Chapter 6: NMR Pulses
The Basic 1D NMR Experiment
Experimental details will effect the NMR spectra and
the corresponding interpretation
NMR Pulse
NMR pulse length or Tip angle (tp)
z
Mo
z
x
qt
tp
x
B1
y
y
Mxy
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.
NMR Pulse
Some useful common pulses
z
z
90o pulse
Mo
Maximizes signal in x,y-plane
where NMR signal detected
x
p/2
90o
y
x
y
z
180o pulse
Inverts the spin-population.
No NMR signal detected
Mo
Mxy
z
x
y
Can generate just about any pulse width desired.
p
180o
x
y
-Mo
NMR Pulse
Impact on the FID
90o
270o
NMR Pulse
Measuring an NMR pulse length
•
Vary pulse width (PW) and measure peak intensity
i.
Start with very short (~1ms) 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 pulse
i.
higher power shorter pulse length
Peak Intensity
•
180o pulse
PW (ms)
NMR Pulse
Measuring an NMR pulse length
Heteronuclear 90o pulse
i.
Measured by observing 1H spectra
ii.
Vary a until no signal is observed
90o pulse (not 180o pulse)
90o pulse
Peak Intensity
•
PW (ms)
NMR Pulse (spin gymnastics)
Selecting Specific Information in an NMR Spectra
•
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 (1H, 13C, 15N)
1H
spectra where peaks are a mixture
of in-phase and antiphase peaks
13C
spectra where peaks
have different phases
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.
NMR Pulse (spin gymnastics)
Selecting Specific Information in an NMR Spectra
•
Different delays between pulses
i.
Coupling constants Hz TIME!
ii.
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
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,
addition to 1H, but usually detect 1H)
1D NMR Pulse Sequence
13C,15N)
in
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
i.
Produces bandwidth (1/4t) centered around single frequency
ii.
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
*
=
tp
Pulse length (time, tp)
The Fourier transform indicates the
pulse covers a range of frequencies
FT
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 (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.
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.
90o-x pulse is the same as a 270ox pulse
iii.
Follows right-hand rule
z
Mo
z
y
270ox
y
B1
w1
x
x
z
Mo
z
y
90o-x
y
B1
w1
x
Mxy w
1
x
Mxy w
1
Right-hand rule
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?
Decoupled spin system
Coupled 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 13C 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)
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
NMR Pulse (spin gymnastics)
Decoupling
•
Heteronuclear
i.
Apply a second strong radiofrequency field (B2)
For a decoupled 13C spectra, pulse is at 1H frequency
1H
If MZ =0, coupling vanishes and 13C resonances reduce to singlet
nuclei continually precess about B2 Mz averages to zero!
g x B2
J ( AX )
2p
13C
1H
pulses
pulses
Decoupling requires the magnitude
of B2 be much greater than the 1H13C coupling constant ( ~140 Hz)
NMR Pulse (spin gymnastics)
13C
NMR Spectra are almost always collected with 1H decoupling
•
dramatic improvement in sensitivity
i.
natural abundance of 13C is 1.1%
ii.
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)
i.
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)
NMR Pulse (spin gymnastics)
Decoupling
•
Off-resonance, broadband and composite pulse decoupling
i.
ii.
iii.
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
NMR Pulse (spin gymnastics)
Decoupling
•
Composite pulse decoupling
Sequence of 1H 180o pulses
i.
Each 180O pulse exchanges 1H a and b spin states
13C
Effectively averages to decoupling 1H and 13C nuclei
–
I
nuclei is alternatively coupled to 1H a and b spin state
Remember: coupling arises from alignment of spin states through bonding
electrons
bb
S
180o
ba
ab
S
I
aa
I
ba
S
bb
aa
S
I
ab
NMR Pulse (spin gymnastics)
Decoupling
•
Composite pulse decoupling
ii.
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)
NMR Pulse (spin gymnastics)
Decoupling
•
Composite pulse decoupling
i.
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
NMR Pulse (spin gymnastics)
Decoupling
•
MLEV-4 composite pulse decoupling scheme
i.
Based on the composite pulse:
(90o)x(270o)y(90o)x = R MLEV-16 decouples efficiently ± 4.5 kHz
RRR R R (reverse phase)
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)
NMR Pulse (spin gymnastics)
Decoupling
•
WALTZ-16
i.
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
3423 1 2 4233 42312423
3 4 2 3 1 2 4 2 3 3 4 2 3 1 2 4 3 2 R (reverse phase )
•
GARP
i.
Computer optimized using non-90o flip angles
Effective decoupling bandwidth of ± 15 kHz
90o ~ 70 ms
NMR Pulse (spin gymnastics)
Decoupling
•
Pulse composition also determines excitation profile
i.
determines region of spectra that is excited
NMR Pulse (spin gymnastics)
Decoupling
•
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
MLEV16 Bandwidth 7000 Hz
WALTZ16 Bandwidth 8000 Hz
Improving Decoupling Pulse Scheme
GARP Bandwidth 18,000 Hz
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 (a) is depleted
–
Spin population equalized Mz = 0
Selective decoupling pulse
(B2). Only Irradiated peak
has been saturated and is
not observed.
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
B22
v
2(v v i )
-
B2 measured 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
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 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
NMR Pulse (spin gymnastics)
Composite Pulses
•
Composite 180o pulse
i.
(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 artifacts
iv.
20 ms 180o pulse ± 12.5 kHz excitation bandwidth (±1/4xPW)
v.
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
NMR Pulse (spin gymnastics)
Refocusing Pulses
•
Spin-Echo
i.
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
Normal signal
ii.
Distortions
due to delay
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
NMR Pulse (spin gymnastics)
Refocusing Pulses
•
Spin-Echo
iii.
Used in more complicated pulse programs (experiments)
“Signal echo”
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.
NMR Pulse (spin gymnastics)
Spin-Lock Pulse Sequence
•
Modified Spin-Echo Pulse
i.
Make t very short and repeat 180o pulse n times
(90o)x – {(180o)y}n
n is a very large number
i.
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
NMR Pulse (spin gymnastics)
BIRD Pulse
•
Selects Nuclei Only Attached to a Second Coupled Nuclei
i.
ii.
iii.
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
180o
90o
d1 = recycle delay
for relaxation
d2 = 1/2J
d3 = delay for 1H-12C
–z magnetization to
decay to zero
phase of pulse
NMR Pulse (spin gymnastics)
BIRD Pulse
•
Selects Nuclei Only Attached to a Second Coupled Nuclei
i.
At the end of the sequence, 1H attached to 13C or 15N will be aligned along +z
ii.
At the end of the sequence, 1H attached to 12C or 14N will be aligned along –z
13C-1H
12C-1H
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
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