Dipolar Recoupling in Magic-Angle-Spinning Nuclear Magnetic

148 Pages·2008·3.14 MB·English

Dipolar Recoupling in
Magic-Angle-Spinning
Nuclear Magnetic Resonance
Andreas Brinkmann
Division of Physical Chemistry
Arrhenius Laboratory
Stockholm University
2001

Dipolar Recoupling in
Magic-Angle-Spinning
Nuclear Magnetic Resonance
Andreas Brinkmann
Division of Physical Chemistry
Arrhenius Laboratory
Stockholm University
2001
Doctoral Dissertation
Division of Physical Chemistry
Arrhenius Laboratory
Stockholm University
Sweden
c Andreas Brinkmann 2001
(cid:13)
ISBN 91-7265-281-0(pages I{IX and 1{122)
Printed in Sweden by Akademitryck, Edsbruk 2001
Dipolar Recoupling in Magic-Angle-Spinning
Nuclear Magnetic Resonance
Akademisk avhandling som fo(cid:127)r avla(cid:127)ggandeav (cid:12)loso(cid:12)e doktorexamen vid
Stockholms Universitet o(cid:11)entligen fo(cid:127)rsvarasi Magn(cid:19)elisalen, KO(cid:127)L, Frescati,
onsdagen den 16 maj 2001, kl.10.00
av
Andreas Brinkmann
Avdelningen fo(cid:127)r fysikalisk kemi Stockholm 2001
Stockholms Universitet ISBN 91-7265-281-0
Abstract
This thesis concerns the development of radio-frequency pulse sequences in
magic-angle-spinningsolid-state nuclear magnetic resonance.
First, two classes of pulse sequences are presented which are synchronized
with the sample rotation. Symmetry theorems are described which link the
symmetry of the pulse sequences to selection rules for the recoupling and/or
decoupling of certain spin interactions. Pulse sequences are demonstrated
whichrecoupledirecthomonucleardipolarinteractionsathighsamplespinning
frequencies. Several applications are shown, including the e(cid:14)cient excitation
ofdouble-quantumcoherences,two-dimensionaldouble-quantumspectroscopy,
transfer of longitudinal magnetization and two-dimensional correlation spec-
troscopy. Inaddition,generalizedHartmann-Hahnsequencesaredemonstrated
in which radio-frequency irradiation is applied simultaneously to two isotopic
spin species. These sequences selectively recouple direct heteronuclear dipolar
interactions and suppress all homonuclear interactions for both spin species.
Experimental demonstrations are given of heteronuclear two-dimensional cor-
relation spectroscopy, heteronuclear multiple-quantum spectroscopy and the
estimation of heteronucleardipolar couplings.
Second, a magic-angle-spinning nuclear magnetic resonance method is de-
velopedwhichdirectlyestimatesthebackbonetorsionalangle inpeptidesand
proteins. Themethodexploitsmultiple-quantum13Ccoherenceevolvingunder
heteronuclear13C{15Ndipolarinteractions. Singletorsionalangles aredeter-
minedwith anaccuracyof 5 {10 inthe tripeptides gly-gly-glyandala-gly-gly
(cid:14) (cid:14)
by exploiting double-quantum and triple-quantum coherences respectively.

Contents
List of Papers IX
I Basic Principles of NMR Spectroscopy 1
1 Introduction 3
2 Nuclear Magnetism 4
2.1 Nuclear Spin and Magnetic Moment . . . . . . . . . . . . . . . 4
2.2 Spin Precession and LarmorFrequency . . . . . . . . . . . . . . 5
2.3 Longitudinal Magnetization . . . . . . . . . . . . . . . . . . . . 6
2.4 Transverse Magnetization and the NMR Signal . . . . . . . . . 6
2.5 Nuclear Spin Interactions . . . . . . . . . . . . . . . . . . . . . 7
2.6 Fourier Transform NMR . . . . . . . . . . . . . . . . . . . . . . 8
2.7 Liquid-State NMR . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Solid-State NMR 11
3.1 Powdered Samples . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Cross Polarizationand HeteronuclearDecoupling . . . . . . . . 11
3.3 Dilute Spins and Selective Labelling . . . . . . . . . . . . . . . 13
3.4 Magic-Angle Spinning . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Dipolar Recoupling . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6 Torsional Angle Determination . . . . . . . . . . . . . . . . . . 15
II Theoretical Framework of Magic-Angle-Spinning
NMR 19
4 Spin States 21
4.1 Zeeman Eigenbasis . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Time Evolution and Propagators . . . . . . . . . . . . . . . . . 23
4.3 Rotation Operators . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 The Nuclear Spin Hamiltonian 25
5.1 Cartesian Representation . . . . . . . . . . . . . . . . . . . . . 25
5.2 Spherical Representation . . . . . . . . . . . . . . . . . . . . . . 25
5.3 Reference Frames in Solid State NMR . . . . . . . . . . . . . . 26
5.4 High Field Approximation . . . . . . . . . . . . . . . . . . . . . 27
5.5 Zeeman Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.6 Interaction with Rf (cid:12)elds . . . . . . . . . . . . . . . . . . . . . 31
5.7 Chemical Shift Interaction . . . . . . . . . . . . . . . . . . . . . 32
V
Contents
5.8 Direct Dipole-Dipole Interaction . . . . . . . . . . . . . . . . . 33
5.9 Indirect Dipole-Dipole Interaction . . . . . . . . . . . . . . . . 34
5.10 Magic-Angle Spinning . . . . . . . . . . . . . . . . . . . . . . . 35
6 Density Operator 38
6.1 Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.2 Rf Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.3 NMR Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7 Average Hamiltonian Theory 41
7.1 Interaction Frame. . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.2 Rf pulse sequences under MAS . . . . . . . . . . . . . . . . . . 42
III Dipolar Recoupling in Magic-Angle-Spinning NMR 45
8 Introduction 47
8.1 Homonuclear Dipolar Average Hamiltonians . . . . . . . . . . . 49
8.2 Heteronuclear Dipolar Average Hamiltonians . . . . . . . . . . 50
8.3 Dipolar Recoupling Rf Pulse Sequences . . . . . . . . . . . . . 51
9 Rotor-Synchronized Pulse Sequences 55
9.1 CN(cid:23) Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
n
9.2 RN(cid:23) Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
n
9.3 Average Hamiltonian and Selection Rules . . . . . . . . . . . . 56
9.4 Scaling Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
9.5 Phase-Time Relationships . . . . . . . . . . . . . . . . . . . . . 60
9.6 Changing the Sign of (cid:23) . . . . . . . . . . . . . . . . . . . . . . . 60
9.7 Dual Rotor-SynchronizedPulse Sequences . . . . . . . . . . . . 61
10 Applications 63
10.1 Homonuclear Double-Quantum Recoupling . . . . . . . . . . . 63
10.2 Homonuclear Zero-QuantumRecoupling . . . . . . . . . . . . . 73
10.3 Heteronuclear Double-Quantum Recoupling . . . . . . . . . . . 73
10.4 Double-Quantum Spectroscopy . . . . . . . . . . . . . . . . . . 76
11 Outlook 80
IV Determination of Molecular Torsional Angles
by Solid-State NMR 81
VI
Contents
12 Introduction 83
12.1 Techniques Based upon 2D ExchangeNMR Spectroscopy . . . 83
12.2 Techniques Using Multiple-Quantum Coherence . . . . . . . . . 85
13 The HCCH-2Q-HLF Experiment 88
13.1 Homonuclear Decoupling. . . . . . . . . . . . . . . . . . . . . . 88
13.2 Experimental Implementation . . . . . . . . . . . . . . . . . . . 89
13.3 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
13.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 91
14 The NCCN-MQ-HLF Experiment 94
14.1 Heteronuclear Recoupling . . . . . . . . . . . . . . . . . . . . . 94
14.2 Di(cid:11)erent NCCN-MQ-HLF Experiments . . . . . . . . . . . . . 94
14.3 Experimental Implementation . . . . . . . . . . . . . . . . . . . 96
14.4 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
14.5 Torsional Angle Estimation in Gly-Gly-Gly . . . . . . . . . . . 99
14.6 Torsional Angle Estimation in Ala-Gly-Gly . . . . . . . . . . . 101
14.7 Bloch-Siegert Shift . . . . . . . . . . . . . . . . . . . . . . . . . 103
15 Conclusions 106
V Appendices 107
A Irreducible Spherical Spin Tensor Operators 109
A.1 One Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 Two Spins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References 111
Acknowledgements 121
VI Included Papers 123
VII