Using Symmetry To Design Pulse Sequences in Solid-State NMR€¦ · Leiden-SSNMR-2000 23 0 200 400 600 800 1000 0 0.005 0.01 0.015 0 0.2 0.4 0 0 200 400 600 800 1000 0 0.005 0.01

Leiden-SSNMR-2000 1

Using Symmetry ToDesign Pulse Sequences

in Solid-State NMR

Malcolm Levitt

Stockholm University

Sweden

Leiden-SSNMR-2000 2

Overview

• Symmetry principles ofrecoupling

• Double-quantum homonuclearrecoupling

• Zero-quantum homonuclearrecoupling

• Heteronuclear recoupling:distances and polarizationtransfer

Leiden-SSNMR-2000 3

MAS + Rf →Recoupling

B0

SAMPLEROTATION

RF FIELD

Leiden-SSNMR-2000 4

Types of Recoupling

Recoupling

HeteroHomo

DD

DD DD

J CSA

2Q ZQ

1-channel 2-channel

Leiden-SSNMR-2000 5

Spin Interactions andtheir Rotational

Symmetries

SPACERANK

SPINRANK

FIELDRANK

Iso-CS 0 1 1

J 0 0 0

CSA 2 1 1

DD 2 2 0

Leiden-SSNMR-2000 6

Rotational Components

SPACERANK

SPINRANK

FIELDRANK

Iso-CS 0 1 1

J 0 0 0

CSA 2 1 1

2 2

1 1

0 0

-1 -1

DD 2

-2

2

-2

0

Leiden-SSNMR-2000 7

SPACERANK

SPINRANK

FIELDRANK

Iso-CS 0 1 1

J 0 0 0

CSA 2 1 1

2 2

1 1

0 0

-1 -1

DD

2

2

2

2

2 -2

2

2

2

2

2 -2

0

0

0

0

0

Component Selection for2Q Homonuclear

Recoupling

Leiden-SSNMR-2000 8

Structure of CNnν

Sequences

0 1 2 3 N-1

n Complete Sample Revolutions

ν Complete Phase Revolutions

Rf Cycle

Rf Phase Incrementation + 2πν / N

Leiden-SSNMR-2000 9

Average HamiltonianSelection Rules

For CNnν :

Η = 0 if mn - µν ≠ N x integer(1)lmλµ

Leiden-SSNMR-2000 10

Selection Rules for C721

CSA

DD


Structure of RNnν

Sequences

0 1 2 3 N-1

n Complete Sample Revolutions

Rf Phase Alternation ± πν / N

π Pulse


Average HamiltonianSelection Rules

For RNnν :

If λ = odd:

If λ = even:

Η = 0 if mn - µν ≠ N/2 x odd integer(1)lmλµ

Η = 0 if mn - µν ≠ N/2 x even integer(1)lmλµ


Recoupling

HeteroHomo

DD

DD DD

J CSA

2Q ZQ

1-channel 2-channel

Symmetry Solutions for2Q Recoupling

C721 C144

5

R1445 R224

9


Measurement of a13C–13C distance with

R2689

2CO

OC2

-

-

spinning frequency = 11.850 kHzfield = 4.7 T

Marina CarravettaMattias Edén

0

0.1

0.2

0.3

0 1 2 3 4

τexc /ms

2Q-filteredsignal

experimentsimulation 0.138 nm(X-ray =0.132 nm)


Measurement of a13C–13C distance with

R2249

spinning frequency = 7.000 kHzfield = 9.4 T


O

-0.1

0

0.1

0.2

0 5 10 15 20 25 30

experimentsimulation 0.299 nm(X-ray = 0.296 nm)

τexc /ms

2Q-filteredsignal


Measurement of13C- 13C distances


1.55

1.3

1.35

1.4

1.45

1.5

2.5

3.0

3.5

4.0

4.5

H N3

+ CO2

-

CO2

-

CO2

-

OO O O

-

OO

-

O O

-

OO

-

O O

R227.0 kHz MAS9.4 T

49

R145.5 kHz MAS9.4 T

26

R145.5 kHz MAS4.7 T

26

X-ray


2Q 13C Spectrum withC144

5

[U-13C]-tyrosinespinning frequency = 20 kHz; field = 9.4 T

Andreas Brinkmann

C = 3600

2Q

1Q


2Q 13C Spectrum withC144

5

[U-13C]-catabolite repression HPr (11 kDa),aliphatic region

spinning frequency = 14 kHz; field = 9.4 T

Anja Bockmann,François PeninAndreas Brinkmann

C = 3600

2Q

1Q

70 60 50 40 30 20 10

C ppm

140

130

120

110

100

90

80

70

60

50

40

30

C ppm

SC14 spectrum of CRH - aliphatic resonances


Recoupling

HeteroHomo

DD

DD DD

J CSA

2Q ZQ

1-channel 2-channel

Symmetry Solutions forZQ Recoupling

R441 R66

2


-8 -6 -4 -2 0 2 4 6 8-8

-6

-4

-2

0

2

4

6

8

13C-13C correlation withR66

2

[U-13C]-tyrosine; spinning frequency = 28 kHz;mixing interval = 1 ms; field = 9.4 T

1Q

1Q frequency /kHzAndreas Brinkmann

Jörn Schmedt auf der Günne

R = 90180 2700


-8 -6 -4 -2 0 2 4 6 8-8

-6

-4

-2

0

2

4

6

8

13C-13C correlation withR66

2

[U-13C]-tyrosine; spinning frequency = 28 kHz;mixing interval = 10 ms; field = 9.4 T

1Q

1Q frequency /kHzAndreas Brinkmann

Jörn Schmedt auf der Günne

R = 90180 2700


Andreas BrinkmannJörn Schmedt auf der Günne

Simulations at 38 kHzMAS

0200

400

600

800

1000

0

0.005

0.01

0.015

0

0.2

0.4

0

0

0200

400

600

800

1000

0

0.005

0.01

0.015

0

0.2

0.4

0.6

0

0

staticfield

magnetizationtransfer

time

R662

RFDR

38kHz spinning;13C2-glycine parameters

(with 38 kHz rf field)

(with 150 kHz rf field)


0200

400

600

800

1000

0

0.005

0.01

0.015

0

0.2

0.4

0

0

0200

400

600

800

1000

0

0.005

0.01

0.015

0

0.2

0.4

0

0

Andreas BrinkmannJörn Schmedt auf der Günne

RFDR / RIL comparison

staticfield

magnetizationtransfer

time

RFDR

13C2-glycine parameters

(38 kHz MAS, infinite rf field)

RIL

(5 kHz MAS, 50 kHz CW rf +infinitely strong

π pulses)

RIL can’t be implementedat high MAS freq


Recoupling

HeteroHomo

DD

DD DD

J CSA

2Q ZQ

1-channel 2-channel

Heteronuclear DD &CSA Recoupling

R1817 R182

5

R1423 R145

3


HeteronuclearRecoupling by R182

5 :CH case

13C spectrum of [15N, 2-13C]-alanine,with R182

5 applied to the protons

Xin Zhao, Mattias Edén

R = 1800

-25 -20 -15 -10 -5 0 5 10 15 20 25

Frequency(kHz)

ωr/2π = 18 kHzB0 = 9.4 T ωnut/2π = 81 kHzexperiment

simulation


HeteronuclearRecoupling by R182

5 :CH3 case

13C spectrum of [3-13C]-alanine,with R182

5 applied to the protons

Xin Zhao, Mattias Edén

R = 1800

experiment

simulation

-25 -20 -15 -10 -5 0 5 10 15 20 25

Frequency(kHz)

ωr/2π = 18 kHzB0 = 9.4 T ωnut/2π = 81 kHz


Conclusions

• Symmetry solutions exist for awide range ofdecoupling/recoupling tasks inMAS NMR

• Capable of good performance athigh spinning frequencies/highfields

• Quantitative spin dynamics --detailed structural information


Coworkers

• Marina Carravetta

• Andreas Brinkmann

• Xin Zhao

• Mattias Edén

• Ole Johannessen

• Henrik Luthman

• Jörn Schmedt aufder Günne

• Clemens Glaubitz

Funding• Swedish Science Foundation (NFR)

• Göran Gustafsson Foundation

• Huub de Groot

• Peter Verdegem

• Johan Lugtenburg

• Angelika Sebald

• Heidi Maisel

StockholmLeiden

Bayreuth

• Anja Bockmann

• Anne Galinier

• François Penin

Lyon (IBCP)

Documents

Using Symmetry To Design Pulse Sequences in Solid-State NMR€¦ · Leiden-SSNMR-2000 23 0 200 400 600 800 1000 0 0.005 0.01 0.015 0 0.2 0.4 0 0 200 400 600 800 1000 0 0.005 0.01