The Nuclear Overhauser Effect (NOE) describes a change in the NMR signal intensity of one nuclear spin when a nearby spin is saturated. There are two main relaxation mechanisms, W0 and W2, that determine whether the NOE will be positive or negative. W0 typically leads to a negative NOE for macromolecules or in viscous solutions, while W2 usually gives a positive NOE for small molecules in non-viscous solutions. The magnitude of the NOE depends on factors like molecular weight, temperature, and solvent and can provide information about internuclear distances that is useful for assigning protein NMR spectra.

1. Nuclear Overhauser Effect

2. Nuclear Overhauser Effect (NNOOEE)
• A change in the integrated NMR absorption
intensity of a nuclear spin when the NMR
absorption of another spin is saturated.

3. Nuclear Overhauser
Effect

4. ( s )
I I W 2 W
0
i i + +
1 2 0
0
0
2W W W
I
-
=
-
h =

5. Macromolecules or in viscous solution
W0 dominant, negative NOE at i due to s
Small molecules in non-viscous solution
W2 dominant, positive NOE at i due to s

6. Nuclear Overhauser Effect
Brownian motion and NOE

7. t
( )
( ( ) )
1 6 2 2
w t
i c
t
c
0 6 2 2
w w t
i s c
t
c
2 6 ( 1
( )2 2 )
12
1
2
1
3
+ +
i s c
i c
r
W
r
W
r
W
w w t
µ
+ -
µ
+
µ
When 1/tc >>w0 (or tc
2
w0
2 <<1 ) extreme narrowing limit
W 3 t 2 t 12
t µ c µ c µ
c
1 6 0 6 2 6
r
W
r
W
r

8. When 1/tc >> w0 (or tc
2
w0
2 <<1 )
extreme narrowing limit
W t t t µ 3 c µ 2 c µ
12
c
1 6 0 6 2 6
r
W
r
W
r
( ) ( -
)
t
12 2 /
6
( ) 1/ 2
W -
W
2 0
2 6 12 2 /
6
1 2 0
s I I
0
0 =
+ +
=
+ +
=
-
=
r
r
W W W
I
c
c
h
i i t
For homo-nuclear hmax = 0.5
For hetro-nuclear hmax = 0.5 (gs/gi)

9. When 1/tc ~ w0 (or tc w0 ~ 1 ) M.W.~ 103
W2 and W0 effect are balanced. h max ~ 0
improvement:
• Change solvent ofr temperature
• Using rotating frame NOE

10. When 1/tc < w0 (or tc w0 >> 1 ) M.W. > 104
W0 dominant , h max = -1
application
Useful technique for assigning NMR spectra of protein

11. Nuclear Overhauser Effect & distance
NOE 1
µ æ 6
t · ÷øö çè
f ( c )
r

12. citraconic acid mesaconic acid