1. More coherence…
Last time we saw (or at least tried) that we can select certain
orders of coherence by cycling the phases of a pulse
sequence appropriately. There are some things worth
remembering:
The phase shift acquired by a certain coherence will
depend on the change in coherence order associated
with it (Dp) and the phase of the pulse that creates it (f):
In order to select a coherence pathway, the pulse (or
receiver) that we are using to select it has to have a
phase such that:
were f is the phase of the pulse that created it...
They are basically the same, because they come from the
same mathematical description (the ‘operators’ used to
determine what happens with coherence after pulses work
the same way…).
We also said that we analyze changes in coherence with
CTPs, in which we only jot down what we want to detect at
the end of the whole experiment.
phase = - Dp * f
phase = - Dp * f

2. Multiple quantum filters
We’ve been saying for a while now that in a coupled spin
system there are zero- (p = 0), single- (p = 1),
double- (p = 2), etc-quantum transitions. In a three-spin
J-coupled system we have:
The big problem is that we can only study the evolution of
single-quantum transitions with our vector representation.
However, if we think of the right phase cycle, we can design
a CTP so that only coherence corresponding to transitions
of a certain order will be detected by the receiver. This is
extremely useful to discard certain signals in COSY spectra.
We can add a pulse (with proper phasing) such that only
double- or higher quantum transitions selected by the first
and second pulses will end up in the p = -1 line.
bbb
p = 0
abb
bba
bab
p =  1
p =  2
aba
aab
baa
p =  3
aaa

3. Multiple quantum filtered COSY (MQF-COSY)
For example, the CTP for selecting double-quantum
coherence or higher is:
Although we may have single-quantum coherence, it is not
affected by the second/third pulses. It will be cancelled out
after co-adding the FIDs resulting from all the different steps
of the phase cycle.
The phase cycle in this case looks like this:
Pulse 1:
Pulse 2:
Pulse 3:
Receiver: 90 90 90
p = + 2
p = + 1
p = 0
p = - 1
p = - 2

4. MQF-COSY (continued)
A normal COSY of a certain sample with singlets, doublets
and other multiplets may look like this. This is not selecting
any coherence in particular:
Now, if we use a MQF sequence with the phase cycle set to
select DQF, singlets would disappear (single-quantum):

5. MQF-COSY (…)
If we design the appropriate phase cycle, we can select only
coherence orders p > 2, and this would filter also double-
quantum transitions. Doublets and their correlations would
disappear from the 2D spectrum:
The phase cycle in this last case goes over 12 steps now (the
angle increment is 30 instead of 90), for a grand total of 96
different phases (less in practice - there are some tricks...).
Needles to say, I will not write all that down.
Why do we want to get rid of certain signals? Usually, singlets
fill the 2D spectrum with junk, so we can do without them.
Also, we may need to analyze an overlapped pattern that can
be simplified by removing some of the correlations.

6. 13C-13C correlations - INADEQUATE
These are all homonuclear correlations with 1H. Why not with
13C? Obvious reasons. The diagonal (single-quantum) is
99 times bigger than any cross-peak. We would need a truck-
load of sample and even then seeing the small peaks is hard.
What we do is use MQ filters to remove single-quantum stuff
(isolated 13C signals), and select only the double quantum
transitions (the J13C-13C coupling).
The pulse sequence is INADEQUATE (Incredible Natural
Abundance DoublE QUAntum Transfer Experiment), and
looks like this:
The first three pulses, which are basically a spin-echo, work
on 13C-13C coupled spins. If D is set to 1 / 4J, right before the
third pulse we have anti-phase vectors. On the other hand,
singlets remain as singlets.
The third pulse creates double-quantum coherence from
the anti-phase magnetization (13C-13C spin-systems), but
leaves the singlets untouched. The last pulse re-generates
coherence with p = -1, and the phase of this pulse and the
receiver need to cycle to eliminate single-quantum stuff.
90x
180y
90x
90f D D t1
13C:
[ y ]

7. INADEQUATE - CTP
Just for fun, we can write down the CTP for the experiment
in order to see which coehrences we are selecting:
The phase cycle that will select the appropriate path goes
over the three pulses (first and third have the same phase)
and the receiver. The phase increments are 8 (45 degrees):
90x
180y
90x
90f D D t1
13C: +2 +1
- 1
- 2
Pulse 1,3:
Pulse 2:
Pulse 3:
Receiver:

8. INADEQUATE
For a singlet, the first three pulses will put magnetization in
the <+z> axis in <-z>, pointing down. Now, if we do a 0, 1, 2,
3 cycle for the fourth pulse, we get:
If we put the receiver running backwards (0, 3, 2, 1), we will
effectively filter the single-quantum stuff.
For doublets, the first two pulses generates anti-phase mag-
netization. y y 1 3 x x y y 2 4 x x y y
90x
D (1 / 4J)
180y
D (1 / 4J) x x

9. INADEQUATE (continued)
The third is, for now, Divine intervention, and creates DQC:
Now we use the same phase cycle as before for the last pulse
and the receiver. The change in phase for the DQF is twice as
for SQF (remember that fcoherence = - Dp * fpulse …):
During the time t2 we acquire a normal FID, which will have
signals for all the 13C with their intensities modulated by
whatever happened in t1 (at the frequency of whatever
happened in t1…). y
90x
Evolution
of DQF
90f x y y 1 3 x x y y 2 4 x x

10. INADEQUATE (continued)
So, what the heck happened in t1? We cannot see it because
it is DQ, and vectors won’t cut it. However, we can more or
less explain it if we look at the 2-spin system energy diagram:
As we’ve seen before, DQ transitions involve processes that
have frequencies equal to the sum of the frequencies from
both SQ transitions.
This means that DQ transitions evolve under the t1 time at
frequencies almost twice as fast as the normal f2 frequency.
After 2D Fourier transformation, the f1 domain will have all
the wC1 + wC2 frequencies.
Since the evolution of the DQ is influenced by both nuclei
giving rise to the multiplet, there will be one cross-peak, or
correlation, for each f2 frequency in the f1 axis.
bb (+1/2, +1/2)
wC2
(-1/2, +1/2) ab
ba (+1/2, -1/2)
wDQ
wC1
wDQ = wC1 + wC2
aa (-1/2, -1/2)

11. INADEQUATE (…)
For an ‘example’ we had seen before, the 2D plot would look
like this:
The pseudo-diagonal is calculated from the cross peaks. If
we follow all the correlations, we can basically establish the
complete net of 13C connectivities.
In other words, we can figure out the carbon skeleton of the
complete molecule. Despite it looks really cool, you need
more than 100 mg in 0.5 ml of solvent...
INADEQUATE is the granddaddy of all MQF experiments. 1 4 2 3 5 6 7
6-7 O H 3 5 7 2 4 6
5-6 1 H O
4-5
2-3
3-4
1-2

12. DQF-COSY in a Bruker ARX-500
How pulse programs really look like
;cosydf
;arx-version
;2D COSY
;with double quantum filter
;A. Wokaun & R.R. Ernst, Chem. Phys. Lett. 52, 407 (1977)
;U. Piantini et al., J. Am. Chem. Soc. 104, 6800 (1982)
;A.J. Shaka & R. Freeman, J. Magn. Reson. 51, 169 (1983)
d0=3u
d13=4u
1 ze
2 d1
3 p1 ph1 d0
d20
p1 ph2
d13
p1 ph3
go=2 ph31
d1 wr #0 if #0 id0 zd
lo to 3 times td1
exit
ph1=
ph2=
ph3=
ph31=
;tl0: transmitter power level (default)
;p1 : 90 degree transmitter high power pulse
;d0 : incremented delay (2D) [3 usec]
;d1 : relaxation delay; 1-5 * T1
;d13: short delay (e.g. to compensate delay line) [3 usec]
;d20: to enhance intensity of DQC
;in0: 1/(1 * SW) = 2 * DW
;nd0: 1
;NS: 8 * n
;DS: 2 or 4
;td1: number of experiments
;MC2: QF
DQF-COSY in a Bruker ARX-500
Pulse program
Pulse 1...
Pulse 2...
Pulse 3...
Receiver...

13. INADEQUATE in a Bruker ARX-500
;arx-version
;2D INADEQUATE
p2=p1*2
d0=3u
d4=1s/(cnst3*4)
d12=20u
d12 dl5
d12 cpd
1 ze
2 d1
3 p1 ph1 d4
p2 ph2
p1 ph1 d0
p1 ph3
go=2 ph31
d1 wr #0 if #0 id0 zd
lo to 3 times td1
d4 do
exit
ph1=(8)
ph2=(8)
ph3=
ph31=
;tl0: transmitter power level (default)
;dl5: decoupler power level for CPD/BB decoupling
;p1 : 90 degree transmitter high power pulse
;p2 : 180 degree transmitter high power pulse
;p31: 90 degree pulse for slave timer (cpd-sequence)
;d0 : incremented delay (2D) [3 usec]
;d1 : relaxation delay; 1-5 * T1
;d4 : 1/(4J(CC))
;d12: delay for power switching [20 usec]
;in0: 1/(2 * SW(X)) = DW(X)
;nd0: 1
;NS: 32 * n
;DS: 4
;td1: number of experiments
;MC2: QF
;cpd: cpd-decoupling according to sequence defined by cpdprg
INADEQUATE in a Bruker ARX-500
Pulse program
Pulse 1...
Pulse 2...
Pulse 3...
Receiver...

14. Summary The phase cycle IS what makes the multiple pulse sequence
to do what we want.
By designing an appropriate pulse cycle we can select
magnetization associated with certain types of coherence.
This means that we can select different type of signals and
filter unwanted stuff from the spectrum.
In the MQF-COSY we only look at things that can give us
coherence order equal or higher than the filter we are using.
In the INADEQUATE experiment we select double-quantum
13C-13C coherence, and therefore allows us to see 13C-13C
coupled pairs.
We are still looking at the 13C-satellites, so we need a boat-
load of sample.
Next time we’ll start with connections through space
(NOESY).