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
Nuclear Overhauser Effect (NOE)
and NOESY
Population Transfer
In population manipulations, the most commonly used technique is
selective population transfer (SPT):
Nuclear Overhauser Effect (NOE)
r
The distance between the two spins therefore can be determined by disturbing
one of them and observing how other is affected.
electron
23
Na
Nucleus-Electron OE:
Mechanism
99
100
=1+5=6
547
550
W2
=422+422=844
98
520
W0
995
1000
547
577
999
550
W2>>W0
Nucleus-Electron OE:
Mechanism
99
100
=1+5=6
547
550
W2
=-410-410=-820
517
107
W0
995
1000
547
990
580
550
W2<<W0
Nucleus-Nucleus OE
(Nuclear OENOE): Mechanism
18
20
=2+10=12
54
60
W2
=32+32=64
24
56
W0
90
54
100
60
58
90
W2>>W0
Nucleus-Nucleus NOE:
Mechanism
18
20
=2+10=12
54
60
W2
=-26-26=-52
50
24
W0
90
54
100
60
90
64
W2<<W0
Example: C-H NOE
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.
w0
w2
Longitudinal Relaxation Rates
Also Affect NOE
 I  R1, I 
18
20
 02  2 4
16 rII
=2+10=12
2
6
[ J (0)  3J ( 0 )  6 J (2 0 )]
60
W2
W0
90
100
=15+15=30
19
34
54R1S
R1I
54
60
W2,W0, R1I, R1S all affect overall NOE.
Here W2 > W0, R1I, R1S
R1S
80
95
Positive NOE
Longitudinal Relaxation Rates
Also Affect NOE
 I  R1, I 
18
 02  2 4
16 rII
=2+10=12
20
2
6
[ J (0)  3J ( 0 )  6 J (2 0 )]
60
W2
W0
R1I
54
90
100
60
W2,W0, R1I, R1S all affect overall NOE.
Here W2 > W0, R1I, but R1S>W2.
=6+6=12
18
24
54R1S
R1S
90
96
No NOE
Longitudinal Relaxation Rates
Also Affect NOE
 I  R1, I 
18
20
 02  2 4
16 rII
=2+10=12
2
6
[ J (0)  3J ( 0 )  6 J (2 0 )]
60
W2
W0
90
100
R1I
54
60
W2,W0, R1I, R1S all affect overall NOE.
Here W0> W2, but R1I>W0, R1S
=3-3=0!
19
22
54R1S
R1S
95
92
Negative NOE
Relaxation Rates and Motion
Fast motion
Slow motion
logW
W0
For slow motions,
W0 is dominant
and NOE tends to
negative.
W2
W1
-4
-3
-2
-1
0
1
log( 0 c )
2
3
4
Homonuclear Steady State NOE
18
20
=2+10=12
54
60
W2
=12+12=24
24
36
W0
90
54
100
60
78
90
NOE factor depends on W2, W0
NOE Difference Spectrum
(NOEdif)
Red: Saturated peak
Black: NOE affected peak
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
85
90
R1
90
90
100
81
R1
W2
W0
90
88
R1
100
90
98
Neither have to be steady
Nor have to be equilibrium
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.
r
When the distance between spins A and B is smaller than ~ 5 Å, NOE
cross peaks are observable.
A
B
3
2
10
6
7
8
9
4
1
5
1
0
2
5
8
74
6
9
3 1
3
2
6
10
7
8
9
4
1
5
1
0
2
5
8
74
6
9
31
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.
ROE Mechanism:
All relaxation rates are changed
into rotating frame.
Z
81
Y
R1rho
90
90
76
81
100
90
R1rho
W2rho
W0,rho
92
95
R1rho
100
90
Rotating frame
98
Note that both W2 and W0 promote ROE!
For homonuclear systems
NOE
 II 
 IIROE 
 02  2 4
16 rII
2
6
 02 2 4
16 rII
2
6
[ J (0)  6 J (2 0 )]
[2 J (0)  3J (2 0 )]
W2 promotes NOE while W0
blocks NOE
Both W2 and W0 promote ROE
c
2
J ( ) 
5 1 2 c2
IS 
NOE
 IS
I
 I  R1, I 
 02  2 4
16 rII
2
6
[ J (0)  3J ( 0 )  6 J (2 0 )]
 02  2 4
NOE
 II

[ J (0)  6 J (2 0 )]
2 6
16 rII
c
2 c
2
J ( ) 

5 1 2 c2
5
c
2

5 1 2 c2
5 2 c
J ( )  2
ROE
 II

2 2 4
0    c
12 2 rII 6
 IS 
NOE
 IS
I
(0)
Sz 
(0)
I z 

NOE
 IS
I
S
I
Some Applications of NOESY
Sterochemistry
Polymers
Hydration of biomolecules
Structure determination of biomacromolecules
 
 
 2 X
I Z ( S Z )  
  IY (  SY )
 t I
1 1 Z


  IY cos( I t1)  I X sin( I t1 )
(  SY cos( S t1)  S X sin( S t1 ))
 
 
 2 X
 
  I Z cos( I t1 )  I X sin( I t1 )
(  S Z cos( S t1 )  S X sin( S t1 ))
 m ( magnetization transfer )
 I Z cos( I t1 )  S Z cos( S t1 ) 

 a ( I Z  S Z )
Sterochemistry
CORMA
CORMA(COmplete
Relaxation Matrix Analysis)
Principle of CORMA
Example of CORMA
CORMA
V(τm)=V0 exp(Rτm)
NOESY of Poly(N-vinyl-carbazole): CHCl3, mixing time:450 ms, 500 MHz, 303 K
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:10-210-8s
Surface water:10-9s
Assignments of water-solute cross peak :
(a) Direct water-solute NOE
(hydration water-solute)
Non-labile
(b) Exchange-relayed NOE
(solute-solute)
Labile
(c) Chemical exchange
(bulk water-solute)
Labile
--- G. Otting, J. Progr. NMR. Spectrosc. 1997, 31 , 259
5
6
2
3
4
Glu1-190 ( mix=0.4 ms )
Significance to Structure Determination
A
B
C
rij=(1.78 Å)×(σkl/σij)1/6
D
Intensity:640
Distance:1.78Å
E
F
Intensity:10
Distance:3.56Å
C-terminal domain of rat Erp29 protein
R2
R1
i+1
N
C
C
iN
C
C
H
O
H
H
O
H
R3
R4
R5
C
C
N
C
C
N
C
C
H
O
H
H
O
H
H
O
COSY
NOESY
NOESY
COSY
CTX II: 44-60
i COSY
NH-CαH
NOESY
iCαH-(i+1)NH
(i+1)
COSY
(i+1)NH-CαH