Two-dimensional correlation spectroscopy in solids

Jeremy Titman,School of Chemistry, University of Nottingham

Two-dimensional correlation spectroscopy

A two-dimensional correlation experiment consists of four time periods: Preparation, evolution, mixing and detection.

★ Magnetization is transferred between the spins during the mixing period.

★ The signal S(t1,t2) is a function of both the evolution and the detection time.

A two-dimensional Fourier transform generates a two-dimensional spectrum S(ν1,ν2).

!2 / ppm

150 100 50

150

100

50

Hmix

preparationmixing

evolution detection two-dimensionalFourier transform

U13C-tyrosine!

2

t1

t2

!1

!1 /

ppm

Richard ErnstRichard Ernst

Cross and diagonal peaks

Two types of peaks can be observed in correlation spectra:

★ Diagonal peaks for which ν1 = ν2. This indicates that the mixing process did not transfer magnetization

between spins.

★ Cross peaks for which ν1 ≠ ν2. This indicates that magnetization has been transferred from a spin

precessing at a frequency ν1 in the first dimension to a spin precessing at ν2 in the second.

The nature of the mixing process dictates the information content of the two-dimensional spectrum.

!2 / ppm

150 100 50

150

100

50

Hmix

preparationmixing

evolution detection two-dimensionalFourier transform

U13C-tyrosine!

2

t1

t2

!1

!1 /

ppm

Types of correlation

Dipolar correlations

★ Cross peaks link pairs of spins which are dipolar coupled to one another. These are close together in space, but not necessarily bonded.

★ Because the magnitude of the dipolar interaction depends on the internuclear distance, these experiments can be used to measure atomic separations in molecules.

★ The dipolar coupling is motionally averaged in solution, so cross relaxation is used. In a solid the magnetization transfer can be achieved coherently.

Scalar correlations

★ Cross peaks link pairs of spins with a mutual J coupling. Because this interaction requires a chemical bond between the coupled spins, cross peaks link sites in the molecule which are bonded together.

★ This is useful for assigning lines in a complicated spectrum to sites in the molecule and for establishing molecular structure.

“Solution-like” approach:Rapid MAS, Efficient Decoupling

H = Hiso

No orientational information; recoupling

“Classical solids” approach:Slow (or no) MAS

H = ?Retain orientational information

Philosophy

Carbon-13 assignment for bacteriochlorophyll a

O

N

N N

N

O

O

Mg

O

OO

200 150 100 50 0ppm

12 3

4

567

8

9

10

11

12

13

14

15

1617

18

!

"

#

$

P1

P2

P3P4

P6

P8

P10

P12

P14

P15

P5

P7

P9

P11

P13

carbon-13 NMR

What is the assignment of the sites to the resonances?

Dipolar recoupling

p 0 1 2 3 n-1 n

Rotor phaseN periods

rf phase2!p/n

Spin part

Space part

carbon-13dipolar couplings

N N

O

N N

O

carbon-13J couplings

Average Hamiltonian

n = 7 N = 2

n = 9 N = 3

The double-quantum dipolar Hamiltonian is recoupled in the mixing period, causing magnetization transfer between dipolar-coupled spins.

Hmix ∝ I1

+I2+ + I1

−I2−( )

Dipolar correlation

200 150 100 50 0ppm

050

100

150

200

ppm

O

N

N N

N

O

O

Mg

O

OO

DecouplingCP

CP

DetectionPreparation

Evolution

1H

13C

p

+2+10-1-2

Mixing

t1

t2

dipolarcouplings

isotropicshifts

isotropicshifts

C7

N N

O

carbon-13dipolar couplings

U-13C-bacteriochlorophyll a

carbon-13 NMR

Pulse sequence symmetry

p 0 1 2 3 n-1 n

Rotor phaseN periods

rf phase2!p/n

Spin part

Space part

carbon-13dipolar couplings

N N

O

N N

O

carbon-13J couplings

Average Hamiltonian

n = 7 N = 2

n = 9 N = 3

Changing the pulse sequence symmetry reintroduces the isotropic mixing scalar Hamiltonian during the mixing time, causing magnetization transfer between scalar-coupled spins.

Hmix = 2πJI2 .I2

C9 sequence

The spin-space selection diagram illustrates which combinations of spin and space components are retained in the average Hamiltonian for the recoupling sequence.

The spin-space selection diagram shows that with n = 9

and N = 3 only space-spin (m, µ) = (0,0) components

are retained in the average Hamiltonian.n = 9

N = 3

Space (m) Spin (µ)

+2

+1

0

-1

-2

-2

-1

0

+1

+2

Nm - µ = nk

A. S. D. Heindrichs, H. Geen and J. J. Titman, Chem. Phys. Lett., 335, 89 (2001).

H0( ) = 2πJI2 .I2

Isotropic mixing

I1xHiso=2πJI1.I2⎯ →⎯⎯⎯⎯ I2x

Tran

sfer

red M

agnet

izat

ion

0.00 0.01 0.02 0.03 0.040.0

0.2

0.4

0.6

0.8

1.0

Mixing time (s)

9 ms

18 ms

27 ms

CO

Me

Isotropic mixing

The isotropic mixing Hamiltonian transfers magnetization directly between in-phase states. This is the basis of the solution-state TOCSY experiment.

Scalar correlation

200 150 100 50 0ppm

050

100

150

200

ppm

O

N

N N

N

O

O

Mg

O

OO

DecouplingCP

CP

DetectionPreparation

Evolution

1H

13C

p

+2+10-1-2

Mixing

t1

t2

Jcouplings

isotropicshifts

isotropicshifts

C9

N N

O

carbon-13J couplings

A. S. D. Heindrichs, H. Geen and J. J. Titman, Chem. Phys. Lett., 335, 89 (2001).

Carbon-13 assignment

The combination of dipolar and scalar correlation information allows all the carbon-13 resonances to be assigned, with the exception of the mobile chain P5 - P15.

O

N

N N

N

O

O

Mg

O

OO

200 150 100 50 0ppm

12 3

4

567

8

9

10

11

12

13

14

15

1617

18

!

"

#

$

2a 9 7c

10a

17,15,12

18

1614

13

P3 6 P2#!,"

$10 P1

4

P47,3,8,10b

4,7a,7b3a,8a

2b

P3a

5a,1a

P1

P2

P3P4

P6

P8

P10

P12

P14

P15

P5

P7

P9

P11

P13

Mechanisms for dipolar transfer

Recoupled dipolar Hamiltonian

A pulse sequence during the mixing period recouples the double- or zero-quantum dipolar Hamiltonian. Both of these cause magnetization transfer between dipolar-coupled pairs of spins.

Proton driven spin diffusion

During the mixing period the decoupler is turned off so that magnetization is transferred between (carbon-13) spins via spin diffusion in the dipolar-coupled proton network.

Cross polarization

In a heteronuclear correlation experiment the mixing period consists of a cross polarization step to transfer magnetization between heteronuclei. To ensure that magnetization is transferred only to near neighbors special cross polarization sequences must be used which eliminate proton dipolar couplings and prevent spin diffusion.

HZQ ∝ 2I1zI2z −

12

I1+I2− + I1

−I2+( )

HDQ ∝ I1

+I2+ + I1

−I2−( )

Zeolite framework structure

★ Zeolite framework structures are not easily solved by X-ray diffraction.

★ The SR26411 recoupling sequence used in this silicon-29 dipolar correlation experiment is a robust method for recoupling weak homonuclear dipolar interactions while decoupling weak heteronuclear ones.

★ The resulting cross peak build up curves can be simulated in terms of a histogram of Si-Si distances which together with the lattice parameters and the space group from X-rays can be used to solve the zeolite framework structure.

D. H. Brouwer, P. Eugen Kristiansen, C. A. Fyfe and M. H. Levitt, J. Am. Chem. Soc., 127, 542 (2005).

Clathrasil Sigma-2 hosting a 1-aminoadamantane template molecule

Natural abundance silicon-29 dipolar INADEQUATE spectrum

Cross peak build-up curves and the extracted Si-Si distance histogram

Problems with dipolar correlations

Dipolar Truncation

In a multi-spin system the spin dynamics is dominated by the largest dipolar couplings which are often between bonded spins and of little use in studies of conformation (although they are very useful for making assignments).

This makes the observation of long-range distance restraints difficult.

Dipolar truncation can be overcome by:

★ uniform labeling and frequency-selective recoupling

★ broadband recoupling and restricted labeling

Structure of SH3 by PDSD

★ This study used a micro-crystalline preparation of the α-spectrin Src-homology 3 (SH3) domain.

★ Proton-driven 13C-13C spin diffusion spectra were obtained from biosynthetically site-directed labelled samples obtained from bacteria grown on [1,3-13C2]glycerol or [2-13C]glycerol.

★ This labeling strategy reduces dipolar truncation and hence allowed 286 inter-residue 13C-13C restraints to be extracted from the spectra.

★ Distances were estimated by measuring the build-up of cross peak intensity as a function of mixing time and comparing this with conformation independent reference distances.

F. Castellani, B van Rossum, A. Diehl, M. Schubert, K. Rehbein and H. Oschkinat, Nature, 420, 98 (2002).

20

30

40

50

60

ppm2030405060

DecouplingCP

CP

1H

13CMixingt

1t

2

Proton-drivenspin diffusion

Decoupling

structure bysolid-state NMR

carbon-13 PDSD spectrum

Heteronuclear correlation experiments

Decoupling

PreparationEvolution Detection

Mixing

BLEW-12

BB-24

LG-CP

LG-CP

1H

13C/29Si

Presaturation

Proton IsotropicShifts

C-13/Si-29 IsotropicShifts

300 200 100 0 -100ppm

** *

*

+10

ppm

0

carbon-13

pro

ton

54˚63˚

two-dimensionalFourier transform

★ The high-resolution spectra which are observed in ν1 and ν2 correspond to different nuclei.

★ The mixing period involves heteronuclear magnetization transfer.

Nature of the interface in PVP-silica nanocomposites

★ Vinyl pyridine is polymerized in the presence of an aqueous silica sol to produce nanocomposite particles 200 nm in diameter.

★ Inorganic phase adds mechanical strength, fire retardancy etc. to the polymer.

What is the nature of the interaction between the inorganic and organic phases?

N

n

SiO

SiO

SiO

Si

O O O OH H H H

HH

N

Ultrafine silica sol Vinyl polymer/silicacolloidal nanocomposite particles

25 °C(NH

4)2S

2O

8

poly(vinylpyridine)

silica

BLEW-LGCP heteronuclear correlation

★ The preparation period involves presaturation to ensure that no carbon-13/silicon-29 magnetization is present at the start of the experiment

★ In the evolution period the experiment measures the high-resolution proton spectrum obtained using CRAMPS (in this case the BLEW-12 windowless decoupling sequence). Note the use of the BB-24 sequence on carbon-13/silicon-29 to decouple these spins from the protons.

★ During the mixing period a selective cross polarization scheme (in this case Lee-Goldberg CP) is used to transfer the proton magnetization to near neighbor carbon-13/silicon-29 spins.

★ In the detection period the experiment measures the high-resolution carbon-13/silicon-29 spectrum using decoupling.

Decoupling

PreparationEvolution Detection

Mixing

BLEW-12

BB-24

LG-CP

LG-CP

1H

13C/29Si

Presaturation

Proton IsotropicShifts

C-13/Si-29 IsotropicShifts

300 200 100 0 -100ppm

** *

*

+10ppm

0

carbon-13

pro

ton

54˚63˚

two-dimensionalFourier transform

G. K. Agarwal, J. J. Titman, M. J. Percy and S. P. Armes, J. Phys. Chem. B., 107, 12497 (2003).

Nature of the interface in PVP-silica nanocomposites

★ Heteronuclear correlation spectra of the starting materials allow the protons to be assigned.

★ The observation of a new proton resonance in the interface at 11 ppm suggests a hydrogen bond.

N

n

SiO

SiO

SiO

Si

O O O OH H H H

HH

0 -50 -100 -150 -200ppm

+10

ppm

0

silicon-29

pro

ton

300 200 100 0 -100ppm

** *

*

+10

ppm

0

carbon-13

pro

ton

N

n

HH

0 -50 -100 -150 -200ppm

+10

ppm

0

silicon-29

pro

ton

SiO

SiO

SiO

Si

O O O OH H H H

starting materials

interface

Mechanisms for scalar transfer

Anti-phase magnetization

Solution-state scalar correlation experiments like COSY and INADEQUATE rely on the generation of magnetization which is anti-phase with respect to the active J coupling.

In-phase

I1x

scalar couplingI1yI2z

/2 pulseI1zI2y

!

magnetizationtransfer

Anti-phase

I1xHiso=2πJI1.I2⎯ →⎯⎯⎯⎯ I2x

Isotropic mixing

The isotropic mixing Hamiltonian transfers magnetization directly between in-phase states. This is the basis of the solution-state TOCSY experiment.

Linewidths in MAS spectra

In solids even for dilute spin-1/2 nuclei with MAS and decoupling the NMR linewidth is significantly broader than in solution due to:

★ Homogeneous contributions. These arise from incomplete decoupling or molecular motion.

★ Inhomogeneous contributions. These arise from an inhomogeneous B0 field or shift distributions due to sample heterogeneity. They can be refocused by a spin echo.

polymeric CsC60400 300 200 100

ppm

inte

nsi

ty

time / ms

Spin echomeasurement

Carbon-13 MAS spectrum

Simulation withhomogeneous linewidth

0 10

Effect on cross peak sensitivity

When J is within the linewidth the multiplet components cancel and experiments based on anti-phase magnetization transfer have very low sensitivity.

J = 100 Hz

x10

Solid-state scalar correlation experiments are usually “refocused” so that the cross peaks are in-phase, resulting in a significant improvement in sensitivity since the multiplet components reinforce.

In-phase

I1x

scalar couplingI1yI2z

/2 pulseI1zI2y

!

Anti-phase In-phaseAnti-phase

scalar couplingI2x

magnetizationtransfer

SAR-COSY

Sensitive, Absorptive, Refocused-COSY

Magnetization transfer occurs via anti-phase magnetization which is refocussed during the mixing period, so that the cross peaks are in-phase and absorptive in both dimensions. This maximizes sensitivity when J is within the linewidth.

The diagonal peaks are anti-phase and dispersive in ν1 which means they have low intensity and their intensities

vary with the preparation time according to:

13C

p

! ! ! !t1

t2

evolution detectionpreparation mixing

magnetizationtransfer

refocusing

150 100 50 0

050

100

150

O

NH2

H3C

OHppm

-2-10

+1+2

ppm

two-dimensionalFourier transform

sin 2πJτ( )cos 2πJτ( )which is zero when τ = 1/(4J).

D. Lee and J. J. Titman, unpublished.

Alkali fullerides

CsC60, RbC60

These materials show interesting phase transitions:

★ the high temperature phase is fcc with alkali metals in octahedral interstices

★ the low temperature phase is formed from a reversible solid-state transformation which involves a shortening of the a lattice dimension

The inter-fullerene distance along a is only 9.138 Å which suggests the formation of polymeric C60 chains by a 2+2 cyclo-addition reaction.

Models for the electronic structure of CsC60

Quasi-1D metal

★ Overlap of MOs along a results in a half-filled conduction band

★ Electronic spin susceptibility depends only weakly on temperature

3D Semi-metal

★ The dispersion perpendicular and parallel to the polymer chains is similar, resulting in a three-dimensional Fermi surface.

!s

/ 10

-4 e

mu m

ol-1

8

4

0

8

4

00 200 400

Temperature / K

Lin

ewid

th /

G

susceptibility

ESR measurements

G MH

0.0

0.5

-0.5

parallelto chains

perpendicularto chains

Fermi level

Band structure

O. Chauvet, G. Oszlànyi, L Forró, P. W. Stephens, M. Tegze, G. Faigel and A. Jánossy, Phys. Rev. Lett., 72, 2721 (1994); S. C. Erwin, G. V. Krishna and E. J. Mele, Phys. Rev. B, 51, 7345 (1995).

Carbon-13 MAS NMR of CsC60

The polymerization reaction lowers the symmetry, resulting in 16 inequivalent carbon sites.

The hyperfine interaction with the unpaired electron donated from the caesium atom results in contact shifts.

400 300 200 100ppm

17 kHz MAS C60

CsC60

hyperfine interaction

|!>

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contact shift

fast electronspin relaxation

1 1 22

3

3

4

4

5

5 6

67

7

8

8

9

9

10

10

11

11

1212

13

13

14

14

15

15

16

16

lower symmetry

looking along a

50% U-13C CsC60

Carbon-13 enriched amorphous carbon packed into graphite tubes; 60 A 25 V dc arc between enriched rods under 3 psi He; Enriched C60 and Cs mixed and heated for 1 week at 350 °C

Comparison with DFT calculations

Starting from the aliphatic inter-fullerene linkage (1) all the experimental carbon-13 lines can be assigned.

DFT calculations on a C60 trimer based on the 3D semi-metal band structure show two groups of carbon sites with large hyperfine couplings.

These are the lines which show the largest experimental contact shifts, so the 3D semi-metal is the correct model.

0100

200

300

400

ppm

100200300400ppm

0

1 1 22

3

3

4

4

5

5 6

67

7

8

8

9

9

10

10

11

11

1212

13

13

14

14

15

15

16

16

11 1014 4,5 13 2 3981

Experiment Calculations

44

5

5

10

10

11

11

14

14

hyperfine coupling / MHz

(14,10,11)

(4,5) 2.2

6.8

T. M. de Swiet, J. L. Yarger, T. Wagberg, J. Hone, B. J. Gross, M. Tomaselli, J. J. Titman, A. Zettl and M. Mehring, Phys. Rev. Lett., 84, 717 (2000).

Refocused INADEQUATE

★ During the preparation period unobservable double-quantum coherences are excited.

★ These evolve at the sum of the chemical shifts of the spins involved in the evolution period.

★ They are reconverted to observable anti-phase magnetization which is refocussed during the mixing period, so that the peaks are in-phase and absorptive.

13C

p

! ! ! !t1

t2

evolution detectionpreparation mixing

magnetizationtransfer

refocusing

-2-10

+1+2

two-dimensionalFourier transform

200 150 100 50 0ppm

100

200

ppm

O

NH2

CH3OH

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|"#>

M = -1

M = +1

DQ transition

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SQ transition

MixingPreparation

A. Lesage, C. Auger, S. Caldarelli, and L. Emsley, J. Am. Chem. Soc., 119, 7867 (1997).

Comparison of methods

400 300 200 100 0

250

500

ppm

ppm

219

70102123168

201

228

168

265

282295

268

318417430456515534550

SQ frequencies / ppm

35 41566888133 114227375378420

1110144,5 13 2 3 9 8 1 sites*

DQ

frequen

cies / ppm

1

1

22

3

3

4

4

5

5 6

67

7

8

8

9

9

10

10

11

11

1212

13

13

14

14

15

15

16

16

400 300 200 100 ppm

11 1014 4,5 13 2 3 981*

SAR-COSY and refocussed INADEQUATE result in similar sensitivity and contain similar information.

G. Grasso, T de Swiet and J. J. Titman, J. Phys. Chem. B, 106, 8676, (2002).

Structures of pyrophosphates

TiP2O7

★ This material has a cubic crystal structure with space group PA3-, a = 23.534 Å, Z=108

★ Scalar correlation experiments can distinguish 5 pairs of inequivalent 31P resonances bonded via a bridging oxygen atom and one equivalent pair.

★ This experiment can be used to distinguish between dynamic and static disorder in the P-O-P bond angle.

-40 -44 -48 -52

-104

-96

-88

-80

SQ / ppm

DQ

/ p

pm

4,756,38 9101,2

F. Fayon, D. Massiot, M. H. Levitt, J. J. Titman, D. H. Gregory, L. Duma, L. Emsley, S. P. Brown, J. Chem. Phys. 122, 194313 (2005).

HMQC-J-MAS

t1

CP

CP

1H

13C

Decoupling

t2

Evolution

Protonchemical shifts

HeteronuclearJ couplings

Carbon-13chemical shifts

DUMBO

Preparation Mixing Detection

HeteronuclearJ couplings

ppm

Si

4'

O

3'

1'

2'

5'

O

4

NH

5

2

6

N

O

O

O

PO

O

Si-CH35-CH3

CH3

2’

O-CH35’ 3’1’

4’ 5=CH2

62 4

C

Si-C

H3

5-C

H3C

H3

2

’O

-CH

3

5’

3’

1’

4’

=C

H2

6

0.0

5.0

Pro

ton

0 50 100 150

Carbon-13

ON

ON

N

NH

O

O

CPG

O O

O

P O

N

NH

O

O

O O

O

P OO

N

ON

N

NH

O

O

O O

O

P O

N

NH

O

O

O

O

P O

N

NH

O

O

HO O

O

50 0 -50ppm

phosphorus-31 MAS

With rapid MAS and efficient decoupling, many solid-state analogues of two-dimensional solution-state NMR experiments can be designed.

A. Lesage, D. Sakellariou, S. Steuernagel and L. Emsley, J. Am. Chem. Soc., 120, 13194 (1998).

Summary

Two-dimensional scalar and dipolar correlation experiments show a high resolution spectrum in each dimension with cross peaks which map the correlations due to the mixing Hamiltonian.

Scalar correlations can be used for structural studies and for assignments, while dipolar correlations provide information about conformation.

Increasingly, solid-state NMR correlation experiments resemble their solution-state counterparts and make use of efficient decoupling, rapid MAS and anti-phase magnetization transfer under scalar couplings.