1) The document discusses nuclear Overhauser effect (NOE) and nuclear Overhauser spectroscopy (NOESY). NOE occurs when the polarization of one coupled spin is perturbed from equilibrium, affecting the polarization of the other spin through cross-relaxation. 2) NOE factors depend on cross-relaxation rates and longitudinal relaxation rates, and can provide inter-proton distance information useful for structure determination. 3) Applications of NOESY discussed include determining polymer and biomolecule structures, and detecting hydration waters around proteins.

1. 無機物理方法（核磁共振部分）
The Physical Methods in Inorganic
Chemistry
(Fall Term, 2004)
(Fall Term, 2005)
Department of Chemistry
National Sun Yat-sen University
Chapter 6

2. Nuclear Overhauser Effect (NOE)
and NOESY

3. Population Transfer
In population manipulations, the most commonly used technique is
selective population transfer (SPT):

4. Nuclear Overhauser Effect (NOE)
N
S
N
S
r
The distance between the two spins therefore can be determined by disturbing
one of them and observing how other is affected.

5. 23Na
electron

6. Nucleus-Electron OE:
Mechanism
547
550
547
550
W2
W0
99 =1+5=6
100
995
1000
W2>>W0
577
999
98
520
=422+422=844

7. Nucleus-Electron OE:
Mechanism
547
550
547
550
W2
W0
99 =1+5=6
100
995
1000
W2<<W0
990
580
517
107
=-410-410=-820

9. Nucleus-Nucleus OE
(Nuclear OENOE): Mechanism
54
60
54
60
W2
W0
18 =2+10=12
20
90
100
W2>>W0
58
90
24
56
=32+32=64

10. Nucleus-Nucleus NOE:
Mechanism
54
60
54
60
W2
W0
18 =2+10=12
20
90
100
W2<<W0
90
64
50
24
=-26-26=-52

11. Example: C-H NOE

12. Whenever a polarization or a transition
of a spin is inverted or saturated, the
polarization or transition of the other
spins that are coupled to it will be
affected.
Perturbation on a Spin (Saturation/Inversion) + Cross Relaxation

The Polarization of Another (Coupled) Spin Is Altered.
Depending on the relative magnitudes of W2 and W0, NOE factor can be
Larger or smaller than 1 and can be both negative and positive.

13. w0 w2

14. Longitudinal Relaxation Rates
Also Affect NOE
2 2 4
m g R J J J
rII I º I = + + 
r 0 w w
1, [ (0) 3 ( 0) 6 (2 0)] 16 p
2 6
54
60
54
60
W2
W0
18 =2+10=12
20
90
100
W2,W0, R1I, R1S all affect overall NOE.
Here W2 > W0, R1I, R1S
80
95
19
34
=15+15=30
R1I
R1S
R1S
Positive NOE

15. Longitudinal Relaxation Rates
Also Affect NOE
2 2 4
m g R J J J
rII I º I = + + 
r 0 w w
1, [ (0) 3 ( 0) 6 (2 0)] 16 p
2 6
54
60
54
60
W2
W0
18 =2+10=12
20
90
100
W2,W0, R1I, R1S all affect overall NOE.
Here W2 > W0, R1I, but R1S>W2.
90
96
18
24
=6+6=12
R1I
R1S
R1S
No NOE

16. Longitudinal Relaxation Rates
Also Affect NOE
2 2 4
m g R J J J
rII I º I = + + 
r 0 w w
1, [ (0) 3 ( 0) 6 (2 0)] 16 p
2 6
18 =2+10=12
20
90
100
54
54
W2,W0, R1I, R1S all affect overall NOE.
Here W0> W2, but R1I>W0, R1S
95
92
19
22
=3-3=0!
60
60
W2
W0 R1I
R1S
R1S
Negative NOE

17. Relaxation Rates and Motion
logW
W2
log( w t ) 0 c W0
W1
-4 -3 -2 -1 0 1 2 3 4
For slow motions,
W0 is dominant
and NOE tends to
negative.
Fast motion Slow motion

19. Homonuclear Steady State NOE
54
60
54
60
W2
W0
18 =2+10=12
20
90
100
78
90
24
36
=12+12=24
NOE factor depends on W2, W0

23. NOE Difference Spectrum
(NOEdif)

28. Red: Saturated peak
Black: NOE affected peak

31. 1D Homonuclear Transient NOE
180o
A single spin is inverted and the spin system response is
read using a 90° pulse after a “mixing” time delay of variable
duration. In the transient mode, the NOE builds up due to
cross-relaxation of nearby spins by the inverted spin as the
entire spin system.
81
90
90
100
88
85
Neither have to be steady
Nor have to be equilibrium
R1
R1
R1
90
100
81
90
W2
W0
98
90

32. NOE: Essence
Whenever the polarization of one of two coupled spins
deviates from its equilibrium value, the polarization of
the other spin is affected by cross relaxations. The
NOE factor (the extent that the polarization of the
unperturbed spin is affected) depends on cross
relaxation rates and longitudinal relaxation rates.
N
S
N
S
r

34. When the distance between spins A and B is smaller than ~ 5 Å, NOE
cross peaks are observable.
A
B

38. 2 3 1
10 5 8 7 4 6 9
3
1 5 2
4
6
7 8
9
10

39. 3
1 5 2
4
6
7 8
9 10
2 3 1
10 5 8 7 4 6 9

40. 1D Homonucelar ROE
180o 90o
A single transition is inverted using a selective 180° pulse (along the x axis), and
then a hard 90° x pulse is immediately applied to the spin system.
This has the effect of placing the “inverted” magnetization along the -y axis while
the rest of the magnetization is aligned along +y. Then, a low-power rectangular
pulse is applied long the y-axis.
This pulse is applied parallel to the magnetization (in the rotating frame) and effects
no net rotation. Instead, it “locks” the magnetization along the y axis, and is referred
to as a spin lock pulse. The magnetization is said to be spin locked because
it doesn’t precess about B0, but the spins now precess aboutB1(the spin lock pulse).
Therefore, under these conditions, the magnetization can be considered to being
analogous to alignment along the z axis in the presence of B0 alone.
Finally, the spins will relax towards a new equilibrium in the presence of B1;
the characteristic time constant for this decay is called T1ρ forT1in the rotation frame.

41. ROE Mechanism:
All relaxation rates are changed
into rotating frame.
95
76
81
100
90
Y
Rotating frame Note that both W2 and W0 promote ROE!
81
90
90
100
98
92
Z
R1rho
R1rho
R1rho
90
W2rho
W0,rho

44. For homonuclear systems
2 2 4
m g J J
NOE
II = - + 
s 0 w
[ (0) 6 (2 0)] 16 p
2 6
rII
2 2 4
m g J J
ROE
II = + 
s 0 w
[2 (0) 3 (2 0)] 16 p
2 6
rII
W2 promotes NOE while W0
blocks NOE
Both W2 and W0 promote ROE

47. t w
( ) 2
5 1 2 2
c
J c
+
w t
=

48. NOE
IS IS r
I
s h =
2 2 4
m g R J J J
rII I º I = + + 
r 0 w w
1, [ (0) 3 ( 0) 6 (2 0)] 16 p
2 6
2 2 4
m g J J
NOE
II = - + 
s 0 w
[ (0) 6 (2 0)] 16 p
2 6
rII

49. J w = t c Þ
2
t
2 2 ( ) c
5
2
5 1
w t
c
+

50. w t 2
2 2 5 2
( ) = 2 Þ
c c
J c
w t w t
5 1
+

51. 2 2 4
0
12 II
s =
m  g t c
2 6
r
ROE
II p

52. S
s
(0)
h = s < >
=
IS g
I
NOE
IS
I
z
(0)
z
NOE
IS
I
S
I
g
r
r
< >

55. Some Applications of NOESY
Sterochemistry
Polymers
Hydration of biomolecules
Structure determination of biomacromolecules

56. p
ö çè
÷ø
æ
I S ¾¾¾¾®- I -
S
( ) X
( )
Z Z Y Y
I t I t
W
¾¾¾¾®- W + W
cos( ) sin( )
Y I X I
1 1
t I
Z
S t S t
- W + W
( cos( ) sin( ))
Y S X S
I t I t
p
ö çè
÷ø
æ
¾¾¾¾®- W + W
cos( ) sin( )
Z I X I
1 1
X
S t S t
- W + W
( cos( ) sin( ))
(magnetization transfer)
Z S X S
1 1
t
I t S t a I S
- W - W ¾¾¾¾¾¾¾¾¾¾¾® +
cos( ) cos( ) ( )
1 1
2
1 1
2
1 1
m
Z I Z S Z Z

61. Sterochemistry

63. CORMA
CORMA(COmplete Relaxation Matrix Analysis)
Principle of CORMA
Example of CORMA

64. V(τm)=V0 exp(Rτm)
CORMA

65. NOE SY of Poly(N-vinyl-carba zole): CHCl3, mixing time:450 ms, 500 MHz, 303 K

66. Detection of hydration water via observation
of NOEs from water-protein
--- G. Otting, E. Liepinsh, K. Wuthrich, Science 1991,254,974
BPTI 牛胰蛋白抑制劑
Residues : 58
Internal water : 4
Residence times:
Interior water:10-2-
10-8s
Surface water:10-9s

67. Assignments of water-solute cross peak :
(a) Direct water-solute NOE
(hydration water-solute)
(b) Exchange-relayed NOE
(solute-solute)
(c) Chemical exchange
(bulk water-solute)
Non-labile
Labile
Labile
--- G. Otting, J. Progr. NMR. Spectrosc. 1997, 31 , 259

68. 2
3
Glu1-190 ( mix=0.4 ms )
4
5
6

69. Significance to Structure Determination
rij=(1.78 Å)×(σkl/σij)1/6
Intensity:640
Distance:1.78Å
Intensity:10
Distance:3.56Å
A
B
C
D
E
F

70. C-terminal domain of rat Erp29 protein

71. R1
C
H
C
O
i i+1
N
H
R2
C
H
C
O
R3
N C C
H H O
N
H
C
H
C
R4
O
N
H
C
H
C
R5
O
COSY
NOESY NOESY
CTX II: 44-60
i COSY NOESY (i+1)
NH-CαH iCαH-(i+1)NH COSY
(i+1)NH-CαH
COSY