NMR Pulse

1
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 gt torque
on bulk magnetization (B1)
A measured quantity instrument and sample
dependent.
2
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
Mo
Inverts the spin-population. No NMR signal
detected
p
x
x
-Mo
180o
y
y
Can generate just about any pulse width desired.
3
NMR Pulse
Impact on the FID
90o
270o
4
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

5
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)
6
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)
• Different delays between pulses
• Coupling constants ? Hz ? TIME!
• Chemical shifts ? ppm ? Hz ? TIME!
• Select specific coupled nuclei or chemical shifts

13C spectra where peaks have different phases
7
NMR Pulse (spin gymnastics)
NMR pulse sequences a) composed of a series of
RF pulses, delays, gradient pulses and phases b)
in a 1D NMR experiment, the FID acquisition time
is the time domain (t1) c) more complex NMR
experiments will use multiple time-dimensions
to obtain data and simplify the
analysis. d) Multidimensional NMR experiments
may also use multiple nuclei (2D, 13C,15N)
in addition to 1H, but usually detect 1H)
1D NMR Pulse Sequence
8
NMR Pulse (spin gymnastics)
Selecting Specific Information in an NMR Spectra

• Pulse width and power level determines bandwidth
  of frequencies that are excited
• produces bandwidth (1/4t) centered around single
  frequency
• Can be used to selectively excite a region of the
  NMR spectra

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
9
NMR Pulse (spin gymnastics)
Selecting Specific Information in an NMR Spectra

• 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
10
NMR Pulse (spin gymnastics)
Selecting Specific Information in an NMR Spectra

• 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
11
NMR Pulse (spin gymnastics)
Decoupling

• Remove the splitting pattern caused by spin-spin
  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?
• Heteronuclear decoupling
• Common decouple protons from carbon in carbon
  spectra
• Homonuclear decoupling
• Selectively decouple one proton
• spin system from another
• Must be chemically distinct
• Can not decouple entire spectra

Decoupled spin system
Incomplete decoupling
Coupled spin system
12
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
13
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
• sensitivity increase is proportional to
  splitting pattern
• additional increase comes from the NOE (h,
  nuclear Overhauser effect)
• will be discussed in detail latter
• 13C signals are enhanced by a factor of

1 h 1 1/2 . g(1H)/g(13C) max. of 2
Completely 1H coupled
1H decoupled at single (10 ppm) frequency
Completely 1H decoupled (WALTZ)
14
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
Completely 1H decoupled (WALTZ)
15
NMR Pulse (spin gymnastics)
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
• 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

180o
16
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
17
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
• WALTZ-16
• Based on the composite pulse
• (90o)x(180o)-x(270o)x ? decouples efficiently
  over 6 kHz
• Corrects imperfections in MLEV
• 90o 100ms ? reduces sample heating
• 1 90o, 2180o, 3270o, 4360o
• GARP
• Computer optimized using non-90o flip angles
• Effective decoupling bandwidth of 15 kHz
• 90o 70 ms

Trajectory of 1H nuclei after two R MLEV-4 pulses
results in an effective 360O pulse. Results is
improved slightly by following with two R pulses
with reverse phase.
NMR IN BIOMEDICINE, VOL. 10, 372380 (1997)
18
NMR Pulse (spin gymnastics)
Decoupling

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

19
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 couple to the irradiated
  nuclei
• Chemical shift difference gtgt 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.
20
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

• B2 measured in Hz where B2ltlt v -vi
• v true (normal) frequency)
• vi frequency of irradiation

Bloch-Siegert Shift B2 20 Hz
Weak RF field applied
Irradiation frequency (vi)
Normal Spectra
21
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
• 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
• 11x 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)

22
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
23
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
• Used in more complicated pulse programs
  (experiments)

Signal echo
24
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)yn
25
NMR Pulse (spin gymnastics)
BIRD Pulse

• Selects Nuclei Only Attached to a Second Coupled
  Nuclei
• 1H attached to 13C or 1H attached 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
90o
180o
d1 recycle delay for relaxation d2 1/2J d3
delay for 1H-12C z magnetization to decay to
zero
26
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