1. Claridge Chapter 9

2. NOE

3. Transient NOEs IS  4{[6/(1 + 4 02c2)] - 1}c/rIS6
In standard 1D NOE, one resonance is saturated, and the system must respond to return to equilibrium by the W0 and W2 cross-relaxation pathways.
Transient NOEs occur when the population is inverted (either selectively in a 1D or all at once in a 2D) and the system responds again through the dipolar cross-relaxation pathways during a mixing period. The results are then read with a 90º pulse.
IS  4{[6/(1 + 4 02c2)] - 1}c/rIS6
IS = cross relaxation rate
c = molecular correlation time
rIS = distance between the nuclei

4. Transient NOEs
A transient NOE builds up for some period of time but then decays away.
For transient NOEs, the steady-state NOE enhancement has not been reached; the saturation period is short.
They develop from the population disturbance created by initial inversion of the resonance.

5. A{B}/X{Y}= rAB-6/ rXY-6
Transient NOEs
Assuming the NOE growth is linear (which is true when m is low), then the NOE enhancement between 2 spins is proportional to the cross-relaxation rate which is proportional to the distance between the nuclei.
A{B} = kAB = k' rAB-6 
And the distance between A and B can be determined from an NOE of known distance X and Y:
A{B}/X{Y}= rAB-6/ rXY-6

6. Mixing Time
Mixing time is when the magnetization is being transferred from one nucleus to another by the NOE, while the magnetization is aligned along the z-axis (so NOE is affected by mostly T1, not T2!).
Shorter mixing times allow for only magnetization transfer only over a short distance, while longer mixing times allow for transfer over longer distances.
However, what is a short mixing time for a small molecule is very long to a large molecule.
Although choosing a mixing time is mostly empirical; there are ways to use theory to predict what is appropriate.
NOEs cannot buildup faster than 1/T1, although they can buildup slower.

7. Mixing Time
Transient NOE builds up for some period time linearly, then decays
Build up rate correlates to T1, different nuclei build up at different rates.
Optimally, one works with all nuclei in the linear range of NOE build up.
Spin diffusion (multiple transfer) is a greater problem at longer mixing times

8. NOESY NOESY = Nuclear Overhauser Effect SpectroscopY
2D NOE experiment where the crosspeaks are NOEs between the two protons, and the volume of the crosspeak is proportional to the distance between the two protons.
Since NOEs are transfer through space, the NOESY is the basic experiment used for determining 3-dimensional structures of molecules with NMR.
The advantages of NOESY versus 1D:
1) All NOEs in the molecule are observed in one experiment.
2) Although transient NOEs are weaker than steady-state NOEs, signal/noise is usually better. Although artifacts are a problem in NOESY, they are less important than in 1D NOE experiments- particularly subtraction artifacts in 1D NOE.
3) Better resolution for protons close in chemical shift and no problems of cross saturation (saturating the proton adjacent in chemical shift)

9. NOESY
The NOESY pulse sequence = DQF-COSY (except mixing time is ms versus s for DQF-COSY)

10. EXSY 2D NOESY = 2D EXSY (Exchange Spectroscopy)
2D EXSY is used to determine which nuclei are in chemical exchange. Resonances of nuclei in chemical exchange, will have a crosspeak between them.
Thus, crosspeaks in a NOESY could be from chemical exchange or NOEs.
However, chemical exchange peaks are ALWAYS the same sign as the diagonal, NOEs are the opposite sign of the diagonal for small molecules
Hydroxyl protons exchanging with water will have an exchange crosspeak to water in a 2D NOESY experiment.
The exchange peaks result from chemical exchange during the mixing time, and thus their presence is correlated to the rate of chemical exchange.

11. Problems with NOESY:
1) Spin Diffusion- multiple transfer of magnetization.
2) NOE goes to 0 at ~1000 MW
3) Chemical exchange peaks and NOESY peaks look alike for large molecules.
4) Zero-quantum artifacts due to strongly J-coupled nuclei.

12. NOESY Parameters

13. ROESY ROESY = ROtating frame Overhauser Effect Spectroscopy
ROESY is similar to NOESY with respect to what is observed, but depends upon the buildup of ROEs which are ALWAYS positive.
Note that chemical exchange peaks are also observed in ROESY, and as in NOESY, same sign as the diagonal.
ROE is cross relaxation in the transverse plane (not the longitudinal axis).
The ROE is created by spin-locking the magnetization in the x-y plane by continuous pulsing that creates no torque on the magnetization.
The spin-lock is on the order of kHz, which means that the product of the frequency and the correlation time << 1; thus, for all values of correlation time, the ROE is positive.

14. ROESY   4{3/(1 + 02 c2) + 2} c/rIS6   54c/rIS6
Cross relaxation for an ROE () is proportional to:
  4{3/(1 + 02 c2) + 2} c/rIS6
For a small molecule (0c << 1),
  54c/rIS6
which is the same as the equation for a transient NOE.
For a large molecule (0c >> 1),
ROE  24c/rIS6
NOE  -4c/rIS6
Thus, for large molecules,
ROE = -2NOE

15. Comparison of ROE buildup (ROESY) versus transient NOE buildup (NOESY)

16. Pulse Sequence of ROESY is similar to that of TOCSY:
Comparison of Transient NOE (NOESY) with Rotating Frame NOE (ROESY)

17. ROESY vs. NOESY Advantages of ROESY:
1) Unaffected by molecular weight, as the experiment is done in the rotating frame; ROE is not 0, even when NOE = 0.
2) Chemical exchange peaks always have opposite sign to ROEs.
3) Spin diffusion is less pronounced, and spin diffusion peaks are opposite in sign to ROEs.
4) ROE build up is twice as fast that of the NOE for large molecules, mixing time is generally shorter.
Mixing time for small molecules is generally about the same for ROESY and NOESY.

18. ROESY vs. NOESY Disadvantages of ROESY:
1) TOCSY artifacts, as the pulse sequences are similar, there can be TOCSY peaks in a ROESY (ROESY peaks in a TOCSY)

19. ROESY vs. NOESY
2) ROEs have a theoretical limit of 67% of the corresponding NOE for large molecules
3) Sample Heating
Since there is constant pulsing during the mixing time, sample heating can be a problem.
Normally lower field spin lock is used, ~ Hz (40-80 s).
4) Lower field spin-lock means that it is hard to cover the entire frequency range if there is large chemical shift dispersion
5) COSY type crosspeaks.
This arises from the low power pulse acts like the last pulse on a COSY to cause coherence between J-coupled spins.

20. ROESY Demo