1. Pulse : 0 1 2 3 Recvr: 0 2 0 2 AB 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. P : 0 1 2 3 ; R: 0 0 0 0 P 1 : 0 1 2 3 2 3 0 1 P 2 : 0 1 2 3 0 1 2 3 R : 0 0 0 0 2 2 2 2 A We need to worry only the first two pulses which gives  p = 0. The cycle design is as follow: However, this scheme does not get ride of axial peak (T 1 noise), thus we need to cycle the first pulse thru 0 and 2 (Difference experiment). Thus the overall phase cycle is as follow: EXOCYCLE: Pulse: 0, 1, 2, 3; Receiver: 0, 2, 0, 2

2. Heteronuclear correlation spectroscopy 1.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 13 C part (spin 2) J-coupling 13 C evolution After 90 o 1 H pulse: At the end of  : - I 1y = = 2I 1x I 2z for  = 1/2J 12 After 2 nd 90 o 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 during 2nd  : J-coupling

3. (HMQC) Since only single quantum coherence is detectable at the detection period we must have p I = -1 and p S = 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: 1.Need to take a minimum shots to go thru phase cycle  Time consuming. 2.Cancellation may be limited by dynamic range or system instability problems. 3.Alternative: Gradient pulses.

4. Gradient: B g = Gz  Larmor frequency:  L (z) =  (B o + B g ) =  (B o + 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 I x will be: The total x-magnetization in the sample is: For t = 2 ms, B g = 0.37 Tm -1 (37 Gcm -1 ), M x = 10 -3 M o 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 p 1 =+1 and p 2 =-1 CTP we need to set  2 = 2  1 or B g,2 = 2B g,1. For the same condition the p 1 = +3, p 2 = -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 p=+2  -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 I z  -I z. The net phase at the end of the sequence shown: Thus,  = 0 if, and only if, p’ = -p, i.e. a perfect 180 o 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: 1.Need a gradient coil. 2.Care must be taken to ensure absorption mode lineshape. 2G 1  - 2G 1 

9.  I =  I (G 1 – G 1 – G 2 ) = -  I G 2  S =  S (-G 1 – G 1 ) = - 2  S G 1  I +  S = -  I G 2 - 2  S G 1 = 0  Only suppress unwanted coherences at a (Imperfect pulse and residual unlabeled signal cause problems). Not recommended.

10.  I = -  I G 2  S = -  S G 1