR Experiment Experimental details will effect the NMR spectra and the corresponding interpretation

  2. NMR Pulse NMR pulse length or Tip angle (tp) z z qt Mo tp x x B1 Mxy y y qt = g * tp * B1 The length of time the B1 field is on => torque on bulk magnetization (B1) A measured quantity – instrument and sample dependent.

  3. NMR Pulse Some useful common pulses z z 90o pulse Mo p / 2 Maximizes signal in x,y-plane where NMR signal detected x x Mxy 90o y y z z 180o pulse Inverts the spin-population. No NMR signal detected Mo p x x 180o -Mo y y Can generate just about any pulse width desired.

  4. NMR Pulse Impact on the FID 90o 270o

  5. 180o pulse Peak Intensity PW (ms) NMR Pulse Measuring an NMR pulse length • Vary pulse width (PW) and measure peak intensity • Start with very short (~1ms) PW and properly phased spectra • Maximum peak intensity at 90o pulse, minimum peak intensity at 180o pulse • PW is dependent on power or attenuation of pulse • higher power  shorter pulse length

  6. NMR Pulse Measuring an NMR pulse length • Heteronuclear 90o pulse • Measured by observing 1H spectra • Vary a until no signal is observed • 90o pulse (not 180o pulse) 90o pulse Peak Intensity PW (ms)

  7. NMR Pulse (spin gymnastics) Selecting Specific Information in an NMR Spectra • Change the NMR pulse: • Different pulse width • Different pulse strength • Different pulse shape • Different pulse phase (x, -x, y, -y) • Different pulse frequency • Use multiple pulses • Pulses exciting different nuclei (1H, 13C, 15N) 1H spectra where peaks are a mixture of in-phase and antiphase peaks 13C spectra where peaks have different phases

  8. NMR Pulse (spin gymnastics) Selecting Specific Information in an NMR Spectra 13C spectra with different excitation profiles – intensity of peaks varies based on pulse width, strength, shape, etc.

  9. NMR Pulse (spin gymnastics) Selecting Specific Information in an NMR Spectra • Different delays between pulses • Coupling constants  Hz  TIME! • Chemical shifts  ppm  Hz  TIME! • Select specific coupled nuclei or chemical shifts Appearance of spectrum changes as a function of the increasing tau delay time

  10. NMR Pulse (spin gymnastics) • NMR pulse sequences • composed of a series of RF pulses, delays, gradient pulses and phases • in a 1D NMR experiment, the FID acquisition time is the time domain (t1) • more complex NMR experiments will use multiple “time-dimensions” to obtain data and simplify the analysis. • Multidimensional NMR experiments may also use multiple nuclei (2D, 13C,15N) in addition to 1H, but usually detect 1H) 1D NMR Pulse Sequence

  11. * = tp Pulse length (time, tp) FT NMR Pulse (spin gymnastics) • In FT-NMR, how are all the individual nuclei excited simultaneously? • RF pulses are typically short-duration (msecs) • Pulse width and power level determines bandwidth of frequencies that are excited • Produces bandwidth (1/4t) centered around single frequency • Shorter pulse width  broader frequency bandwidth • Heisenberg Uncertainty Principal:Du.Dt ~ 1/2p A radiofrequency pulse is a combination of a wave (cosine) of frequency wo and a step function The Fourier transform indicates the pulse covers a range of frequencies

  12. NMR Pulse (spin gymnastics) • Shape of pulse also determines excitation profile • Frequency of pulse also determines region of spectra that is excited Not selective, residues distant from excitation frequency are excited Square pulse Sinx/x Gaussian

  13. NMR Pulse (spin gymnastics) • Short pulses (msecs) at high power will simultaneously excite the entire NMR spectrum • Long shaped pulses (msecs) at low power will selectively excite a small region (single peak) of the NMR spectrum Very Important! – probes have a finite power-load. A long pulse at high power will fry the probe.

  14. NMR Pulse (spin gymnastics) • Phase of pulse determines direction of X,Y precession and sign of signal • Frequency of pulse also determines region of spectra that is excited • 90o-x pulse is the same as a 270ox pulse • Follows right-hand rule z z Mo 270ox y y B1 Mxy w1 x x w1 z z Mo 90o-x y y B1 Mxy w1 x x w1 Right-hand rule

  15. NMR Pulse (spin gymnastics) Decoupling • Remove the splitting pattern caused by spin-spin J-coupling • Simplifies the spectra • Makes it easier to count the number of peaks • Clarifies overlapping spin patterns (second-order spin coupling) • Is the spin system a quartet or two closely spaced doublets? Decoupled spin system Incomplete decoupling Coupled spin system

  16. NMR Pulse (spin gymnastics) Decoupling • Remove the splitting pattern caused by spin-spin coupling • Heteronuclear decoupling • Common: decouple protons from carbon in carbon spectra • Also, increases the signal-to-noise of 13C spectrum

  17. NMR Pulse (spin gymnastics) Decoupling • Remove the splitting pattern caused by spin-spin coupling • Homonuclear decoupling • Selectively decouple one proton spin system from another • Must be chemically distinct • Can not conveniently decouple the entire spectra (until very recently) Selective irradiation of peak at 7.3 ppm partially decouples peak at 5.25 ppm Selective irradiation of peak at 8.5 ppm partially decouples peak at 5.25 ppm Fully coupled spectrum

  18. NMR Pulse (spin gymnastics) Decoupling • Heteronuclear • Apply a second strong radiofrequency field (B2) • For a decoupled 13C spectra, pulse is at 1H frequency • 1H nuclei continually precess about B2  Mz averages to zero! • If MZ =0, coupling vanishes and 13C resonances reduce to singlet Decoupling requires the magnitude of B2 be much greater than the 1H-13C coupling constant ( ~140 Hz) 13C pulses 1H pulses

  19. NMR Pulse (spin gymnastics) • 13C NMR Spectra are almost always collected with 1H decoupling • dramatic improvement in sensitivity • natural abundance of 13C is 1.1% • g1H/g13C = 64x - 1H nuclei 64x more sensitive then 13C nuclei • sensitivity increase is proportional to splitting pattern • additional increase comes from the NOE (h, nuclear Overhauser effect, discussed latter) • 13C signals are enhanced by a factor of: 1 + h = 1 + 1/2 .g(1H)/g(13C) ~ max. of 2 Completely 1H coupled Completely 1H decoupled (WALTZ)

  20. NMR Pulse (spin gymnastics) Decoupling • Off-resonance, broadband and composite pulse decoupling • Off-resonance – placed decoupling frequency at a single frequency • higher field strength, too far from many protons to decouple • Only decouples weaker 2,3J(13C1H), 1J(13C1H) ~ 140 Hz • Broadband – use band of frequencies • Requires higher power heat samples broaden peaks lower S/N • Again, more difficult to completely decouple at higher field strengths • Composite pulse – series of effective 180o pulses that rapidly exchange a,b spin states and decouple 1H from 13C Completely 1H coupled 1H decoupled at single (10 ppm) frequency Only partial “collapse” of some spin systems

  21. NMR Pulse (spin gymnastics) bb ba I I S S ba bb aa ab S S I I aa ab Decoupling • Composite pulse decoupling • Sequence of 1H 180o pulses • Each 180O pulse exchanges 1H a and b spin states • 13C nuclei is alternatively coupled to 1H a and b spin state • Effectively averages to decoupling 1H and 13C nuclei • Remember: coupling arises from alignment of spin states through bonding electrons 180o

  22. NMR Pulse (spin gymnastics) Decoupling • Composite pulse decoupling • Composite pulse – • series of 180o pulses is inefficient • Errors in accurately measuring a pulse length lead to cumulative errors in a series • Use combination of different pulses that combined equal 180o • Pulse errors are minimized by a combination of different errors with different pulse lengths and phases • Diagram of a common decoupling scheme • each rectangle represents an individual pulse • Width of rectangle is proportional to pulse length • QggQ cycle is repeated indefinitely • q is inverted Q element (opposite phase)

  23. NMR Pulse (spin gymnastics) Decoupling • Composite pulse decoupling • Sequence of 1H 180o pulses • Each spin precess in the X,Y plane at a rate equal to the sum of its chemical shift and ½ its coupling constants • Each 180O pulse inverts the evolution of the two spins in the X,Y plane • Result is the two spins for the coupled doublet precess as the same rate of a decoupled singlet • Effectively removes the coupling constant contribution to its rate of precessing in the X,Y plane The relative evolution in the X,Y plane for the separation of the coupled doublets relative to the decoupled singlet. The 180o pulse flip the direction of the evolution of the two components of the doublet in the X,Y plane such that the effective motion resembles the decoupled singlet

  24. NMR Pulse (spin gymnastics) Decoupling • MLEV-4 composite pulse decoupling scheme • Based on the composite pulse: • (90o)x(270o)y(90o)x = R  MLEV-16 decouples efficiently ± 4.5 kHz Trajectory of 1H nuclei after two R MLEV-4 pulses results in an effective 360O pulse. Result is improved slightly by following with two R pulses with reverse phase. NMR IN BIOMEDICINE, VOL. 10, 372–380 (1997)

  25. NMR Pulse (spin gymnastics) Decoupling • WALTZ-16 • Based on the composite pulse: • (90o)x(180o)-x(270o)x  decouples efficiently over± 6 kHz • Corrects imperfections in MLEV • 90o ~ 100 ms  reduces sample heating • 1 = 90o, 2 =180o, 3 = 270o, 4 = 360o • GARP • Computer optimized using non-90o flip angles • Effective decoupling bandwidth of ± 15 kHz • 90o ~ 70 ms

  26. NMR Pulse (spin gymnastics) Decoupling • Pulse composition also determines excitation profile • determines region of spectra that is excited

  27. NMR Pulse (spin gymnastics) Decoupling • Comparison of MLEV-16, WALTZ-16 and Garp • Want largest bandwidth possible to cover the entire NMR spectrum • Want profile to be flat so each peak is equally irradiated GARP Bandwidth 18,000 Hz WALTZ16 Bandwidth 8000 Hz MLEV16 Bandwidth 7000 Hz Improving Decoupling Pulse Scheme

  28. NMR Pulse (spin gymnastics) Decoupling • Homonuclear • Selective irradiation of one nuclei in the spectra • Decoupling pulse must be on during the acquisition of the FID • Actually, only on between collection of data points (DW) • Only decouples nuclei coupled to the irradiated nuclei • Chemical shift difference >> coupling constant • Nuclei that is irradiated is “saturated”  no signal • Excess of low-energy spin state (a) is depleted • Spin population equalized  Mz = 0 Peaks coupled to irradiated peak are now singlets Selective decoupling pulse (B2). Only Irradiated peak has been saturated and is not observed.

  29. NMR Pulse (spin gymnastics) Bloch-Siegert Shift • Measure weak, homonuclear decoupling fields • Bloch-Siegert shift – displacement of a signal from its usual frequency caused by nearby irradiation • B2measured in Hz where B2<< v -vi • v – true (normal) frequency) • vi – frequency of irradiation Bloch-Siegert Shift B2 = 20 Hz Weak RF field applied Irradiation frequency (vi) Normal Spectrum

  30. NMR Pulse (spin gymnastics) Selective Pulses • Short low power pulse • Bandwidth is dependent on pulse width • 0.1s pulse will only have a bandwidth of ± 2.5 Hz • But excitation profile contains multiple peaks and valleys • Other peaks 10s of Hz from pulse will also be excited • Not very selective As the pulse length is increased, the excitation profile is decreased Fewer peaks are excited and the relative magnitude decreases and then inverts

  31. NMR Pulse (spin gymnastics) Selective Pulses • DANTE pulse • Instead of a single 180o pulse, use n pulses of 180o/n length separated by a time t • Excitation bandwidth is determined by the total time of the pulse sequence • 11 x 16.4o pulses separated by 10t (0.01s)  0.1s  ±2.5 Hz bandwidth • Additional excitations occur at ± m/t, where m is an integer • Need to adjust t to avoid exciting other resonances • Need to calibrate DANTE  no perfect square pulse (rise and fall times) excitation profile Further the trajectory is off-resonance less of a pulse is experienced On resonance trajectory experience full 90o pulse

  32. NMR Pulse (spin gymnastics) Composite Pulses • Composite 180o pulse • (90o)x(180o)y(90o)x • Difficult to accurately determine a 90o or 180o pulse • Effect of pulse may vary over the coils in the probe, especially at edges • Depends on the exact tuning of the probe • Results in loss of S/N and creates artifacts • 20 ms 180o pulse  ± 12.5 kHz excitation bandwidth (±1/4xPW) • Problem when spectral width is larger than excitation bandwidth • Composite pulses have larger excitation bandwidths Trajectory of (90o)x(180o)y(90o)x composite pulse with an incorrect 180o pulse length, where the effective pulse is 160o. Even with the significant error, the net magnetization still winds up very close to -z

  33. NMR Pulse (spin gymnastics) Refocusing Pulses • Spin-Echo • If a 90o pulse is followed by a delay before acquiring the FID: • Spins precess at different rates in X,Y plane • Function of chemical shift and coupling constants • Peaks will have different phase  distorted spectra • Placing a 180o (refocusing pulse) in the middle of the delay period will reverse the direction the spins precess bringing them all back to the origin Distortions due to delay Normal signal

  34. NMR Pulse (spin gymnastics) Refocusing Pulses • Spin-Echo • Used in more complicated pulse programs (experiments) • Used to “refocus” a select set of peaks • Still detect the signal after a “process” that occurred during the delay period modulates the signal intensity  relaxation, diffusion, chemical exchange, etc. “Signal echo”

  35. NMR Pulse (spin gymnastics) Spin-Lock Pulse Sequence • Modified Spin-Echo Pulse • Make t very short and repeat 180o pulse n times • n is a very large number • B1 field is continuous and magnetization is now locked in the y’ direction • Effective magnetic field is now B1 (not Bo) • nuclei precess around B1 • nuclei tumble rapidly relative to B1 (90o)x – {(180o)y}n

  36. NMR Pulse (spin gymnastics) BIRD Pulse • Selects Nuclei Only Attached to a Second Coupled Nuclei • 1H attached to 13C or to 15N • Common component of multidimensional pulse sequences • 1H attached to inactive nuclei (12C or 14N) experience a 180o-t-90o pulse sequence • t is chosen to give zero signal (t = 1/2J) • Coupled nuclei will precess in X,Y plane at a rate equal to 1/2J • Uncoupled nuclei remain static (ignoring chemical shift) Width determines pulse length phase of pulse 180o 90o d1 = recycle delay for relaxation d2 = 1/2J d3 = delay for 1H-12C –z magnetization to decay to zero

  37. NMR Pulse (spin gymnastics) BIRD Pulse • Selects Nuclei Only Attached to a Second Coupled Nuclei • At the end of the sequence, 1H attached to 13C or 15N will be aligned along +z • At the end of the sequence, 1H attached to 12C or 14N will be aligned along –z • Magnetization will relax back to +z, will pass through null • Wait long enough to achieve null and detect signals of coupled nuclei with 1H 90o pulse 13C-1H 12C-1H

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