ITALIAN PHYSICAL SOCIETY

PROCEEDINGS OF THE

INTERNATIONAL SCHOOL OF PHYSICS «ENRICO FERMI»

COURSE CXXIII edited by B. MARAVIGLIA

Director of the Course VARENNA ON LAKE COMO

VILLA MONASTERO

13-21 October 1992

Nuclear Magnetic Double Resonance

1993

NORTH-HOLLAND AMSTERDAM - OXFORD - NEW YORK - TOKYO

I N D I C E

B.MARAViGLiA-Preface pag. xv

Gruppo fotografico dei par tecipant i al Corso fuori testo

M. GOLDMAN - Introduction to some basic aspects of NMR.

1. Nuclear interactions pag. 1 l ' l . The Zeeman interaction » 1 1'2. Electron-nucleus interactions » 3

1'2.1. Magnetic interactions » 4 1'2.2. Electric interactions » 7 T2.3. The case of metals » 9

1'3. Dipole-dipole interactions » 9 1'4. Exchange interactions » 11 1*5. Appendix: transformation properties of 2nd-rank tensors upon

rotation » 12 2. Spin-lattice relaxation revisited » 14

2 1 . Derivation of the master equation » 15 2'1.1. Evolution in the interaction representation » 18 2'1.2. Evolution in the Schrödinger representation » 20 21.3. Relation between both approaches » 21 2'1.4. Conditions ofvalidity of thetheory » 22 21.5. Extension to solids » 23

2'2. Drawbacks of alternative approaches. A selection » 24 2'2.1. Use of an interaction representation that does not remove

all of 5T0 » 25 2'2.2. Premature assumption that the average of a product

equals the product of the averages » 26

VII

VIII INDICE

2'2.3. Calculation of the time evolution of all elements of the density matrix pag. 27

2'2.4. Guesses about the form of the density matrix » 28 2'2.5. Use of the memory function formalism » 29

3. Spin temperature » 31 3*1. Spin temperature in zero field » 31 3'2. Spin temperature in low field » 34 3'3. Spin temperature in high field » 35 3'4. R.f. irradiation in high field » 38 3'5. Value and evolution of the spin temperature » 39

3'5.1. Sudden change of the Hamiltonian » 40 3'5.2. Adiabatic Variation of the Hamiltonian » 40

3'6. What gives rise to a r.f. signal? » 42 3'7. Verification of spin temperature theory » 44

37.1. General » 44 37.2. The case of effective Hamiltonians » 45

4. The case of a periodic Hamiltonian » 52 4 1 . Introduction » 52 4'2. Fast modulation » 55

4'2.1. The basic equations » 55 4'2.2. The next-order approximation » 56 4'2.3. The general expansion » 57

4'3. Large anisotropic chemical shifts » 63 4'3.1. Spin-spin relaxation » 65 4'3.2. Application of the theory. Generalities » 66

C H . P . S L I C H T E R - Double resonance.

1. What is double resonance, and why do it? » 69 2. Discovery of the Pound-Overhauser family » 70 3. AmodelSystem » 71 4. The electron-nuclear case: the Overhauser effect » 71 5. Cross-relaxation double resonance » 78 6. Spin coherence double resonance—S-flip-only echoes » 82 7. Spin coherence double resonance—coherence transfer » 85 8. Spin echo double resonance (SEDOE) » 88 9. SEDOR Signals when there are several S spins » 92 10. Examples of SEDOR studies » 94 Explanatory note » 101

Polarization of nuclear spins in metals » 101 Measurement of the spin and gyromagnetic ratio of 13C by the collapse of spin-spin Splitting » 104 Effects of perturbing radiofrequency fields on nuclear-spin coupling » 106 Method of polarizing nuclei in paramagnetic substances » 117 Polarization of phosphorous nuclei in Silicon , » 120

L. E M S L E Y and A. P I N E S - Lectures on pulsed NMR (2nd edition).

Introduction » 123 1. Multiple-quantum NMR » 123

l ' l . Dipolar couplings and molecular structure » 123 1'2. Onset of spectral complexity » 124

INDICE IX

1*3. Simplification by multiple-quantum transitions pag. 127 1'4. Analogy to chemical isotopic labeling » 128 1'5. Obtaining multiple-quantum spectra » 129 1"6. Theory of multiple-quantum NMR: preliminaries » 130 17. Multiple-quantum signal » 132 1'8. Special case: one-quantum FID pointbypoint » 132 1'9. General case: multiple-quantum FID » 133 HO. Time-reversal (conjugate) detection » 134 111. Effect of phase shifts » 135 1'12. Time-proportional phase incrementation (TPPI) » 137 113. Double-quantum NMR in solids » 137 114. Double-quantum spin locking » 138 115. Molecular structure by multiple-quantum NMR » 141 116. Selective w-quantum excitation » 145 117. Multiple-quantum NMR in solids » 147 118. Selection rules in multiple-quantum dynamics » 151 119. Total coherence transfer » 151 1'20. Bilinear rotation pulses » 153

2. Coherent-averaging theory » 153 2 1 . Introduction..... » 153 2'2. Multiple-pulse line narrowing » 155 2'3. Magic-angle spinning » 157 2'4. Double rotation » 160

3. Spin decoupling » 165 3 1 . Spin/ = l /2pa i r » 165 3'2. One-quantum offset and r.f. amplitude dependence » 166 3'3. Double-quantum decoupling » 168 3'4. Double-quantum offset and r.f. amplitude dependence » 168 3'5. Comment on the relationship between spin decoupling an multi­

ple-quantum excitation » 171 4. Interaction of radiation and matter » 171

4 1 . Two-level system in a quantized field » 171 4'2. Fictitious spin / = 1/2 Operators » 173 4'3. Evolution of the two-level system » 174 4'4. Evolution off resonance » 175 4'5. Adiabatic rapid passage » 175 4'6. Three-level system in a quantized field » 177 4'7. Fictitious spin / = 1 Operators » 178 4'8. Double-quantum (two-photon) Hamiltonian » 178 4'9. Evolution of the system » 179 410. Double-quantum adiabatic rapid passage » 180

5. Group theory and dynamics » 182 5 1 . Molecular motion » 183 5'2. Group theory and exchange » 185 5'3. Relevant representations » 186 5'4. Summary of symmetry considerations » 187 5'5. Example: dynamics of solid benzene » 188 5'6. Macroscopic motional averaging » 190 5'7. Sample spinning » 190 5'8. Group theory of motional averaging » 191 5'9. Averaging under cubic and icosahedral symmetry » 193

X INDICE

'510. Dynamic-angle spinning pag. 195 511. Isotropic-anisotropic correlation spectra » 199 512. Variable-angle correlation spectroscopy » 201

6. Cross-polarization » 203 6 1 . Spin temperature » 203 6'2. Methods for obtaining thermal contact » 204 6'3. Statistical picture of cross-polarization » 206 6'4. Hartmann-Hahn mismatch » 208 6'5. Thermodynamics of heteronuclear cross-polarization » 210 6'6. Resolved heteronuclear coupling » 213

7. Unitary bounds on spin dynamics » 216 7 1 . Unitary evolution » 216 7'2. The entropy limit » 217 7'3. Bounds on unitary evolution » 217 7'4. Redfield's description of polarization transfer » 218 7'5. Bounds in INS Systems » 219 7'6. The thermodynamic limit » 220 77. Two-dimensional bounds » 221 7'8. Transfer of basis Operators » 223 7'9. Nonunitary evolution » 223 710. Cross-polarization echoes » 225

8. Zero-field NMR >» 226 8 1 . Zero-field NQR of deuterium » 228 8'2. Two-dimensional zero-field NMR » 230 8'3. Zero-field pulses » 233 8'4. Calculation of the zero-field spectrum » 236 8'5. Average over orientational distribution » 237 8'6. Dipolar coupled spin / = 1/2 pair or quadrupolar spin / = 1 » 237 8'7. Effects of motion » 240 8'8. Magnetic resonance with a SQUID detector » 241 8'9. Comment on relationship of spatially selective pulses to zero-field

NMR » 242 9. Geometrie phases » 243

9 1 . Context for geometric phases » 243 9'2. Classical holonomy » 244 9'3. Quantum holonomy » 245 9'4. Equations for the geometric phase » 248 9'5. Explicit calculation for s p i n / = 1/2 » 249 9'6. The Aharonov-Bohm effect » 251 9'7. Geometric phase in NMR interferometry » 252 9'8. Fractional quantum numbers » 254 9'9. Nonunitary behavior, quantum protection » 256 910. Geometry of light » 257 911. Rotation of cats » 258

M. M E H R I N G - A guided tour through double-resonance phenomena.

1. Introduction » 267 2. Double resonance in three- and multi-level Systems » 269

2 1 . Population trasfer » 270

INDICE XI

2*1.1. Saturation ofthe 2-3 transition pag. 271 2'1.2. Inversion of the 2-3 transition » 272

2*2. Spin alignment and pulsed ENDOR experiments » 272 2"3. Spin echo double resonance (SEDOR) » 276

2*3.1. The 1-2 spin echo » 277 23.2. SEDOR effect » 277 2*3.3. Spinor experiments » 278

2*4. Cross-polarization in the rotating frame » 280 2*5. Coherence transfer » 281

3. Many-spin Systems » 282 3 1 . Spin temperature and spin density matrix » 283 3*2. Spin calorimetry » 284 3*3. From Hilbert space to Liouville space » 285 3*4. Spin calorimetry in Liouville space » 286

3*4.1. Energy conservation » 287 3*4.2. Isentropic mixing » 288

3*5. SEDOR » 289 3*6. Double-resonance spin dynamics » 291

4. Unconventional double-resonance experiments » 294 4*1. Rb-Xe double resonance and rotating the frame » 294 4*2. Hyperfine spectroscopy with correlation to an electron spin

(HYSCORE) » 295 4*3. Optical Zeeman double resonance with a laser diode » 296

5. Summary » 298

B. H. M E I E R - Polarization t ransfer experiments .

1. Introduction » 301 1*1. A simple application: the two-spin System » 305

2. Application to the MOIST experiment » 309 3. Larger spin Systems » 314 4. Time-dependent Hamiltonians » 317 5. Spin diffusum » 324 6. Polarization echoes » 330

R. F R E E M A N - Introduction to two-dimensional N M R in liquids.

1. Introduction : » 335 2. Pseitdo-two-dimensional spectroscopy » 337 3. Correlation spectroscopy (COSY) » 340 4. Total-correlation spectroscopy » 345 5. Chemical-exchange spectroscopy » 346 6. Nuclear Overhauser effect » 346 7. Nuclear Overhauser spectroscopy (NOESY) » 349 8. Forbidden transitions » 349 9. «INADEQUATE» » 350 10. Spin echoes » 353 11. «Broad-band decoupled» proton spectra » 356 12. Discussion » 359

XII INDICE

R. FREEMAN - Selective excitation in high-resolution NMR.

1. Introduction pag. 363 2. The DANTE sequence » 364 3. Shaped pulses » 365 4. Phase gradients » 366 5. «Spin pinging» » 367 6. Practical implementation » 368 7. Resolution enhancement » 368 8. Reduction of dimensionality » 370 9. The Hartmann-Hahn experiment » 373 10. Stepwise coherence transfer (DAISY) » 374

R. FREEMAN - Fine structure in two-dimensional spectra.

1. Introduction » 381 2. The structure of COSY cross-peaks » 381 3. Extractionofcouplingconstants » 386 4. J-extension » 387 5. J-deconvolution » 389 6. /-doubling » 393

C. ZWAHLEN, S. J. F. VINCENT and G. BODENHAUSEN - Selective

double resonance and coherence transfer.

1. Introduction » 397 2. Doubly selective irradiation » 398 3. Matrix representations » 401 4. Evolution, coherence transfer and detection » 404 5. Conclusions » 410

R. CAMPANELLA, S. CAPUANI, F. D E LUCA and B. MARAVIGLIA -

Double-resonance J-coupling imaging.

1. Introduction » 413 2. Double resonances to increase the signal-to-noise ratio » 413 3. /-coupling imaging » 416 4. Results and conclusions » 418

E. W. RANDALL - Some double-resonance methods in imaging experi-ments.

Introduction » 423 1. Some thoughts on definition » 424 2. Classification » 426 3. Introduction to double-resonance imaging » 434

31. Nitrogen » 435 32. Imaging 14N » 436 3'3. Imaging 15N » 439

3*3.1. Direct method » 439 3-3.2. ^NfH} Overhauser method » 439 33.3. Indirect methods, ' H ^ N } » 444

INDICE XIII

N. LUGERI, F . D E LUCA, B. C. D E SIMONE and B. MARAVIGLIA - Ro-

tating-frame spectroscopy and imaging under radio- and audio-frequency excitation.

1. Introduction pag- 449 2. General features of RCF experiments » 450 3. Theoretical backgrounds » 450 4. Magic-angle rotating-frame experiments » 455

41. Interaction representation » 455 4'2. TRCF Hamiltonians » 459

5. Applications of MARF experiments » 462 51. MARF imaging » 462 5'2. Relaxation studies » 466

M. BLOOM - A proposed Stern-Gerlach experiment on individual spins in solids.

1. Introduction » 473 2. Review of the Stern-Gerlach experiment » 474

21. Classical description » 474 2'2. Quantum description » 475

3. The transverse Stern-Gerlach experiment » 475 31. Resonance in the TS-G experiment—quantizationof/^ » 476

4. Thefolded Stern-Gerlach experiment » 476 41. Analysis of the FS-G experiment for a frictionless oscillator » 477 4'2. Inclusion of oscillator damping » 478 43. Some practical considerations concerning mechanical oscilla-

tors » 478 4'4. Criterion for detectability of a Single proton spin by FS-G

resonance » 479 5. Basic differences between Stern-Gerlach experiments and NMR » 480 6. Stern-Gerlach experiments on macroscopic spin Systems » 481

61. Polarized samples » 482 6"2. Unpolarized samples » 482

Note added (January, 1993) » 483

D. J. LURIE and I. NICHOLSON - Proton-electron double-resonance imaging of exogenous and endogenous free radicals in vivo.

1. Introduction » 485 2. Summary of relevant results from dynamic nuclear polarization the-

ory » 486 21. The DNP enhancement » 487 2"2. The coupling factor » 487 2"3. The leakage factor » 487 2'4. The Saturation factor » 487 2'5. The maximum theoretical enhancement » 488 26. EPR irradiation power » 488

3. Implementation ofPEDRI » 489 31. Magnetic-field strength considerations » 489 3'2. Basic PEDRI pulse sequence » 490

XIV INDICE

3*3. Interleaved PEDRI pulse sequence pag. 490 3*4. Field-cycled PEDRI » 491 35 . Snapshot PEDRI » 492

4. Hardware for PEDRI » 492 4 1 . The magnet » 492 4*2. The double-resonance r.f. coil assembly » 494

5. Applications of PEDRI » 496 5 1 . Imaging exogenous free radicals in vivo » 496

5*1.1. Desirable features ofa PEDRI contrast agent » 496 5*1.2. Nitroxide free radicals » 496 5*1.3. In vivo PEDRI studies » 498

5*2. Imaging endogenous free radicals in vitro and in vivo » 498 5*2.1. Spin trapping » 499 5*2.2. PEDRI with spin trapping » 500

6. Summary and conclusions » 501