chapter 6: nmr pulses

The Basic 1D NMR Experiment

Experimental details will effect the NMR spectra and the corresponding interpretation

NMR PulseNMR Pulse

z

x

Mxyy

z

x

y

Mo

B1

ttp

t = * tp * B1

NMR pulse length or Tip angle (tp)

The length of time the B1 field is on => torque on bulk magnetization (B1)

A measured quantity – instrument and sample dependent.

NMR PulseNMR Pulse

z

x

Mxyy

z

x

y

Mo / 2

Some useful common pulses

90o

Maximizes signal in x,y-planewhere NMR signal detected

z

x

-Moy

z

x

y

Mo

180o

90o pulse

180o pulseInverts the spin-population.No NMR signal detected

Can generate just about any pulse width desired.

NMR PulseNMR Pulse

Impact on the FID

90o

270o

NMR PulseNMR PulseMeasuring an NMR pulse length

PW (s)

Pea

k In

tens

ity 180o pulse

• Vary pulse width (PW) and measure peak intensityi. Start with very short (~1s) PW and properly phased spectra ii. Maximum peak intensity at 90o pulse, minimum peak intensity at 180o pulse

• PW is dependent on power or attenuation of pulsei. higher power shorter pulse length

NMR PulseNMR PulseMeasuring an NMR pulse length

• Heteronuclear 90o pulsei. Measured by observing 1H spectraii. Vary a until no signal is observed

90o pulse (not 180o pulse)

PW (s)

Pea

k In

tens

ity

90o pulse

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)

13C spectra where peaks have different phases

• Change the NMR pulse:i. Different pulse width ii. Different pulse strengthiii. Different pulse shapeiv. Different pulse phase (x, -x, y, -y)v. Different pulse frequencyvi. Use multiple pulsesvii. Pulses exciting different nuclei (1H, 13C, 15N)

Selecting Specific Information in an NMR Spectra

1H spectra where peaks are a mixture of in-phase and antiphase peaks

NMR Pulse (spin gymnastics)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.


• 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 (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



FT

* =tp

Pulse length (time, tp)

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

• 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 frequencyii. Shorter pulse width broader frequency bandwidth

Heisenberg Uncertainty Principal: t


• Shape of pulse also determines excitation profilei. Frequency of pulse also determines region of spectra that is excited

Square pulse

Sinx/x

Gaussian

Not selective, residues Not selective, residues distant from excitation distant from excitation frequency are excitedfrequency are excited

NMR Pulse (spin gymnastics)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.

270ox

Mo

z

yB1

z

y

Mxyx x

1

1

Right-hand rule

NMR Pulse (spin gymnastics)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 excitedii. 90o

-x pulse is the same as a 270ox pulse

iii. Follows right-hand rule

90o-x

Mo

z

yB1

z

y

Mxyx x

1

1

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Decoupling

• Remove the splitting pattern caused by spin-spin J-couplingi. 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 systemCoupled spin system

Decoupled spin systemDecoupled spin system

Incomplete decouplingIncomplete decoupling


• Remove the splitting pattern caused by spin-spin couplingii. Heteronuclear decoupling

Common: decouple protons from carbon in carbon spectra Also, increases the signal-to-noise of 13C spectrum


• Remove the splitting pattern caused by spin-spin couplingiii. 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


• Heteronucleari. 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

1313C pulsesC pulses

11H pulsesH pulses

)(2

2 AXx JB

Decoupling requires the magnitude of B2 be much greater than the 1H-

13C coupling constant ( ~140 Hz)

13C NMR Spectra are almost always collected with 1H decoupling• dramatic improvement in sensitivity

i. natural abundance of 13C is 1.1%ii. 1H/13C = 64x - 1H nuclei 64x more sensitive then 13C nuclei

• sensitivity increase is proportional to splitting pattern• additional increase comes from the NOE (, nuclear Overhauser effect, discussed latter)

i. 13C signals are enhanced by a factor of:

Completely Completely 11H decoupled (WALTZ)H decoupled (WALTZ)

Completely Completely 11H coupledH coupled


1 + = 1 + 1/2 . (1H)/(13C) ~ max. of 2


• Off-resonance, broadband and composite pulse decouplingi. 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

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 180o pulses that rapidly exchange , spin states and decouple 1H from 13C

Completely Completely 11H coupledH coupled

11H decoupled at single (10 ppm) frequencyH decoupled at single (10 ppm) frequencyOnly partial “collapse” of some spin systemsOnly partial “collapse” of some spin systems


• Composite pulse decouplingi. Sequence of 1H 180o pulses

Each 180O pulse exchanges 1H and spin states 13C nuclei is alternatively coupled to 1H and spin state Effectively averages to decoupling 1H and 13C nuclei

– Remember: coupling arises from alignment of spin states through bonding electrons

S

S

I

I

S

S

I

I180o


• Composite pulse decouplingii. 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)


• Composite pulse decouplingi. 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 The relative evolution in the X,Y plane for the separation of the coupled doublets relative to separation of the coupled doublets relative to the decoupled singlet. the decoupled singlet.

The 180The 180oo pulse flip the direction of the evolution pulse flip the direction of the evolution of the two components of the doublet in the X,Y of the two components of the doublet in the X,Y plane such that the effective motion resembles plane such that the effective motion resembles the decoupled singlet the decoupled singlet


• MLEV-4 composite pulse decoupling schemei. Based on the composite pulse:

(90o)x(270o)y(90o)x = R MLEV-16 decouples efficiently ± 4.5 kHz

)( phasereverseRRRRR

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)


• WALTZ-16i. Based on the composite pulse:

(90o)x(180o)-x(270o)x decouples efficiently over ± 6 kHz Corrects imperfections in MLEV 90o ~ 100 s reduces sample heating 1 = 90o, 2 =180o, 3 = 270o, 4 = 360o

• GARPi. Computer optimized using non-90o flip angles

Effective decoupling bandwidth of ± 15 kHz 90o ~ 70 s

)(234213243324213243324213243324213243

phasereverseR


• Pulse composition also determines excitation profilei. determines region of spectra that is excited

Decoupling


• Comparison of MLEV-16, WALTZ-16 and Garpi. Want largest bandwidth possible to cover the entire NMR spectrumii. 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


• Homonucleari. 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 Mz = 0

Selective decoupling pulse Selective decoupling pulse (B(B22). Only Irradiated peak ). Only Irradiated peak has been saturated and is has been saturated and is

not observed.not observed.

Peaks coupled to Peaks coupled to irradiated peak irradiated peak

are now singletsare now singlets

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Bloch-Siegert Shift

• Measure weak, homonuclear decoupling fieldsi. Bloch-Siegert shift – displacement of a signal from its usual frequency caused by

nearby irradiation

Weak RF field appliedWeak RF field applied

Normal SpectrumNormal Spectrum

Bloch-Siegert ShiftBloch-Siegert ShiftBB22 = 20 Hz = 20 Hz

)(2

22

ivvB

v

- B2 measured in Hz where B2<< v -vi

- v – true (normal) frequency)- vi – frequency of irradiation

Irradiation Irradiation frequency (frequency (vvii))

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Selective Pulses

• Short low power pulsei. 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 As the pulse length is increased, the excitation increased, the excitation

profile is decreasedprofile is decreased

Fewer peaks are excited and the relative magnitude decreases and then inverts

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Selective Pulses

• DANTE pulsei. Instead of a single 180o pulse, use n pulses of 180o/n length separated by a time

Excitation bandwidth is determined by the total time of the pulse sequence– 11 x 16.4o 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 profileexcitation profile

On resonance trajectory On resonance trajectory experience full 90experience full 90oo pulse pulse

Further the trajectory is Further the trajectory is off-resonance less of a off-resonance less of a pulse is experiencedpulse is experienced

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Composite Pulses

• Composite 180o pulsei. (90o)x(180o)y(90o)x

ii. 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

iii. Results in loss of S/N and creates artifactsiv. 20 s 180o pulse ± 12.5 kHz excitation bandwidth (±1/4xPW)

Problem when spectral width is larger than excitation bandwidthv. 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

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Refocusing Pulses

• Spin-Echoi. 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

ii. 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

Normal signal Distortions due to delay

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)Refocusing Pulses

• Spin-Echoiii. 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)NMR Pulse (spin gymnastics)Spin-Lock Pulse Sequence

• Modified Spin-Echo Pulsei. Make very short and repeat 180o pulse n times

n is a very large numberi. B1 field is continuous and magnetization is now locked in the y’ direction

ii. Effective magnetic field is now B1 (not Bo) nuclei precess around B1

nuclei tumble rapidly relative to B1

(90o)x – {(180o)y}n

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)BIRD Pulse

• Selects Nuclei Only Attached to a Second Coupled Nucleii. 1H attached to 13C or to 15Nii. Common component of multidimensional pulse sequencesiii. 1H attached to inactive nuclei (12C or 14N) experience a 180o--90o 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 d1 = recycle delay for relaxationfor relaxation

d2 = 1/2Jd2 = 1/2J

d3 = delay for d3 = delay for 11H-H-1212C C –z magnetization to –z magnetization to decay to zero decay to zero

phase of pulsephase of pulse

9090oo 180180oo

Width determines Width determines pulse lengthpulse length

NMR Pulse (spin gymnastics)NMR Pulse (spin gymnastics)BIRD Pulse

• Selects Nuclei Only Attached to a Second Coupled Nucleii. At the end of the sequence, 1H attached to 13C or 15N will be aligned along +zii. 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

1313C-C-11HH

1212C-C-11HH

chapter 6: nmr pulses

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