Pulse : 0 1 2 3

1
A
B
Pulse 0 1 2 3 Recvr 0 2 0 2
A DQF-COSY
B Treat only the last pulse Pulse 0 1 2 3
Rcvr 0 3 2 1

• Essentially the same as the DQF COSY. We can
  combine with EXOCYCLE for the 180o
• pulse (0, 1, 2, 3) and the receiver set to
  (1, -1, 1, -1) to cancel pulse imperfection to
• become a 16 pule cycle.

A
We need to worry only the first two pulses which
gives ?p 0. The cycle design is as follow
P 0 1 2 3 R 0 0 0 0
However, this scheme does not get ride of axial
peak (T1 noise), thus we need to cycle the first
pulse thru 0 and 2 (Difference experiment). Thus
the overall phase cycle is as follow
P1 0 1 2 3 2 3 0 1 P2 0 1 2
3 0 1 2 3 R 0 0 0 0 2 2 2 2
EXOCYCLE Pulse 0, 1, 2, 3 Receiver 0, 2,
0, 2
2
Heteronuclear correlation spectroscopy

• Heteronuclear Multiple Quantum Correlation
  (HMQC)
• For spin 1, the chemical shift evolution is
  totally refocused at the beginning of detection.
  So we need to analyze only the 13C part (spin 2)

J-coupling
J-coupling
After 90o 1H pulse
At the end of ? - I1y

2I1xI2z for ? 1/2J12 After 2nd 90o
pulse The above term contains both zero and
double quantum coherences. Multiple quantum
coherence is not affected by J coupling. Thus, we
need to consider only the chemical shift
evolution of spin 2.
J-coupling
13C evolution
J-coupling during 2nd ?
3
(HMQC)
Since only single quantum coherence is detectable
at the detection period we must have pI -1 and
pS 0. Other pathway is irrelevant. The major
concern is how to suppress the enormous signal
from uncoupled spins. This can be achieved by
cycling thru only S pulses by 0 2 to either
pulses. Adding a EXOCYCLE pulse give a 8 cycle of
the following
Pulse I 0 0 1 1 2 2 3 3 Pulse
S 0 2 0 2 0 2 0 2 Receiver
0 2 1 3 2 0 1 3
EXOCYCLE Pulse 0, 1, 2, 3 Receiver 0, 2,
0, 2

• Disadvantage of phase cycling
• Need to take a minimum shots to go thru phase
  cycle ? Time consuming.
• Cancellation may be limited by dynamic range or
  system instability problems.
• Alternative Gradient pulses.

4

• Gradient Bg Gz ? Larmor frequency ?L(z)
  ?(Bo Bg) ?(Bo Gz)
• Phase accumulated after a time t ?(z) ?(Bo
  Gz)t
• The spatial dependent phase ?(z) ?Gzt
• The effect of gradient on the spatial dependent
  evolution of Ix will be

The total x-magnetization in the sample is
For t 2 ms, Bg 0.37 Tm-1 (37 Gcm-1), Mx
10-3Mo In general, the pulse is not uniform in
time and the spatial dependent phase can be
written as
Where p is the coherence order and s is the
gradient shape function and ? is the time
duration of the gradient pulse. The sum is over
all orders and over all nuclei.
To select a particular CTP we need to make ?1
?2 0 or
For selecting p11 and p2-1 CTP we need to
set ?2 2?1 or Bg,2 2Bg,1. For the same
condition the p1 3, p2 -1 CTP will have
5

• For more complicated CTP more gradients may be
  needed and part of the gradients can be used to
  select different part of the CTP. Alternatively,
  the pathway may be consistently dephased and the
  magnetization only refocused the final gradient,
  just before detection.
• ? There may be many ways to select the same
  pathway.
• ? A particular pair of gradient pulse selects a
  particular ratio of
• coherence orders, so it is not unique.
• No single pair can select pathway of different
  ratio.
• Example below shows that we cannot selct both
  p2 ? -1 CTP
• but not -2 ? -1 CTP simultaneously. Thus,
  results in a lost of sensitivity by ½.

Purge gradient Gradient pulse will not affect p
0 coherence, thus by applying a gradient will
suppress all p ? 0 coherences. Such a gradient is
called a purge gradient. Gradient on other axes
It is possible to generate gradients in which the
field varies along x or y. The spatially
dependent phase generated by a gradient applied
in one direction cannot be refocused by a
gradient applied in a different direction. Thus.
In sequence where more than one pair of gradient
are used it may be convenient to apply further
gradient in different directions to the first
pair, so as to avoid the possibility of
accidentally refocusing unwanted CTPs.
6
A refocusing pulse causes p ? -p and Iz ? -Iz.
The net phase at the end of the sequence shown
Thus, ? 0 if, and only if, p -p, i.e. a
perfect 180o pulse. A pair of gradients place on
eihter sides of a refocusing pulse selects the
CTP associated with a perfect refocusing pulse. ?
Clean up gradient for the refocusing pulse. A
pair of gradients of equal strength but different
in polarity will maximize the dephasing of
unwanted coherences both those ppresent before
the pulse and those might be generated by the
pulse ? Clean up gradient for the inversion
pulse. Similarly, a Clean up gradient for the
inversion pulse in a heteronuclear sequence can
be devised.
7
Phase error introduced due to chemical shift
evolution in ?1
Phase error accumulated during ?2 and ?2
This frequency dependent phase shift cannot be
corrected easily. ? Remedy Add a refocusing
gradient
Movement of spins causes attenuation of M in the
presence of a gradient. D is the diffusion
constant.
? Signal loss increases w/ increasing ? D for a
given ?
8

• Diffusion causes line broadening and signal
  loss.
• To reduce diffusion effect one must keep the
  separatin
• between a gradient pair to a minimum.
• Sequence (a) is preferred due to shorter time
  separation
• between the two gradient pulses.

• Advantages of gradient
• 1. Time saving No need to complete a phase
  cycle.
• 2. Better spectral quality due to less dynamic
  range problem (No need to substrate two big
  signals).
• Disadvantages
• Need a gradient coil.
• Care must be taken to ensure absorption mode
  lineshape.

2G1?
- 2G1?
9
?I ?I(G1 G1 G2) - ?IG2
?S ?S(-G1 G1) - 2?SG1
?I ?S - ?IG2- 2?SG1 0 ?
Only suppress unwanted coherences at a (Imperfect
pulse and residual unlabeled signal cause
problems). Not recommended.
10
?I - ?IG2
?S - ?SG1