Modern Techniques in High-Resolution FT-NMR

395 Pages·1987·7.41 MB·English

by  Narayanan Chandrakumar

Modem Techniques in High-Resolution FT-NMR
Narayanan Chandrakumar
Sankaran Subramanian
Modern Techniques
in High-Resolution
FT-NMR
With 259 Figures
Springer-Verlag
New York Berlin Heidelberg London Paris Tokyo
Narayanan Chandrakumar Sankaran Subramanian
Scientist-in-Charge Professor of Chemistry
FT-NMR Laboratory Regional Sophisticated
Central Leather Research Institute Instrumentation Center
Adayaru, Madras-600 020 Indian Institute of Technology
Tamil Nadu Madras-600 036
India Tamil Nadu
India
Library of Congress Cataloging in Publication Data
Chandrakumar, N" 1951-
Modern techniques in high resolution FT-NMR.
Bibliography: p.
Includes index.
I. Liquids--Spectra. 2. Solids--Spectra.
3. Nuclear magnetic resonance spectroscopy.
4. Fourier transform optics. I. Subramanian, S.,
1942- . II. Title.
QCI45.4.06C48 1986 543'.0877 86-6583
© 1987 Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1987
All rights reserved. No part of this book may be translated or reproduced in any form without
written permission from Springer-Verlag, 175 Fifth Avenue, New York, New York 10010,
U.S.A.
The use of general descriptive names, trade names, trademarks, etc. in this publication,
even if the former are not especially identified, is not to be taken as a sign that such names,
as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used
freely by anyone.
Typeset by Asco Trade Typesetting, Ltd., Hong Kong.
987654321
ISBN-13: 978-1-4612-9089-6 e-ISBN-13: 978-1-4612-4626-8
DOl: 10.1007/978-1-4612-4626-8
Kalvi kaLayila karpavar nalsila ...
Nflladiyflr 2:14:135
Learning is endless, (and) l{fe so short . ..
Excerpt from Tamil Anthology of Quartets,
Nflladiyar, circa 50 B.C.- ISO A.D.
Preface
The magnetism of nuclear spin systems has proved an amazingly fertile
ground for the creativity of researchers. This happy circumstance results
from the triple benediction that nature appears to have bestowed on nuclear
spins: they are sporting spies-being infinitely manipulable (one is even
tempted to say malleable), not unduly coy in revealing their secrets, and
having a whole treasure house of secrets to reveal in the first place.
Since spin dynamics are now orchestrated by the NMR researcher with
ever more subtle scores, it is important to be able to tune into the pro
ceedings with precision, if one is to make sense of it at all. Fortunately,
it is not terribly difficult to do so, since in many ways spin dynamics are
the theoretician's dream come true: they are often finite dimensional and
quite tractable with basic quantum mechanics, frequently allowing near
exact treatments and readily testable predictions.
This book was conceived two years ago, with the objective of providing
a simple, consistent introduction to the description of the spin dynamics
that one encounters in modern NMR experiments. We believed it was a
good time to attempt this, since it was possible by then to give sufficiently
general descriptions of powelful classes of new NMR experiments. The
choice of experiments we discuss in detail is necessarily subjective, al
though we hope to have given a flavor of most of the important classes
of pulse sequences, including some surface coil imaging applications. Ex
cept for brief treatments of the nuclear Overhauser effect, 2D NOESY
and exchange spectroscopy. and cross-relaxation dynamics in the solid
state, however. we have limited the exposition essentially to coherent
spin dynamics. In paliicular, therefore. classical relaxation measurements
and their relation to moleclIlar dynamics are not treated. We have at
tempted to make the book self-contained within this scope and have for-
VIII Preface
matted it in a manner we hope will encourage self-teaching. We have in
cluded the relevant algebra in substantial quantity throughout the book,
because we believe: (a) it is simple enough and deserves to be commonly
used, and (b) one pays a heavy price in precision and detail in choosing
to ignore it.
We record our deep appreciation and gratitude to Professor Dr. E. Fluck,
who displayed great faith in our project and encouraged us to go ahead.
We were also egged on to wrap up the work without undue delay, haunted
as we were by the spectre of a book rendered unmanageable by having
to include the ever newer NMR experiments that continue to be invented
with every passing month!
A large number of examples have been used from the literature in il
lustrating the new techniques we discuss, and we have received unstinted
cooperation from researchers and publishers around the world in kindly
permitting us the use of their work. As is customary, we acknowledge
these permissions individually in the relevant figure captions. In particular,
we have employed a number of illustrations from works of research groups
of Professors R.R. Ernst, R. Freeman and A. Pines, and we acknowledge
here their kind, prompt courtesy in according us their permission to do
so.
We would like to thank the Directors of our respective Institutes, Dr.
G. Thyagarajan (CLRl) and Dr. L.S. Srinath (lIT Madras), for their sup
port and encouragement. One of us (N.C) also thanks Dr. D. Ramaswamy,
Assistant Director, CLRI, for his kind encouragement. G.V. Visalakshi
and D. Srinivas cheerfully presided over the metamorphosis of a perfectly
illegible manuscript through a confused typescript, into a final, usable
version. They deserve our thanks; we are afraid we must take all the
credit for the remaining errors, however! We also thank the editors at
Springer-Verlag for their friendly cooperation in seeing this work through
the throes of final production.
Finally, our primary debt of gratitude is to our long-suffering better
halves: Parvathy Chandrakumar and Rajalakshmi Subramanian who were
quite willing to have us work at the book even when, as was frequently
the case, we were less willing to do so. They let us know, in unmistakable
terms, when the occasion demanded advice!
August, 1986 N.C
S.S
Contents
Preface .............................................. VII
Chapter 1. Introduction and General Theory ................. 1
Chapter 2. One-Dimensional Experiments in Liquids........ 33
Chapter 3. Coherence Transfer................................ 67
Chapter 4. Two-Dimensional Experiments in Liquids........ 124
Chapter 5. Multiple-Quantum Spectroscopy.................. 226
Chapter 6. High-Resolution Pulse NMR in Solids............ 260
Chapter 7. Experimental Methods............................. 330
Appendix I. Matrix Algebra of Spin-~ and Spin-I Operators.. 350
Appendix 2. The Hausdorff Formula ..... , ... " .. . .. .. .. . . . .. . .. 356
Appendix 3. Fourier Transformation............................ 359
Appendix 4. Dipolar Relaxation ................................. 365
Appendix 5. Magnus Expansion and the Average
Hamiltonian Theory................................ 370
Appendix 6. Tensor Representation of Spin Hamiltonians..... 375
Selected Bibliography.............................. 381
Index................................................ 385
CHAPTER 1
Introduction and General Theory
Nuclear magnetic resonance (NMR), which originated some 40 years ago
primarily as a potentially accurate method for measuring nuclear magneto
gyric ratios, turned out to be something of an embarrassment in that applica
tion when it transpired that the rf magnetic susceptibility it measured could be
a quite complicated function, exhibiting many sharp, close-lying resonances.
When it was realized however, that this complexity rather subtly reflected
exceedingly fine characteristics of the electronic environment in which the
nuclei were embedded, NMR began being developed as a high-resolution (HR)
spectroscopic technique for the elucidation of molecular structure, dynamics,
and, most recently, distribution (i.e., NMR imaging). Here again it soon
became apparent that HR-NMR spectra were generally too complicated to
admit of straightforward, unambiguous interpretations of molecular struc
tures. Major effort, since then, has been spent on developing ever more
powerful methods to help produce and interpret HR-NMR spectra. On the
experimental side, this has, on the one hand, led to attempts (a) to develop
NMR as a truly multinuclear technique, and (b) to improve the sensitivity or
signal-to-noise ratio of NMR spectra as well as their resolution. On the other,
people have sought to devise NMR experiments that can generate unambigu
ous, clearly recognizable features in the spectra by various means of selectively
monitoring different kinds of nuclear magnetic interactions while suppressing
others as required. Pulse Fourier transform (FT) NMR has emerged as the
method of choice, allowing the spectroscopist maximum flexibility in the
pursuit of practically any combination of these objectives. In conjunction with
the rapid advances in the commercially available instrumentation, this situa
tion has led to an explosion in the development of new techniques in NMR
that shows no signs of letting up.
We attempt in this book to capture the spirit of NMR as it is practiced
2 1. Introduction and General Theory
today, by presenting a coherent view of the fundamentals on which it rests.
We make in the process no claims to exhaustiveness in cataloging the emerg
ing techniques and their applications.
Introduction
A large number of nuclear isotopes have a nonzero spin angular momentum
1h/2n, where h is the Planck's constant. In accordance with the principles of
quantum mechanics, 1 can take on only the values 1/2, 1, 3/2, 2, 5/2, etc.
Associated with this spin quantum number 1 is the magnetic dipole moment
11, of the isotope in question:
J1 = yhI/2n (1)
y being the magnetogyric ratio, which is a nuclear property. In an external
magnetic field Bo, the magnetic moment can take up one of (21 + 1) allowed
orientations, each with its characteristic energy corresponding to the Hamil
tonian:
yt = -J1" Bo
= - yhI . Bo/2n (2)
= -yhBolz/2n
the direction of the dc magnetic field Bo being, by convention, chosen to be
the z axis of the laboratory coordinate frame. Measurements of the magnetic
("Zeeman") energy in such a situation lead to the values:
E = - yhBomd2n (3)
where m[takes on the (21 + 1) values ±I, ±(I -1), ... , ±1/20rO,depending
on whether 1 is a half-odd integer or an integer. Successive Zeeman levels are
thus displaced in energy by the constant value, yhBo/2n. Values of yBo/2n
range from 100 to 103 MHz, depending on the magnetogyric ratio of the
isotope in question and the intensity of the external magnetic field Bo. This
energy gap, expressed in frequency units, is called the Larmor frequency of
the isotope in the field Bo. It in fact is the frequency of precession of the nuclear
spins in the magnetic field, originating in the torque exerted by the field on
their spin angular moments.
In an ensemble of nuclear spins I, the (21 + 1) allowed energy levels are
populated in thermal equilibrium in accordance with the Boltzmann distribu
tion. For 1 = 1/2, for example, the ratio of the number (N;) of spins per unit
volume in the upper energy state (m[ = -1/2 if y > 0, called the spin-down
state, 1fJ)) to that in the lower state (m[ = 1/2 if y > 0, called the spin-up state,
10:)), is given by:
N2/Nl = exp [ -(E2 - Ed/kT] = exp( -yhBo/2nkT) (4)
T being the absolute equilibrium temperature, known as the "lattice" tempera
ture. The spin system in fact requires some time to attain the state of thermal
Introduction 3
equilibrium after a magnetic field is switched on. The approach to thermal
equilibrium is often by a first-order process known as spin-lattice or longitu
dinal relaxation, characterized by a single time constant, T1•
In most practical applications, the quantity (yhBo/2nkT) is very much less
than 1. With this approximation
(5)
where:
e = yhBo/2nkT (6)
This leads at once to:
+
Nl = N[1 (e/2)]/2
(7)
N2 = N[1 - (e/2)]/2
correct to terms linear in e, where:
(8)
the total number of spins per unit volume. The difference in population,
(Nl - N2), is a measure of the "order" induced in the nuclear spin system by
the magnetic field: the spins are "polarized" in the field. In this sense there is
total disorder when Bo vanishes, for Nl is then equal to N2: the energy levels
are populated equally in the absence of the magnetic field. The order induced
by the field leads to a bulk magnetization (M) of the nuclear spin ensemble
that may be calculated readily. It is given by:
(9)
For J = 1/2, this turns out to be:
M = Nyh[[1 + (e/2)] - [1 - (e/2)]]/8n
= Ny2(h/2n)2 Bo/4kT (10)
In general, the quantity
X(O) = (Ny2J(I + 1)/3kT)(h2/4n2) (11)
is termed the Curie susceptibility of the ensemble of nuclear spins. It may be
noticed that the magnetization induced in the ensemble of "bare" nuclei at
thermal equilibrium is aligned with Bo, and no magnetization exists transverse
to Bo. At the level of the individual nuclei in the ensemble, their precession is
"incoherent," leading to zero net magnetic moment in the xy plane, while
giving rise to M parallel to Bo in accordance with Eq. (9). This situation is
depicted in Fig. 1.1. Numerically, the dc nuclear paramagnetic susceptibility
X(O) is so small that the electron diamagnetic susceptibility completely swamps
it in closed shell molecules at all but the very lowest attainable temperatures,
making it a dauntingly difficult quantity to measure directly. Nuclear mag-