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