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

NMR Pulse z x M xy y z x y MoMo B1B1 tt tptp  t =  * t p * B 1 NMR pulse length or Tip angle (t p ) The length of time the B 1 field is on => torque on bulk magnetization (B 1 ) A measured quantity – instrument and sample dependent.

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

NMR Pulse Impact on the FID 90 o 270 o

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

NMR Pulse Measuring an NMR pulse length Heteronuclear 90 o pulse i.Measured by observing 1 H spectra ii.Vary a until no signal is observed  90 o pulse (not 180 o pulse) PW (  s) Peak Intensity 90 o pulse

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

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

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

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 (t 1 ) more complex NMR experiments will use multiple “time-dimensions” to obtain data and simplify the analysis. Multidimensional NMR experiments may also use multiple nuclei ( 2 D, 13 C, 15 N) in addition to 1 H, but usually detect 1 H) 1D NMR Pulse Sequence NMR Pulse (spin gymnastics)

FT *= tptp Pulse length (time, t p ) A radiofrequency pulse is a combination of a wave (cosine) of frequency w o and a step function The Fourier transform indicates the pulse covers a range of frequencies In FT-NMR, how are all the individual nuclei excited simultaneously? RF pulses are typically short-duration (  secs) Pulse width and power level determines bandwidth of frequencies that are excited i.Produces bandwidth (1/4  ) centered around single frequency ii.Shorter pulse width  broader frequency bandwidth Heisenberg Uncertainty Principal:  t 

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

NMR Pulse (spin gymnastics) Short pulses (  secs) 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.

270 o x MoMo z y B1B1 z y M xy xx 11 11 Right-hand rule NMR Pulse (spin gymnastics) Phase of pulse determines direction of X,Y precession and sign of signal i.Frequency of pulse also determines region of spectra that is excited ii.90 o -x pulse is the same as a 270 o x pulse iii.Follows right-hand rule 90 o -x MoMo z y B1B1 z y M xy xx 11 11

NMR Pulse (spin gymnastics) Decoupling Remove the splitting pattern caused by spin-spin J-coupling i.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? Coupled spin system Decoupled spin system Incomplete decoupling

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

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

NMR Pulse (spin gymnastics) Decoupling Heteronuclear i.Apply a second strong radiofrequency field (B 2 )  For a decoupled 13 C spectra, pulse is at 1 H frequency  1 H nuclei continually precess about B 2  M z averages to zero!  If M Z =0, coupling vanishes and 13 C resonances reduce to singlet 13 C pulses 1 H pulses Decoupling requires the magnitude of B 2 be much greater than the 1 H- 13 C coupling constant ( ~140 Hz)

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

NMR Pulse (spin gymnastics) Decoupling Off-resonance, broadband and composite pulse decoupling i.Off-resonance – placed decoupling frequency at a single frequency  higher field strength, too far from many protons to decouple  Only decouples weaker 2,3 J( 13 C 1 H ), 1 J( 13 C 1 H ) ~ 140 Hz ii.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 iii.Composite pulse – series of effective 180 o pulses that rapidly exchange ,  spin states and decouple 1 H from 13 C Completely 1 H coupled 1 H decoupled at single (10 ppm) frequency 1 H decoupled at single (10 ppm) frequency Only partial “collapse” of some spin systems

NMR Pulse (spin gymnastics) Decoupling Composite pulse decoupling i.Sequence of 1 H 180 o pulses  Each 180 O pulse exchanges 1 H  and  spin states  13 C nuclei is alternatively coupled to 1 H  and  spin state  Effectively averages to decoupling 1 H and 13 C nuclei – Remember: coupling arises from alignment of spin states through bonding electrons    S S I I     S S I I 180 o

NMR Pulse (spin gymnastics) Decoupling Composite pulse decoupling ii.Composite pulse –  series of 180 o 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 180 o  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)

NMR Pulse (spin gymnastics) Decoupling Composite pulse decoupling i.Sequence of 1 H 180 o 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 180 O 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 180 o 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

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

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

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

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

NMR Pulse (spin gymnastics) Decoupling Homonuclear i.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 (  ) is depleted – Spin population equalized  M z = 0 Selective decoupling pulse (B 2 ). Only Irradiated peak has been saturated and is not observed. Peaks coupled to irradiated peak are now singlets Peaks coupled to irradiated peak are now singlets

NMR Pulse (spin gymnastics) Bloch-Siegert Shift Measure weak, homonuclear decoupling fields i.Bloch-Siegert shift – displacement of a signal from its usual frequency caused by nearby irradiation Weak RF field applied Normal Spectrum Bloch-Siegert Shift B 2 = 20 Hz - B 2 measured in Hz where B 2 << v -v i - v – true (normal) frequency) - v i – frequency of irradiation Irradiation frequency (v i )

NMR Pulse (spin gymnastics) Selective Pulses Short low power pulse i.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

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

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

NMR Pulse (spin gymnastics) Refocusing Pulses Spin-Echo i.If a 90 o 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 ii.Placing a 180 o (refocusing pulse) in the middle of the delay period will reverse the direction the spins precess bringing them all back to the origin Normal signal Distortions due to delay

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

NMR Pulse (spin gymnastics) Spin-Lock Pulse Sequence Modified Spin-Echo Pulse i.Make  very short and repeat 180 o pulse n times  n is a very large number i.B 1 field is continuous and magnetization is now locked in the y’ direction ii.Effective magnetic field is now B 1 (not B o )  nuclei precess around B 1  nuclei tumble rapidly relative to B 1 (90 o) x – {(180 o ) y } n

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

NMR Pulse (spin gymnastics) BIRD Pulse Selects Nuclei Only Attached to a Second Coupled Nuclei i.At the end of the sequence, 1 H attached to 13 C or 15 N will be aligned along +z ii.At the end of the sequence, 1 H attached to 12 C or 14 N 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 1 H 90 o pulse 13 C- 1 H 12 C- 1 H