The Nuclear Overhauser Effect (NOE)
I
IS
S
I
IS
S I
IS
S
Inversion Saturation(NOESY) (1D-NOE)
The sign of the NOE
positive NOE negative NOE
A B C
≈≈
500°C 10°C
10°C
10°C
10°C
t
T
t
T
t
T
t
T
t
T
t
T
t
T
500°C
500°C
500°C
t
T
A
B
C
D
αα
βααβ
ββ
W ++W −−
W −+
W +−
αα
βααβ
ββ
W α−
W −βW +β
W −α
W β−
W β+
W +α
W α+
Possible NMR transitions in a 2-spin system
The Nuclear Overhauser Effect (NOE):
€
η = fIS =I − Io( )Io
€
η = f τ c r−6( )
€
dIzdt
= − Iz − Iz0( )(W0IS + 2W1I +W2IS ) − Sz − Sz
0( )(W2IS −W0IS )
0 = − Iz − Iz0( )(W0IS + 2W1I +W2IS ) + Sz
0(W2IS −W0IS )
Iz − Iz0
Sz0 =
(W2IS −W0IS )(W0IS + 2W1I +W2IS )
at equilibrium, dIz/dt=0, Sz=0
€
Sz0 =
γ Sγ IIz0
The derivation of the Solomon equations
fI S = γ I
γ S
σ IS
ρ IS
€
ρ =W0 + 2W1 +W2
ρ is the auto-relaxation rate (or leakage rate). This is the relaxation rate of the saturated spin without
changing populations of other spins
€
σ IS = W2QC −WZQC
σ is the cross-relaxation rate. It determines how fast the NOE is being transferred to other
spins during longitudinal relaxation
τc /ns
R /s-1auto
0.2 0.4 0.6 0.8 1
0.2
0.4
0.6
0.8
1
1.2
τc /ns
0.2 0.4 0.6 0.8 1.
0.4
0.6
-0.2
0
0.2R /s-1cross
0.0
0.5
1.0
NOE
-1.0
-0.5
0.01 0.1 1.0 10 100τc (ns)
ηmax
τmτm
selective 180
Buildup Curves
mixing time mixing time
NO
E
NO
Esteady-state NOE transient NOE
Spin Diffusion
3
1 2
The steady-state NOE
€
fIS = ηmaxrIS−6
rIS−6 + rIX
−6
x∑
− ηmaxfXSrIX
−6
rIS−6 + rIX
−6
x∑
%
&
' ' '
(
)
* * * x
∑
direct contribution
indirect contribution (3-spin effect, spin-diffusion)
• Most enhancements are positive but some can also be
negative, depending on the geometry.
• T1 and T2 values are very similar.
• The lines are rather sharp (hence the name extreme-narrowing).
• The influence of the indirect effect is smaller but noticeable.
Extreme narrowing (ηmax >0):
The influence of relaxation sinks
0 20 40 60 80 100 120 140 160 180
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
angle α
NOE
α
Α Β
C
3
1 2
fAB
In the negative NOE regime (large molecules), all enhancements are negative.
The T2 values are very much shorter than T1.
The lines are broad.
Spin-diffusion is very effective and steady-state NOE measurements are
completely useless. When the molecules have gained a certain size the spin-
diffusion effect spreads the NOE out to all other protons (see the magnitude of
the NOE for τc > 100) irrespective of what their distance to the irradiated proton
is!
€
fIS ≠ fSI
Spin-diffusion (ηmax <0):
irrespectively whether spin S has another proton close in space
(which quenches the NOE in the steady state case dramatically).
Using short mixing times NOE information is still usefull in the spin-
diffusion case. Spin-diffusion can be recognized from the buildup
curves of the NOEs (a number of NOESY experiments are recorded
with increased mixing times. Spin-diffusion cross peaks should show a
characteristic induction phase).
1D transient and NOESY experiments give identical enhancements.
The three-spin effect in the spin-diffusion regime
0.01 0.1 1 10 100 1000
0.6
-0.6
0.4
-0.4
0.2
-0.2
0.0
-0.6
ωτc
ΝΟΕ
A B C D1 2 1fAB
fCBfDB
The transient NOE
The transient NOE has some features that are remarkably different from the
steady-state NOE:
Enhancements are symmetrical
€
fIS = fSI
simulated NOE buildup curves
30 ps 300 ps
3 ns 30 ns
NOESY Buildup Curves
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
NO
E (a
rbitr
ary
units
)
mixing time om [sec]
0
0.5
1.0
1.5
2.0
2.5
3.0
0.1 1 10 100 1000
×108
ω/2π [MHz]
0.0
0.5
1.0
NOE
-1.0
-0.5
0.01 0.1 1.0 10 100
τc (ns)
ηmax
0
0.5
1.0
1.5
2.0
2.5
3.0
0.1 1 10 100 1000
×108
ω/2π [MHz]
€
σ IS = W2QC −WZQC
€
W0 =110b2J(0)
€
W2 =35b2J(2ω0)
NOE vs ROE
0.0
0.5
1.0
NOE
ROE
-1.0
-0.5
0.01 0.1 1.0 10 100
τc (ns)
ηmax
€
σ IS = W2QC −WZQC
€
W0 =110b2J(0)
€
W2 =35b2J(2ω0)
Lab.Frame :ω 0 = 600MHz, 2ω 0 =1.2GHzRot.Frame :ω 0 = 20KHz, 2ω 0 =40KHz
Bo
ω0
Bo
B1
ω1
The heteronuclear NOE
-4-3-2-1 0 1 2 3
0.01 0.1 1 10 100
13C31P
19F
15N
ηmax
τc (ns)
the conditions for measurement must be very stable
(as always true for methods that rely on differences). Especially, the
temperature must be stable. For the same reason, never use spinning for
NOE measurements! Measuring over night or on weekends is preferred
because of less traffic in the building. Optimize the lock power, adjust
lock power just below saturation to give a strong lock signal.
the mixing time has to be optimized for the molecule size, do not use
too long mixing times in order to avoid spin diffusion.
Avoid paramagnetic impurities!
Practical tips for NOE measurements:
if very small effects should be measured, remove oxygen (degas the
sample; oxygen is a biradical).
The sample should be concentrated enough but not too concentrated
(little lock signal).
For observation of NOE's between methyl groups and other protons,
irradiate the methyl group, because relaxation of methyl protons is mainly
governed by the other methyl protons.
Pay attention to the choice of the solvent. Use a solvent, that gives an
intense lock signal (DMSO, acetone, rather not CDCl3 or D2O if possible),
because than the lock is more stable. D2O also has a large temperature
shift of the solvent line, so that the lines easily shift when the temperature is
not stable.
if the NOE is very small, that means if the tumbling time is such that the
NOE is near to the zero-crossing, going from a non-viscous solvent
(acetone) to a viscous solvent (DMSO) or measuring at lower temperatures
may increase the size of the NOE dramatically (note that at low
temperatures the danger is high that the temperature is not stable).
Use sufficiently long relaxation delays (3-5 times T1).
O
O
O
OH
H
1
2
3
8a
3a
8
7
45
6
9
O
O
O
OH
H8a
3a
H3e
H3a
H2e
H2a
H1aDistances:
H1ĺH2e = 2.47 Å
H1ĺH2a = 3.02 Å
H1ĺH3e = 2.52 Å
H1ĺH3a = 3.71 Å
H H
Br
RR'
H
H
RH
R'
H
1 2a 2b
2D NOESY
H
H
NOESY
NOE ~ 1/d6
d1 2 3 4 5 6 7 8
12345678
Upot = Ubond + Uangle + Udihedral + Uchiral + Uv.d.Waals
+ Ucoulomb + UNMR
UNMR = UNOE + UJ + ….
E pot
ddNOE
2-Dimensional NMR
2D NMR
• dispersion of signals into two orthogonal dimensions and
• identification of correlations
• homonuclear correlated spectra
• heteronuclear correlated spectra
• shift-correlated 2D experiments
100
120
140
7.0 6.8 6.6ppm
a) b)
AQ
DW
(td =16)
sampling in 1D acquisition is done stroboscopically..
ΩΩ Ω Ω Ω
Ω
Resolution
(Excitation of spin A)
(Chemical Shift labelling of spin A)
(Coherence transfer to spin B)
Detection
Preparation
Evolution
MixingF1
F2
ΩΑ
ΩΑ ΩΒ
ΩΒC
CD
D
Homonuclear correlation experiments
Excitation Evolution Mixing DetectionExcitation Evolution Mixing Detection
t1
FT
t1
x
y
z
y x
90 degree pulse along y
H
H
HH
H
H
H
H
H
H
H
H
H
H
H
H
HH
H
H
H
COSY TOCSYNOESY ROESY
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
HSQC HMBC
HSQC-TOCSY INADEQUATE
COSY
• correlates geminal and vicinal
protons
• one of the most commonly used
experiments
• very sensitive, but only for molecules
with sharp lines
• requires high proton density
H
H
HH
H
H
H
ppm
2.00 ppm
4.00
F1
J(A,B)
J(A,B)
F2
COSY cross peak fine structure
A
B
C
ppm
2.00 ppm
4.00
F1
J(A,B)
J(A,B)
F2
J(A,C)
Ω2
Ω1
Ω10
Ω20
Ω10Ω2
0Ω30
Ω30
COSY: 1 AMX spin systems, no chemical shift degeneracy
A
B
C
ppm
2.00 ppm
4.00
F1
J(A,B)
J(A,B)
F2
J(A,C)
TOCSY (total correlation spectroscopy)
• multiple proton-proton transfer
• depending on the mixing time
complete correlations through
the whole spin system may be
derived
• only a single resolved resonance
required (carbohydrates)
• not sensitive for large moelcules
H
H
H
H
H
H
H
0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
1
1
10 5 -7
2 3 4
1
10 5 -7
2 3 4
1
10 5 -7
2 3 4
1
10 5 -7
2 3 4
τ /sm
Ω2
Ω1
A
A
A'
A'
M
M
X'
X'
M'
M'
X
X
Diagonal
COSY: 2 AMX spin systems, no chemical shift degeneracy
0.12.14.16.18.10.22.24.26.28.20.32.34.3 mpp
3.045
3.014
2.034
2.005
2.005
2.009
2.012
mpp8.9
1.000
mpp57.9
This is a mixture of butanal and butylbromide. Which signals belong to which molecule?
mpp
0.12.14.16.18.10.22.24.26.28.20.32.34.36.3 mpp
0.1
2.1
4.1
6.1
8.1
0.2
2.2
4.2
6.2
8.2
0.3
2.3
4.3
6.3
mpp
7.9 mpp8.9
0.1
2.1
4.1
6.1
8.1
0.2
2.2
4.2
6.2
8.2
0.3
2.3
4.3
6.3
Diagonal
Ω2
Ω1
A
A
A'
A'
M,M'
M,M'
X'
X'
X
X
COSY: 2 AMX spin systems, M spins are overlapped
Diagonal
Ω2
Ω1
A
A
A'
A'
M,M'
M,M'
X'
X'
X
X
TOCSY: 2 AMX spin systems, M spins are overlapped
4.0
1
2
3
4
4.84.95.0 ppm 4.84.95.0 ppm ppm
AB−System
(J =10Hz)AB
ABX−System
(J =10Hz, J =6Hz, J =4Hz)AB BXAX
z
y
x
z
y
x
z z
Δt Δt180°
Δt Δt
Suppressing chemical shift evolution in TOCSY spectra
πy(π/2)x πy πy πy πy πy
1 32 4
t1
τm
t2....
Hartmann-Hahn condition: γ1B1 ~ γ2B2
(ω1 ~ ω2)
ppm
6.46.66.87.07.2 ppm
6.5
7.0
ppm
6.46.66.87.07.2 ppm
6.5
7.0
mixing time 15ms mixing time 100ms
ppm
3.03.5 ppm
2
4
6
Artefacts in COSY spectra
Resolution in COSY spectra
NOESY (nuclear Overhauser spectroscopy)
• correlates protons that are close in
space, irrespective of how many
bonds are in between
• strength of NOE is prop. d-6
• works the best for large molecules,
less for small, badly for medium-sized
• THE experiment for determining
stereochemistry
H
H
H
H
H
H
H
2D NOESY
Magnetization transfer via dipolar couplings
• transferred via space (dipole-dipole interaction)
• magnitude depends on
• distance between dipolar-coupled nuclei.
• motional characteristics (correlation time).
• magnitude of gyromagnetic ratios(γ) of interacting nuclei.
» NOESY, ROESY
H
H
x
y
Bo=z
x
y
Bo=z
B1=y
NOE ROE
Small molecules in
low-viscosity
solvents positive negative
Medium-sized
molecules positive
Very weak signals (positive or negative)
Large molecules,
viscous solvents positive positive
NOESY peak phases
Artefacts in ROESY spectra
•TOCSY-Peaks, (in-phase, positive), observed for geminal
protons, whose chemical shift difference is small
•spin-diffusion peaks (ROE-ROE relay peaks) (in-phase, positive)
•TOCSY-ROESY transfer Peaks (in-phase, negative)
•exchange peaks (positive)
ppm
3.03.54.04.55.0 ppm
3
4
5
NO
H
N
O
H
ppm
234567 ppm
2
4
6
ppm
7.07.5 ppm
7.0
7.5
EXSY: Exchange Spectroscopy
Polarization transferHeteronuclear NMR
Sensitivity(fully relaxed, 100% isotopic abundance)
(13C)5/2
(13C)5/2 + NOE
(1H)(13C)3/2
(1H)5/2
Decoupling
RD
Decoupling
RD
RD Decoupling
RD
t 1 Decoupling
1H
13C
1H
13C
1H
13C
1H
13C
inverse-gated 13C
13C1H
INEPT
HSQC
homonuclear
Excitation
Evolution
Mixing
Detection
heteronuclear(1H detection mode)
PT-Transfer back to proton
Preparation
Evolution
Detection
PT-Transfer to X-nucleus
Preparation
Evolution
Detection
PT-Transfer to X-nucleus
heteronuclear(X detection mode)
€
Int ∝ γ ex γ det3 / 2
The HSQC Experiment
t1
DEC
Preparation INEPT Evolution Re-INEPT Detection
Hz Hy 2HxCz
2HzCy 2HzCycos( Ct1)
2HyCzcos( Ct1) 2HyCzcos( Ct1)cos( Ht2)
1H
13C
The HSQC (heteronulear single quantum coherence) experiment
• correlates protons with their
directly bonded carbons via 1JC,H
• helps to recognize geminal
protons
• is very sensitive and yields
carbon chemical shifts of
PROTONATED carbons
H
H
H
H
H
H
H
N
N C CH3
HH3 CO
O
125
10 8
9
117
6
H
Melatonin
[13C,1H]-HSQC of melatonin
HMBC (heteronuclear multiple-bond correlation)
• correlates protons with carbons at
ADJACENT positions via 2J and 3J (4J)
couplings
• very useful to assign quarternary carbons
• ambiguity always exists whether 2J or 3J
correlations are seen
• correlations follow a Karplus-type relation
and hence the coupling may be zero!
H
H
H
H
H
H
H
N
N C CH3
HH3 CO
O
125
10 8
9
117
6
H
Melatonin
[13C,1H]-HMBC of melatonin
HSQC-TOCSY
• correlates prtons with their directly
bonded carbons
• additionally displays correlations to
protons on NEIGHBOURING carbons
• in principle gives information similar
to COSY, but with increased
resolution
• is much less sensitive (transfer via
13C)
H
H
H
H
H
H
H
ppm
1.41.61.82.02.22.4 ppm
1.4
1.6
1.8
2.0
2.2
2.4
ppm
1.41.61.82.02.22.4 ppm
28
30
32
34
36
38
40
42
44
46
48
50
52
HSQC−TOCSY
DQF−COSY
OH
OH
O
OH
OH
OH6
15
1118
INADEQUATE
• directly correlates carbon nuclei
• is very useful when the molecule
contains only few protons
• extremely insensitive
H
H
H
H
H
H
H
2
1
10
10
20
20
ppm
110120130140150 ppm
140
150
160
170
C5C6C7/C8C9
C10C11C12
N
N C CH3
HH3 CO
O
125
10 8
9
117
6
H
Melatonin
Inadequate of melatonin
Hyphenated 2D experiments
F1=13 C
F2=1H
HSQC
F2=1H
F1=13 C
C
HSQC-TOCSY
CA-CB-CC
H H H
1H
13C t1
HC
HSQC
DEC
1H
13C t1
HC
HSQC-TOCSY
DEC
spinlockspinlockt1
TOCSY
CA-CB-CC
H H H
Phasecycling
1JC,H
1=x
Rec =x
FID1
1=-x
Rec =-x
FID2
1 H
1 3 C t1
HSQC
DEC
An Alternative: Pulsed Field Gradients
DQF-COSY
€
G1τ1G2τ 2
= −p2p1
refocussing condition