Double-Quantum NMR Spectroscopy:Investigating Structure and Dynamics

of Abundant Spin Systems.

DoubleDouble--Quantum NMR Spectroscopy:Quantum NMR Spectroscopy:

Investigating Structure and Dynamics Investigating Structure and Dynamics

of Abundant Spin Systems.of Abundant Spin Systems.

Robert Graf

Max-Planck Institute for Polymer Research

Robert Graf

Max-Planck Institute for Polymer Research

Double-quantum NMR methods: investigating (supra) molecular structure

Double-quantum NMR methods: investigating (supra) molecular structure

H H''H'

H

H'H''

CH' CH2CH

O

OCH2

H'H

H

H'

rHH

H

H'

rNH

5 3 1 –1 –3 –5

1 H-1 H

hom

onuc

lear

1 H-13

C/15

N h

eter

onuc

lear

internuclear proximities,chemical shifts and π-shifts

measurement ofinternuclear distances

π

7 -79 -9

5 3 1 –1 –3 –57 -79 -9

0.21 nm

0.24 nm

0.27 nm

0.16 nm

0.18 nm

0.20 nm

NMR methods: investigating molecular dynamicsNMR methods: investigating molecular dynamics

10210110010-110-210-310-410-510-610-7

motional correlation time [seconds]

loss of NMR signal exchange NMR experiments

fast local dynamics

mobile

rigid

slow reorientations

jump sites

jump angle

Averaging of dipolar couplings

fast slow staticintermediate

Merging solid-state and solution-state NMR methodsMerging solid-state and solution-state NMR methods

Solution State Solid State

InverseDetection (1H)

Dipolar Decouplingand Recoupling

Fast Magic-AngleSpinning

Pulsed FieldGradients

GZ 1HX

θm

RFTech

niqu

esG

oals

Resolution Enhancement Sensitivity Enhancement MeasuringMolecular Structure

and Conformation/Packing

Solids and Materials at the Solid/Liquid Borderline

1H

15N

1Hnatural abundance15N in L-histidine

Outline of the TalkOutline of the Talk

Homonuclear DQ NMR spectroscopy under fast MAS

Residual dipolar couplings and order parameters in nematic LC

Multi-Spin Effects in abundant spin systemstwo spin approximation and it‘s limitsdouble-quantum relay in dipolar systemsmulti-spin coherences envolving more than 2 spins

Conclusions for homonuclear DQ NMR in dense spin systems

Heteronuclear MQ NMR spectroscopy and REDOR

Shape persistent polymers with dentritic sidegroups

Inverse detection of 15N in natural abundance

Conclusions

High Resolution Double-Quantum NMR in SolidsHigh Resolution Double-Quantum NMR in Solids

reconversionevolution detection

t2t1excitation

ωR ≈ 0 ωR ≈ 0ωR > Dij ωR > Dij

high resolution solid-state NMR spectroscopy: average out dipolar coupling via

Problem: Coupling between the spins is needed for double-quantum excitation !

Multi pulse sequence (WAHUHA, MREV-8)

Magic Angle Spining (MAS)

properties of double-quantum coherences :

ω ωDQ SQ ii

= ∑ , I f D tDQ ij ij, ( )= ⋅ d Mdt ≈ 0

Dipolar Couplings and Sample Rotation at the Magic AngleDipolar Couplings and Sample Rotation at the Magic Angle

ωR

θ

θm

ωR

θm

ωR

Dipole Dipole Coupling:

i

jθij

rij

B0

Magic Angle Spinning:

$ II$ ( cos ) ( $ ), ,Hrij

ij i j Z i Z j∝ - +1 3 1 2312

2 θ γ γ⋅ $ II $, ,+ i - j + $ II $

, ,- i + j

0

spatial part spin part

B0 B0 B0 B0

unchanged

Excitation of Double-Quantum Coherences under MASExcitation of Double-Quantum Coherences under MAS

Direct Excitation

Dij > ωR Dij < ωR

Recoupling

τ= n·τR

3 Pulse Sequence

no synchronization rotor synchronization

t1 t2

DRAMA

C7BABA

τt1 t2

(+ z-filter)

τ < 0.5 ·τR

τ τ τ

In the regime of fast MAS only recoupling techniques are applicable.

Recoupling Pulse SequencesRecoupling Pulse Sequences

Laboratory-System Pulse Sequences Rotor-System Pulse Sequences

2π/7 4π/7 6π/7 8π/7 10π/7 12π/70

x x }{ x x x x x x x x x x x x

Phase Δφ'

examples: DRAMA, Back-to-Back, REDOR... examples: C7, POST C7, MELODRAMA ...

Average Hamiltonian of Pulse Sequences : H I I I Iav PF i j PF i ji j

0 = ++ + − −

<∑ω ω *

0 21-1-2 ω/ωR-30 21-1-2 ω/ωR-3

orientation dependence of DQ exciationefficiency

orientation dependence of DQ exciationefficiency

Double Quantum Spectroscopy under fast MASDouble Quantum Spectroscopy under fast MAS

Δt1

2⋅Δt1

t

t

t

H(γ) H(γ+ωRt1)

Dij texc.

0.0 1.0 1.5 2.00.50.0

1.0

0.5

0 100 200-200 -100 kHz

1 τR

2 τR

3 τR

IDQ

The rotor modulation of the recoupled dipolar Hamiltonian due to t1-increments Δt1≠τR leads to MAS sideband pattern in the t1 dimension, which depend on the

recoupling time and the dipolar coupling only.

ωR⋅t

γ

Local Order in Nematic Liquid CrystalsLocal Order in Nematic Liquid Crystals

A BC

D

E

F

G

G-GF-FE-E

D-E

D-D

C-D

B-CA-C

ppm

8 7 6 5 4 3 2 ppm16

14

12

10

8

6

4

2

doub

le-q

uant

um d

imen

sion

single-quantum dimension

DQ build-up behaviour

DQ sideband pattern }⇒

Double-quantum measurements are in good agreement with 2H experiments

Structure of a nematicliquid crystal

local order parameter

S = 1/2(3cos2θ-1) =0.6

2.54 Å

1.83 Å

2.49 Å

2.48 Å

1.83 Å

2.56 Å

A

B

C

CD

F

G

FE

D

Chemical structure of nematic model

compound.

0,0 0,1 0,2 0,3 0,4 0,5 0,60,0

0,1

0,2

0,3

0,4

0,5

BC DQ coherences

DQ

Inte

nsity

[a.

u.]

DQ-Preparation Time [ms]

BC DQ coherence

-100100 0 kHz

DQ coherence A-C B-C D-D E-E F-F G-G

SBP 4.8 4.9 5.2 5.2 4.8 3.1Dij,eff.

[kHz] Build-up 4.4 4.3 4.5 5.6 4.3 2.4

SBP 0.58 0.59 0.25 0.25 0.23 0.15Sij

Build-up 0.52 0.53 0.21 0.27 0.20 0.11

0

0,1

0,2

0,3

0,4

0,5

0,6

A-C B-C D-D E-E F-F G-G

DQ coherence

orde

r par

amet

er S

Dipolar Coupling and Order ParametersDipolar Coupling and Order Parameters

DQ coherence A-C B-C D-D E-E F-F G-G

SBP 4.8 4.9 5.2 5.2 4.8 3.1Dij,eff.

[kHz] Build-up 4.4 4.3 4.5 5.6 4.3 2.4

SBP 0.58 0.59 0.50 0.50 0.46 0.30Sij

Build-up 0.52 0.53 0.42 0.54 0.40 0.22

orde

r par

amet

er S

0.0

0.1

0.2

0.3

0.4

0.5

0.6

A-C B-C D-D E-E F-F G-G

Multi-Spin Effects in Double-Quantum Build-UpMulti-Spin Effects in Double-Quantum Build-Up

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

exp. DQ intensity analytical Fit: IDQ= t2e-t/τ

2 spin calculation

DQ

Inte

nsity

DQ preparation time [µs]

2-spin approximation discribes only the initial behavior.

Multi-Spin Effects in Double-Quantum Build-UpMulti-Spin Effects in Double-Quantum Build-Up

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

exp. DQ intensity

2 spin simulation 3 spin simulation 4 spin simulation

DQ

Inte

nsity

DQ preparation time [µs]

Multi-spin effects lead to exponential decay of the DQ intensities

Multi-Spin Effects in DQ Sideband PatternMulti-Spin Effects in DQ Sideband Pattern

1st order sidebands are under estimated by 2-spin approximation

-100100 0 kHz -100100 0 kHz

-100100 0 kHz -100100 0 kHz

A - C DQcoherence

E - E DQcoherence

A - C DQcoherence

(4 spin simulation)

E - E DQcoherence

(4 spin simulation)

A - C DQ coherence

E - E DQ coherence

A - C DQ coherence

E - E DQ coherence

DQ Polarisation Transfer: 1. Order RelayDQ Polarisation Transfer: 1. Order Relay

8 7 6 5 4 3 2 1 ppm

ppm

16

14

12

10

8

6

4

2

single quantum dimension

doub

le q

uant

um d

imen

sion

tt22 detectiondetectionreconversionreconversiontt11 evolutionevolution

double-quantum experiment :

excitation reconversiont1 t2

1. Order DQ relay

Double-quantum polarisation transfer leads to negative signal intensities

DQ Polarisation Transfer: 2. Order RelayDQ Polarisation Transfer: 2. Order Relay

8 7 6 5 4 3 2 1 ppm

ppm

16

14

12

10

8

6

4

2

single quantum dimension

doub

le q

uant

um d

imen

sion

tt22 detectiondetectionreconversionreconversiontt11 evolutionevolution

2. order double-quantum relay

For longer double-quantum recoupling times coherences get delocalised and can obscure the double-quantum spectrum

excitation reconversiont1 t2

double-quantum experiment :

Time Dependence of Dipolar DQ Relay Intensities Time Dependence of Dipolar DQ Relay Intensities

0 50 100 150 200 250

-50

0

50

100re

lay

inte

nsity

[a.u

.]

recoupling time [µs]

5k-4k-5kExperimental Data Simulations

4k-5kB - C → DA - C → DD - D → CC - D → BC - D → A

Dipolar couplings lead to more complicated realy behavior than J-coupling

Multi-Spin Coherences: 4 Spin 2 QuantumMulti-Spin Coherences: 4 Spin 2 Quantum

8 7 6 5 4 3 2 1 ppm

ppm

16

14

12

10

8

6

4

2

single quantum dimension

doub

le q

uant

um d

imen

sion+−−−−+++ += lkjiijkllkjiijklQS IIIIaIIIIaH *

24

4 spin 2 quantum coherences

coherence−+ −−+−++−+ )( DCCADCCA IIIIIIII

Multi-spin DQ coherences can be observed, but are hard to analyse.

Conclusions for 1H DQ NMR SpectroscopyConclusions for 1H DQ NMR Spectroscopy

High resolution DQ spectra under fast MAS can be obtained using appropriate recoupling sequences.

DQ build-up behavior and DQ spinning sideband pattern provide quantitative information about dipolar couplings.

Even though, multi-spin effects are observed, a carefull 2-spin analysis provides reasonable dipolar coupling values.

In favorable cases, multi-spin effects can be analyzed and additional information can be obtained.

DQ relay intensities due to dipolar couplings are harder to analyze than those due to J-couplings.

How dipolar interactions “explore” spaceHow dipolar interactions “explore” space

homonuclear case:

random walkcharacteristics,

delocalized

heteronuclear case:

well-localized probing of the 13C environment

approaching incoherentdiffusive processes

Rotational Echo Double Resonance (REDOR)Rotational Echo Double Resonance (REDOR)

I (1H)

S (13C)"detected"

AQ

CP

N-1 N-1

CP

DD DD

L (15N, 19F, …)"passive"

0 1 N 2N

~ ~ ~ ~rotor position

+ - + -

+ - + -

+-+-

(dephased)echo

transverse S-magn.

st nd1 half: 2 half: 2 2 2 2cos( )

cos ( ) sin ( )2 sin( ) cos(2 )

R Z Z R Z ZYN NY Y

X

Y

Z Y

NN N

NNτ τΦ

Φ ΦΦ Φ

⋅ ⋅ ⎧⎡ ⎤⎯⎯⎯⎯→ ⎯⎯⎯⎯→ ± = ⎨⎣ ⎦− ⎩

S L S LSS S

S SS

L

Internuclear distances from REDOR curvesInternuclear distances from REDOR curves

0 1 2 3

DISτrcpl / 2π

Inte

nsity

0.5

0.4

0.3

0.2

0.1

0

relaxation/signal lossdue to multi-spin couplings

ideal curve with dipolar oscillations

Experiments in Asparagine

Coherent polarisation transferCoherent polarisation transfer

I

S

I

S

I

S

REDOR scheme

Heteronuclear correlation (SQ-SQ) via transferred

echo double resonance (TEDOR)

Heteronuclear single-quantum correlation

(HSQC) via recoupledpolarisation transfer

(REPT)t1

t1

From deuterons to CHn groupsFrom deuterons to CHn groups

Selectively placed deuterons as probes for molecular dynamics(quadrupole coupling of spin-1 nucleus)

DC

HC

H

CH

H

CH

H

Regular CHn groups

• use of dipole-dipole coupling between C and H• no additional synthetic effort

no selective placement of probing nucleusno isotopic enrichment

• assignment of dynamics by 13C chemical shifts• handling of CH, CH2 and CH3 groups• interferences of multiple C-H couplings• decoupling from surrounding 1H

Signal build-up versus rotor-encodingSignal build-up versus rotor-encoding

I

S

REDOR scheme

I

S

t1

Rotor-encodedREDOR scheme

trcpl

Two alternative concepts for measuring recoupled interactions:• following the signal intensity as a function of the recoupling time(resulting in build-up or dephasing curves)

• recording rotor-encoded signal (resulting in MAS sideband patterns)

trcpl trcpl t1

Cylindrical self-assembly of dendritic sidegroups (I)Cylindrical self-assembly of dendritic sidegroups (I)

polymer main-chain

dendritic sidegroup

OO

O

O

O

O

DCH = 6.0 kHz(S = 29%)

τexc = 8 τR = 320µs

ν/νR-1 -3 -5+5 +3 +1+7

REPT-HDORaromatic CH group

DCH = 17.0 kHz(S = 81%)

REREDOR OCH2 group

ν/νR-1 -3 -5+5 +3 +1+7

τexc = 4 τR = 133µs

DCH = 12.0 kHz(S = 57%)τexc = 4 τR = 133µs

ν/νR-1 -3 -5+5 +3 +1+7

aromatic CH group DCH = 21.0 kHz(S ~100%)

ν/νR-1 -3 -5+5 +3 +1+7

OCH2 group

τexc = 4 τR = 133µs

⇒OC H25

O

O

CH2

O

O

OCH2

CH2CH2 O C

OC CH3

CH2

H

H

H

H

H

12

C H2512

C H2512

n

DCHDCH

DCH

DCH

Materials:V. Percec

Cylindrical self-assembly of dendritic sidegroups (II)Cylindrical self-assembly of dendritic sidegroups (II)

OO

O

O

O

OX

dendriticsidegroup

polymer chain stack ofaromatic molecules

cylindrical assemblyindependent of molecule in the center (chain, discs)

Sensitivity enhancement by inverse (1H) detectionSensitivity enhancement by inverse (1H) detection

N

N

CHCOO

NH3

H

H

+

+

-

δ1

ε2

-160 -180 -200 -220 -240 -260 -280 ppm

S/N = 80

-160 -180 -200 -220 -240 -260 -280 ppm

S/N = 8

inverse1H detection

conventional15N detection

33% 15N-enriched

Hb

HcN

O

Ha

NO

Hd

C13H27

N

Na

b c

ppm

-424 20 16 12 8 4 0 ppm

-100

-200

-300

-400

-424 20 16 12 8 4 0 ppm

ppm

-100

-200

-300

-400

NH3+

ε2

δ1

x 10

0.35% 15N (natural abundance)

Natural-abundance 15N-1H correlation NMRNatural-abundance 15N-1H correlation NMR

x yDD

t1 detectionrecouplingdephasingCP

1H

15N

dephasing

GZ

preparation (1H 15N)

φ

TEDOR/REPT experiment (15N 1H transfer) with/without rotor-encoding

x

x

y

15N

1H

recouplingt1'

rotorencoding

pulsed fieldgradients

(PFGs)15N-1H dipolar couplings from rotor-encoded MAS sideband patterns

15N-1H chemical-shiftcorrelation

RRR pulses

NH⋅⋅⋅O hydrogen bonds in L-histidineNH⋅⋅⋅O hydrogen bonds in L-histidine

ppm

24 20 16 12 8 4 0 ppm

-150

-200

-250

-300

-350

-400

24 20 16 12 8 4 0 ppm

NH3+ε2-NH

δ1-NH NH3+ε2-NHδ1-NH

N

N

CHCOO

NH3

H

H

+

+

-

δ1

ε2

-100

-50

1H chemical shift 1H chemical shift

15N

che

mic

al s

hift

2D chemical shift correlation: 2D chemical shift correlationplus NH coupling information:

700 MHz 1H frequency, 30 kHz MAS, ~ 15 mg sample.

8096 transients in total 65536 transients in total

N-H bond stretching due to hydrogen bondingN-H bond stretching due to hydrogen bonding

ω/ωR-7 -5 -3 -1 1 3 5 7

δ1-NH

ε2-NH

NH dipolar coupling from rotor-encodedspinning sideband pattern:

rNH = (107 ± 2) pm

rNH = (111 ± 2) pm

20480 transients in total

N

N

CHCOO

NH3

H

H

+

+

-

δ1

ε2

Conclusions for heteronuclear methodsConclusions for heteronuclear methods

Similarities of homo- and heteronuclear are sufficient to pursue the strategies known form 1H DQ NMR.

Rotor encoding can be used to measure heteronuclear dipolar couplings with REDOR based techniques.

The larger spread of chemical shifts of rare low γ nuclei provides site selective information about molecular dynamics.

1H detection of low γ nuclei can increase the sensitivity and NMR measurements in natural abundance become feasible.

NMR on supramolecular systemsNMR on supramolecular systems

Homonuclear double-quantum measurements

Dipolar couplings and order parameters in LC systemAnalysis of 1H DQ relay

Heteronuclear method development in solid-state NMR

13C site-resolved dynamics of CHn groupsnatural abundance 15N-1H correlation spectroscopyN-H distance measurements

Investigations of complex systems

Dynamics and self-assembly of dendritic sidegroups

Michael NeidhöferRobert Graf

Kay Kay SaalwächterSaalwächterIngo SchnellIngo Schnell

AlmutAlmut RappRapp