A Primer of NMR Theory with Calculations in Mathematica

249 Pages·2015·2.618 MB·English

by  Alan J. Benesi

A Primer of Nmr Theory
wiTh cAlculATioNs iN
mAThemATicA®

A Primer of Nmr
Theory wiTh
cAlculATioNs
iN mAThemATicA®
AlAn J. Benesi
former Director
Nmr facility
The Pennsylvania state university
university Park, PA, usA
Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Benesi, Alan J., 1950–
A primer of NMR theory with calculations in Mathematica® / Alan J. Benesi.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-58899-4 (cloth)
1. Nuclear magnetic resonance spectroscopy–Data processing. I. Title. II. Title: Primer of nuclear
magnetic resonance theory with calculations in Mathematica.
QD96.N8B46 2015
538′.362028553–dc23
2014048320
Set in 10/12pt Times by SPi Global, Pondicherry, India
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
Mathematica® is a registered trademark of Wolfram Research, Inc.
1 2015
Contents
PrefaCe ix
Chapter 1 IntroduCtIon 1
Chapter 2 usIng MatheMatICa; hoMework PhIlosoPhy 3
Chapter 3 the nMr sPeCtroMeter 5
Chapter 4 the nMr exPerIMent 9
Chapter 5 ClassICal Magnets and PreCessIon 13
Chapter 6 the BloCh equatIon In the laBoratory
referenCe fraMe 19
Chapter 7 the BloCh equatIon In the rotatIng fraMe 23
Chapter 8 the VeCtor Model 27
Chapter 9 fourIer transforM of the nMr sIgnal 33
Chapter 10 essentIals of quantuM MeChanICs 35
Chapter 11 the tIMe‐dePendent sChrödInger equatIon,
MatrIx rePresentatIon of nuClear sPIn angular
MoMentuM oPerators 39
Chapter 12 the densIty oPerator 43
Chapter 13 the lIouVIlle–Von neuMann equatIon 45
Chapter 14 the densIty oPerator at therMal equIlIBrIuM 47
Chapter 15 haMIltonIans of nMr: IsotroPIC lIquId‐state
haMIltonIans 51
Chapter 16 the dIreCt ProduCt MatrIx rePresentatIon
of CouPlIng haMIltonIans h and h 57
J d
Chapter 17 solVIng the lIouVIlle–Von neuMann equatIon
for the tIMe dePendenCe of the densIty MatrIx 61
Chapter 18 the oBserVaBle nMr sIgnal 67
Chapter 19 CoMMutatIon relatIons of sPIn angular MoMentuM
oPerators 69
v
vi CONTENTS
Chapter 20 the ProduCt oPerator forMalIsM 73
Chapter 21 nMr Pulse sequenCes and Phase CyClIng 77
Chapter 22 analysIs of lIquId‐state nMr Pulse sequenCes
wIth the ProduCt oPerator forMalIsM 81
Chapter 23 analysIs of the InePt Pulse sequenCe wIth PrograM
shortsPIn and PrograM PoMa 87
Chapter 24 the radIo frequenCy haMIltonIan 91
Chapter 25 CoMParIson of 1d and 2d nMr 95
Chapter 26 analysIs of the hsqC, hMqC, and dqf‐Cosy 2d
nMr exPerIMents 99
Chapter 27 seleCtIon of CoherenCe order Pathways wIth Phase
CyClIng 107
Chapter 28 seleCtIon of CoherenCe order Pathways wIth Pulsed
MagnetIC fIeld gradIents 115
Chapter 29 haMIltonIans of nMr: anIsotroPIC solId‐state Internal
haMIltonIans In rIgId solIds 123
Chapter 30 rotatIons of real sPaCe axIs systeMs—CartesIan
Method 133
Chapter 31 wIgner rotatIons of IrreduCIBle sPherICal tensors 137
Chapter 32 solId‐state nMr real sPaCe sPherICal tensors 143
Chapter 33 tIMe‐IndePendent PerturBatIon theory 149
Chapter 34 aVerage haMIltonIan theory 157
Chapter 35 the Powder aVerage 161
Chapter 36 oVerVIew of MoleCular MotIon and nMr 165
Chapter 37 slow, InterMedIate, and fast exChange In
lIquId‐state nMr sPeCtra 169
Chapter 38 exChange In solId‐state nMr sPeCtra 173
Chapter 39 nMr relaxatIon: what Is nMr relaxatIon
and what Causes It? 183
Chapter 40 PraCtICal ConsIderatIons for the CalCulatIon
of nMr relaxatIon rates 189
Chapter 41 the Master equatIon for nMr relaxatIon—sIngle
sPIn sPeCIes I 191
Chapter 42 heteronuClear dIPolar and J relaxatIon 205
Chapter 43 CalCulatIon of autoCorrelatIon funCtIons,
sPeCtral densItIes, and nMr relaxatIon tIMes
for JuMP MotIons In solIds 211
CONTENTS vii
Chapter 44 CalCulatIon of autoCorrelatIon funCtIons
and sPeCtral densItIes for IsotroPIC rotatIonal
dIffusIon 221
Chapter 45 ConClusIon 225
BIBlIograPhy 227
Index 231