NUCLEAR MAGNETIC RESONANCE
SPECTROSCOPY

Contents

Overview

Principles

Instrumentation

Overview

A Bainbridge

, University College London Hospitals

Trust, London, UK

& 2005, Elsevier Ltd. All Rights Reserved.

Introduction

Nuclear magnetic resonance spectroscopy (NMRS)
has become a useful tool for the nondestructive ana-
lysis of small samples and increasingly for non-
invasive in vivo tissue analysis. In this article, an
overview of the theory, equipment, and methodolo-
gies of NMRS are presented.

Theory

The interaction of certain atomic nuclei with a strong
magnetic field gives rise to the NMR signal and con-
sequently NMR spectra. This section contains a brief
overview of the physics of signal generation leading
onto a discussion of the physics behind the specific
structure of NMR spectra.

The Physics of NMR

Atomic nuclei that have odd mass numbers and/or
odd atomic numbers possess a nonzero quantum spin
number, I, made up of the vector sum of the spins of
its constituent protons and neutrons. The component
of the vector I along an arbitrarily defined axis (z in
this case) has a magnitude I

z

given by

I

z

¼ m

I

_

½1

where

_ is Plank’s constant divided by 2p. The quan-

tum number m

I

can take (2I

þ 1) values (such that

m

I

¼  I,  [I  1],y, [I  1], I); one can only mea-

sure a component of I in any one direction at any one
time. The nuclei most commonly probed in NMR
experiments (

1

H,

31

P,

13

C, and

19

F) have I

¼ 1/2 and

so m

¼ 71/2. These two states are normally energy

degenerate. However, in the presence of a strong
magnetic field, B

0

, applied along the same arbitrarily

defined z-axis as in eqn [1], the strong field Zeeman
effect causes the states to split into two energy levels
separated by energy DE:

DE ¼ g_B

0

½2

The gyromagnetic ratio, g, is defined as the ratio of
magnetic moment to angular momentum of the nu-
cleus and impacts on the sensitivity of NMRS ex-
periments. Assuming that the coupling between the
individual spins is weak, the relative populations of
the two levels are given by a Boltzmann distribution:

n

m

n

k

¼ exp

DE

kT





½3

where k is the Boltzmann constant and T is the tem-
perature of the spin system. A collection of spins will
distribute themselves between the energy levels re-
sulting in a small excess of spins in the lower (n

m –

spin up) state at thermal equilibrium. This leads to a
sample obtaining a net magnetization, M

0

, lying

parallel to the main field. This is the property that is
detectable using NMR and its amplitude is depend-
ent on g

2

, B

0

, and the number of equivalent nuclei

per unit volume, n:

M

0

¼

ng

2

_

2

B

0

4kT

½4

As M

0

is a property of the bulk system, one can

define all three components simultaneously and use
classical mechanics to describe its evolution. M

0

will

precess around B

0

at the Larmor frequency, o

0

(see

Figure 1). The Larmor frequency is equivalent to the
frequency of photons required to induce transitions
between the energy levels and is defined as:

o

0

¼ gB

0

½5

Manipulation of the orientation of M

0

relative to

B

0

using circularly polarized radio frequency (RF) at

this resonant frequency leads to the generation of the
NMR signal. To illustrate this it is commonplace to

NMR SPECTROSCOPY

/ Overview

203

define a set of axes rotating about B

0

at the Larmor

frequency. With the introduction of RF at this fre-
quency, right-hand circularly polarized along the
z-axis, the equivalent magnetic field in this frame, B

1

,

becomes oriented in the x

0

–y

0

plane and has an am-

plitude equal to the amplitude of the B-field compo-
nent of the RF. M

0

will precess around B

1

with a

frequency o

1

equivalently to eqn [5] (see Figure 2).

By adjusting the length and power of the RF pulse it
is possible to flip M

0

vector into the x

0

–y

0

plane; this

is equivalent to equalizing the populations of the
quantum mechanical energy levels and is known as a
90

1 pulse. The amplitude of the NMR signal is pro-

portional to the component of M

0

in the x–y plane

and its precession about B

0

causes an oscillating cur-

rent to be induced in a suitably arranged RF coil
(described below). This signal decays exponentially
with a time constant T2



due to field inhomogenei-

ties causing spins to precess at different rates and
dephase. The result is a free induction decay (FID)
(see Figure 3).

Chemical Shift

NMR spectra consist of a series of peaks identifiable
to specific chemical structures on particular mole-
cules rather than just a single peak resonating at o

0

;

the position of a peak in the spectrum is termed its
chemical shift. Peaks occur at different chemical shifts
because the magnetic field at an atomic nucleus is not

equal to the applied magnetic field. The electrons in
electronic orbitals shield the nucleus from the app-
lied field, thus altering the resonant frequency. Elec-
trons in atoms and molecules are described by a series
of quantum numbers. Technically, the shape of an
atomic orbital occupied by an electron with a given
set of quantum numbers is best described by the
square of its quantum mechanical wavefunction.

z

B

0

M

0

y

x

0

Figure 1

The net magnetization of the sample M

0

will precess

around the applied magnetic field vector with an angular fre-
quency o

0

. This is equivalent to the frequency of RF required to

stimulate a transition between the spin-up and spin-down energy
states.

z

′

x

′

y

′

B

1

M

0

1

Figure 2

The tilting of M

0

into the x

0

–y

0

frame due to the ap-

plication of RF at the Lamor frequency o

0

. This is represented in

a frame of reference rotating about B

0

at o

0

. The equivalent field

in the rotating frame is B

1

, which appears stationary along y

0

. M

0

precesses B

1

with an angular frequency o

1

.

Time

Amplitude

Figure 3

An example of FID consisting of a single frequency

decaying exponentially.

204

NMR SPECTROSCOPY

/ Overview

The principal quantum number, N, is dominant in
determining the shape of an orbital; for a rigorous
treatment of quantum mechanics and the physics of
electronic orbitals, the reader can refer to the Further
Reading. For the purpose of this discussion it is suf-
ficient to recognize that s-orbitals (N

¼ 1) have a

spherical symmetry and higher orbitals (p, N

¼ 2; d,

N

¼ 3; etc) have more complex shapes. Thus the sim-

plest example of nuclear shielding is that arising from
electrons in s-orbitals. A schematic of how an s-elec-
tron shields the nucleus is shown in Figure 4. In the
presence of an applied field, the electron’s orbital
forms an effective current loop resulting in a magnetic
field that opposes the applied field. Thus the nucleus
experiences a reduced magnetic field and resonates at
a lower frequency. The magnitude in hertz of the
chemical shift is proportional to the size of the ap-
plied field, as this determines the magnitude of the
effective currents produced by the electrons. In order
to eliminate the dependence on B

0

, chemical shifts are

generally quoted in units of parts per million (ppm) of
the static magnetic field strength.

Proton Chemical Shifts

Only s-electrons have orbitals around hydrogen
nuclei. However, the degree of shielding that they pro-
vide is further influenced by their chemical environ-
ment. Electronegative elements near to the proton
withdraw electron density and reduce the extent of
the shielding. An example of oxygen bonded to car-
bon influencing the chemical shifts of the protons
also bonded to the carbon is shown in Figure 5. The
larger the electronegativity of the directly bonded
atom, the larger its influence on the chemical shift of
its NMR visible neighbors. Double bonds (p-bonds)
between carbon atoms in organic molecules also
have a significant effect on proton chemical shift.

For a portion of their time, these molecules will be
oriented with their p-bonds perpendicular to applied
field, as illustrated in Figure 6. The current distribu-
tion of the p-electrons is such that a magnetic field is
produced that opposes the applied field above and
below the bond, but reenforces the applied field at
the attached proton. An exception to this is the ter-
minal alkyne group (Figure 6), where the proton is
oriented in the same plane as the p-bond. The major
contribution comes when the p-bond is oriented
parallel to the applied field. The current distribution
from the p-electrons leads to an induced field that
opposes the applied field at the proton. All of the
above effects are additive in determining the final
chemical shift of a proton and the position of reso-
nances can be suggestive of specific function groups
(see Table 1).

Other Nuclei and Chemical Shift Mechanisms

Nuclei other than

1

H that are typically used for

NMRS, such as

31

P and

13

C, have electrons in higher

orbitals that do not have spherical symmetry. These
can produce comparatively large magnetic fields at
the nucleus. Thus the range of chemical shifts is
larger; typically, the range of chemical shifts for

13

C

(0–200 ppm) is 10–20 times the range of proton
chemical shifts. The chemical shifts of some reso-
nances are variable depending on the environment of

B

0

Current due to

s-electron

Induced magnetic

field

Nucleus

Figure 4

Shielding of the nucleus from the applied magnetic

field due to an orbital s-electron. The current due to the electron
induces a magnetic field at the nucleus that acts to oppose the
applied field.

O

C

H

Electron density moves

toward oxygen

Figure 5

Electronegative elements such as oxygen draw elec-

tron density toward them reducing the shielding of the proton.

C

C

H

H

C

C

H

Electron

current

Electron

current

B

electron

B

electron

(A)

(B)

B

0

Figure 6

(A) p-Bonds between carbon atoms can lead to the

magnetic field at a proton being enhanced when oriented in the
plane perpendicular to the main field. (B) An exception is the
terminal alkyne. In this example the shielding is increased.

NMR SPECTROSCOPY

/ Overview

205

the sample. Hydrogen bound (acid) and unproton-
ated (base) chemicals have different chemical shifts.
As the acid and base states are in rapid chemical
exchange, a single resonance with the average chemi-
cal shift of the relative equilibrium populations is
observed. The local concentration of hydrogen ions
(and hence pH) determines the acid–base popula-
tions and so alters the chemical shift. Similarly, met-
al-ion concentration can influence chemical shift.
Uncomplexed adenosine triphosphate (ATP) is ob-
servable using

31

P spectroscopy. Free intracellular

magnesium exists in equilibrium with complexed
MgATP and so the observable ATP chemical shifts
are sensitive to changes in free intracellular magne-
sium levels. Temperature is also important as in-
creases in temperature lead to intensification of
molecular motion. The chemical bonds weaken al-
tering the degree of nuclear shielding. Thus the reso-
nant frequency decreases. The

1

H chemical shift of

water has an almost linear dependence on tempera-
ture between 0

1 and 401 changing by approximately

 0.01 ppm1C

 1

.

Spin–Spin Coupling

Spins of adjacent nuclei affect resonance energy
levels, splitting the observed peaks into various multi-
plet structures. The coupling is not direct but is
mediated by electrons in the chemical bonds between
nuclei and allows a given nucleus to ‘sense’ the spin
states of its neighbors. The coupling can be between

similar (homonuclear) or different nuclei (heteronu-
clear). However, chemically equivalent protons do
not couple to each other. The chemical structure of
lactate is shown in Figure 7 with its corresponding

1

H

spectrum consisting of two resonances, a doublet and
a quartet due to the –CH

3

and –CH protons, re-

spectively. The –CH proton has two possible spin
orientations, parallel or antiparallel to B

0

, and is

constantly changing between the spin states. Half of
the time the –CH

3

protons will sense the –CH proton

parallel state and the remaining time the antiparallel
state. The spin states of the –CH proton are at slightly
different energy levels and due to electron mediation
a slight change in the local magnetic field is experi-
enced by the three equivalent –CH

3

protons. Across

the whole sample this results in a doublet with com-
ponents of approximately equal amplitude. The –CH
proton experiences eight possible combinations for
the –CH

3

protons, these are illustrated in Figure 8.

However, some of these combinations are indis-
tinguishable resulting in four effective combinations
of spin states. The result is the quartet with the re-
lative amplitudes of the components depending on
the relative probabilities of the possible states,
B1:3:3:1. The total intensity of the doublet is three
times that of the quartet as there are three times as
many equivalent protons contributing to the reso-
nance. The separation of multiplet components is
known as the coupling constant J. This is measured in
hertz and is independent of the applied field strength.

Phase Modulation

Where a spectrum is obtained using a sequence that
involves acquiring an echo rather than direct

Alkenes

Alkanes

Alkynes

Alcohols

Aldehydes

Carboxylic acids

Chemical

name

R

CH

3

C

C

CH

C

C

H

ROH

C

H

O

C

OH

O

Functional

group

Approximate chemical

shifts relative to

TMS (ppm)

0.5

−2

2

−4

1.5

−3

3

−5

9.5

−10

10

−12

Table 1

The chemical shift of a peak can indicate the type

functional group producing the peak.

Chemical shifts are expressed relative to that of tetramethylsilane
(TMS) at 0 ppm

CH

CH

3

COO−

HO

4.10

1.31

ppm

Figure 7

The chemical structure and multiplets of lactate. The

CH

3

group produces the doublet at 1.31 ppm. The CH group

produces the quartet at 4.1 ppm. Spectra were acquired on a
7 T Bruker Biospec spectrometer.

206

NMR SPECTROSCOPY

/ Overview

observation of the signal following excitation, spin–
spin coupling affects the amplitudes and phases of
spectral peaks. Consider the case of the lactate dou-
blet observed using a spin–echo experiment with the
resonant frequency, o

0

, set half way between the two

peaks for convenience (see Figure 9). In a frame of
reference rotating at o

0

, the spins in each peak of the

doublet will disperse away from each other. Spins
also dephase because of inhomogeneity in the main
field. A 180

1 pulse applied along the y-axis has the

effect of flipping the spins about this axis. Subse-
quently, the dephasing due to applied field in-
homogeneity is refocused. However, the dephasing
due to spin coupling is not refocused and the com-
ponents of the lactate doublet will fall out of phase
with other uncoupled signals in the spectrum. The
echo time, TE, of a sequence is the time between
excitation of the spin system and formation of the
echo. At TE the components of the doublet are sepa-
rated in phase, f, by:

f

¼ 2pJTE

½6

In the case of the lactate doublet, J

¼ 7 Hz. If a spin

echo is acquired at TE

¼ 135 ms, the doublet will

appear inverted relative to the prominently visible
singlets (see Figure 10).

Equipment

The specific hardware used for NMRS studies is de-
pendent on the application but is generally very simi-
lar to that used for medical magnetic resonance
imaging studies.

Magnet and Shim Coils

The central piece of equipment is the magnet that
generates the static magnetic field. The strength of
the applied magnetic field is the main variable that
can be exploited to improve the sensitivity of NMRS
experiments. Persistent superconducting magnets are
the most common type used. These have coil wind-
ings made of superconducting material through

Lactate
doublet

Dephasing

Phase modulation of

components in doublet

Original
position

y

′

x

′

180

° pulse

Original
position

(A)

(B)

Figure 9

The phase modulation of the lactate doublet due to spin coupling. The view is of the x

0

–y

0

rotating frame with the rotation

frequency set halfway between the two spectral components. (A) The two components phase modulate away from each other
and spins in each component de-phase because of field inhomogeneities. (B) Following a 180

1 pulse, which flips the spins about the

x

0

-axis, the dephasing of the spins due to field inhomogeneities is refocused. However, the phase modulation due to spin coupling is

not refocused. Eventually the doublet will become 180

1 out of phase with its original orientation.

− CH

3

spins

− CH spins

− CH quartet

− CH

3

doublet

Figure 8

The spin–spin coupling of lactate. The three protons

in the CH

3

group can arrange themselves in eight different com-

binations of orientations. Arrangements with two spins ‘up’ are all
equivalent with respect to their effect on the CH proton. The result
of spin coupling is that the peak from the CH group splits into a
quartet with the middle two components being three times the
amplitude of the outer two components. The CH

3

peak splits into

a doublet.

NMR SPECTROSCOPY

/ Overview

207

which the energizing current flows continuously. The
materials that are used for these windings must be
kept below their critical temperature for supercon-
ductivity and are immersed in liquid helium for this
purpose. The presence of a magnetic field lowers the
critical temperature placing a limit on the field
achievable using a particular material. Niobium–
titanium alloy is commonly used and can support a
field up to 10 T in liquid helium; newer materials
offer even better performance. Horizontal bore
systems, suitable for in vivo use, are currently avail-
able up to

B11 T. Vertical bore systems, suitable

for high-resolution NMRS of samples, are currently
available up to 21 T. The stability of superconducting
magnets is very good with field drift typically less
than 0.05 ppm h

 1

. Equally as important as stability

is the uniformity of the magnetic field. Spatial in-
homogeneities in the magnetic field mean that a res-
onance at a specific ppm will have a different actual
resonance (in hertz) depending on its location within
the field. The result is that spectral lines are broad-
ened and resolution between lines is lessened. Typ-
ically the nonuniformity over the region of interest
must be less than the minimum chemical shift it is
desired to resolve. A magnet may have a set of su-
perconducting coils to shim (remove inhomo-
geneities from) the main field; currents in these coils
are established that produce magnetic fields that
oppose the inhomogeneities in field produced by the
main coil. Introducing a sample into the magnet
poses an additional problem, especially for in vivo
samples. Boundaries between materials of different
magnetic susceptibility generate field gradients that
lead to broadening of spectral lines. These are
corrected for by adjusting the currents in a set of

room temperature resistive shim coils. Typically the
observation of the linewidth of a prominent spectral
line is used as feedback for the iterative adjustment of
these shim currents.

Gradient Coils

In the case of a narrow bore vertical spectrometer
designed for studying homogeneous samples, signals
are typically collected from the whole of the sample.
However, when studying heterogeneous samples,
typically in vivo samples in a wide bore horizontal
spectrometer, it is often necessary to localize the ac-
quisition of signal to specific structures within the
sample. The methods for localization are similar to
those used in magnetic resonance imaging and
involve the use of sequences of temporally applied
field gradients along with RF. Spectrometers for
medical applications include gradient coils that are
designed to produce field gradients in three ortho-
gonal directions. Gradient coils also allow for an
imaging as well as a spectroscopy capability.

RF Coil

RF coils are resonant circuits that are designed to
produce oscillating magnetic fields with a suitable
geometry to excite a sample and reciprocally to de-
tect the subsequent NMR signal. The choice of coil is
strongly influenced by the application for which it is
to be used. In the simplest arrangement, a single coil
is used to both transmit RF and to detect the signal.
Alternatively, it may be advantageous to use one coil
for excitation, typically a volume coil generating a
uniform oscillating field, and one for signal detection
whose geometry is matched to a region of interest in
the sample, particularly in vivo. For a coil to work
efficiently it must be tuned to the resonant frequency
of the nuclei under investigation and impedance
matched to the transmitter, receiver, or both depen-
ding on the mode of operation. Often a coil will be
designed to tune to both the proton resonant fre-
quency and that of the nuclei under investigation or
be used in conjunction with a second coil tuned to
protons. The larger NMR signal from protons is
typically used to provide interactive feedback whilst
shimming.

Signal Acquisition and Processing

When the FID is acquired, it is mixed with an arti-
ficially generated reference signal so as to convert the
RFs to the audio frequency range. The frequencies
contained in the converted signal are now equivalent
to the difference between the original signal and the
reference. Thus if the original signal contains simply

Lactate

N -Acetyl aspartate

Creatine

Choline

Figure 10

A

1

H spectrum from a chick brain in ovo at 135 ms

echo time. The major peaks are labeled and lactate is inverted
relative to the uncoupled peaks in the spectrum. Spectrum taken
using a 7 T Bruker Biospec spectrometer.

208

NMR SPECTROSCOPY

/ Overview

a frequency n

1

and was mixed with a reference n

r

, the

resulting signal would be (n

1

 n

r

). It is this converted

signal that is then sampled and processed to produce
the final spectrum. The signal is sampled into two
channels that correspond to the projection of M

0

along orthogonal directions in the x–y plane. If a
quadrature coil is used the data in these channels are
measured independently. If a single channel coil-
receiver arrangement is used then the second channel
is simulated. These two channels, termed real and
imaginary, have a 90

1 phase difference and are com-

bined to form a complex dataset. This is then Fourier
transformed and, following a suitable phase adjust-
ment, the real component is displayed as the final
spectrum.

Dwell Time and Sampling Time

The NMR signal is sampled continuously over the
acquisition time, T, with a dwell time between sam-
ples Dt. For a given dwell time a signal can only be
unambiguously identified if its frequency n is below a
critical threshold termed the Nyquist frequency.
Above the Nyquist frequency, signals will be aliased
(see Figure 11). Aliasing occurs when a high fre-
quency appears to look like a low frequency because
the sampling rate is too low, thus the signal is mis-
represented or aliased as the lower signal. If quad-
rature detection is used, then negative frequencies

can be distinguished from positive frequencies and
the spectral width, SW - the range of frequencies that
can be unambiguously detected, is centered round
the reference frequency and covers the interval:



1

2Dt

on

r

o

1

2Dt

½7

For one-channel detection it is impossible to dis-

tinguish between positive and negative frequencies
and so SW covers the interval 0

on

r

o1/2Dt. The

acquisition time determines the spectral resolution of
the final spectrum, Dn:

Dn ¼

1

T

½8

The acquisition parameters T, Dt, and n

r

are chosen

so as to have an SW sufficiently large and properly
centered to cover the chemical shift range of the
spectrum with an appropriate spectral resolution.

Filtering the FID

Often it is desirable to apply a filter to the digitized
FID. Sometimes the sampling of the FID is completed
before reaching the noise level and can be thought of
as multiplying a complete FID by a step function.
Fourier transforming these two functions would give
a convolution of the spectrum with a sinc function
producing lineshape distortions. A function can be
applied to smooth the FID to zero within the acqui-
sition period. Typically the FID is multiplied by a
decaying exponential function. The resulting spec-
trum will be convoluted with Lorentzian function,
the Fourier transform of the decaying exponential,
resulting in the removal of the artifact but at the cost
of broadening the spectral components. This tech-
nique is also used to improve the signal-to-noise ratio
(SNR) of a spectrum but with the same costs.

Broad spectral components have large amplitudes

in the first few digitized points of the FID, whereas
narrow spectral components have longer signals. It is
often advantageous to suppress these broad compo-
nents. If the signal at the start of FID is reduced then
the broad components are reduced relative to the
narrow components. A suitable function to use is the
linear ramp. The function increases from zero to one
over the first few points and is used to multiply the
FID. A further consequence is to apparently increase
the decay constant T2



, resulting in narrower spec-

tral lines. The cost is to increase the level of the noise
relative to the signal in the FID resulting in a noisier
spectrum. When filtering, there are always trade offs
between spectral resolution and SNR; resolution en-
hancement leads to SNR degradation and vice versa.

Data sample point

Figure 11

Data sampling. The solid line represents a wave that

is sampled at a rate sufficient to identify its frequency. The
dashed line represents a wave with a frequency that is above the
Nyquist limit. The frequency of this wave cannot be properly
identified and will be aliased as having a frequency equal to that
of the solid line.

NMR SPECTROSCOPY

/ Overview

209

Zero Filling

Once the FID has decayed below the noise level there
is little more useful information that can be gained.
However, increasing the number of data points at the
end by filling with zeros can improve spectral reso-
lution. The apparent increased sampling results,
after Fourier transform, in a spectrum with more
data points consequently improves the visibility of
otherwise unresolved peaks. Filtering of the FID is
usually applied before zero filling to avoid trunca-
tion artifacts.

Analysis Methods

Analysis of NMR spectra may be performed on ei-
ther the FID (in the time domain) or on the Fourier
transformed spectrum (in the frequency domain).
Determining the chemical shift and J-coupling of
spectral peaks aids the identification of constituent
molecules present in a sample, the measurement of
physiological parameters such as pH, and also the
determination of chemical structure of specific mole-
cules. An analysis technique must be reliable, ob-
jective, and ideally fully automatic. It must also be
able to cope with spectral imperfections and be
accurate in accounting for lineshape distortions,
phase modulation effects, and determining the base-
line upon which the peaks sit. Spectra obtained
in vivo typically do not have the resolution of in vitro
biological or inorganic samples studied at high field
and, for

1

H NMRS in particular, peaks will overlap

to a greater degree. The method of analysis chosen
reflects both the application and the inherent limita-
tions of the experiment. Below are brief descriptions
of two commonly used analysis methods.

Analysis in the Time Domain (Linear Combination
of Decaying Exponentials)

Time domain analysis avoids the need for a Fourier
transform prior to processing. The first few data
points, in which signals from rapidly decaying im-
mobile nuclei are mostly contained, and the last few
that are at the noise level can be ignored in the anal-
ysis, leaving a section of FID that has good SNR and
has a simplified baseline. Algorithms such as time
domain analysis algorithm (VARPRO) and time do-
main analysis method (AMARES) are usually used to
fit a sum of exponentially decaying sinusoids to the
FID using nonlinear least squares. Prior knowledge is
used to aid the fitting procedure. The precision of the
fit may be significantly improved by fixing para-
meters whose values are known a priori such as the
multiplicity, J-coupling, and relative intensities of a
multiplet.

Analysis in the Frequency Domain (LCModel)

LCModel is a widely used method of analysis, espe-
cially for in vivo

1

H spectra. Spectra are analyzed as

a linear combination of model spectra of metabolite
solutions in vitro. The model spectra provide a priori
information about chemical shifts, relative areas,
number of equivalent protons, and phase modulation
effects. However, these spectra must be obtained for
each echo time at which in vivo spectra are to be
obtained. A full basis set is required for the analysis
at each specific echo time and consists of model
spectra for all the metabolites that are likely to be
observed in vivo. The method is model-free such that
smooth lineshapes and baselines consistent with the
data are determined rather than assumed.

See also: Nuclear Magnetic Resonance Spectroscopy:
Principles; Instrumentation. Nuclear Magnetic Reso-
nance Spectroscopy-Applicable Elements: Hydrogen
Isotopes; Carbon-13; Fluorine-19; Nitrogen-15; Phospho-
rus-31; Organometallic Compounds. Nuclear Magnetic
Resonance Spectroscopy Applications: Food; Foren-
sic; Pharmaceutical; Proton NMR in Biological Objects
Subjected to Magic Angle Spinning. Nuclear Magnetic
Resonance Spectroscopy Techniques: Nuclear Over-
hauser Effect; Multidimensional Proton; Solid-State;
Surface Coil; In Vivo Spectroscopy Using Localization
Techniques.

Further Reading

Bachelard H (ed.) (1997) Magnetic Resonance Spectro-

scopy and Imaging in Neurochemistry, Advances in
Neurochemistry, vol. 8. New York: Plenum Press.

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Principles

J B Grutzner

, Purdue University, West Lafayette, IN,

USA

& 2005, Elsevier Ltd. All Rights Reserved.

Introduction

Nuclear magnetic resonance (NMR) spectroscopy is
a rich source of molecular information. It is widely
used for molecular structure analysis and for medical
imaging under the name MRI (magnetic resonance
imaging). NMR is a nondestructive quantitative
method for the analysis of complex mixtures such
as reactions, petroleum, materials, and foods. It finds
major application in the determination of molecular
structure and dynamics, especially of pharmaceuti-
cals, polymers, and proteins. Diverse applications
include measurement of internuclear distances, water
content of food, characterization of oil deposits using
the earth’s magnetic field, in vivo studies of metabolic
pathways in cells and humans, diffusion of adsorb-
ates into porous materials, reaction dynamics, fluid
flow, generation and measurement of temperatures
in the millikelvin range, and online monitoring of
manufacturing processes. Samples may be gases,
liquids, or solids.

This article provides a description of the basic

principles of NMR spectroscopy. The many applica-
tions of this technique, which make it indispensable
as a tool for the analytical chemist, are described in
subsequent articles, which also include discussion of
advanced techniques such as the NMR of solids,
multidimensional NMR, and MRI.

Principles of NMR

NMR detects signals from nuclei in atoms and mole-
cules when they are excited in a strong homogeneous
magnetic field (B

0

in tesla). NMR was invented

independently by Bloch and Purcell to accurately
measure nuclear magnetic moments (m). It is now
used to measure magnetic field strength with high
precision based on known m values.

The nuclear magnets are ordered into 2I

þ 1 states

determined by the nuclear spin quantum number I.
The spin angular momentum is quantized in units of
_ and the change in the z component is detected in
the NMR experiment. For many common NMR nu-
clei I

¼ 1/2 (

1

H,

13

C,

19

F,

29

Si,

31

P) and there are two

allowed states labeled spin up and spin down. Irra-
diation with radiofrequency (RF) electromagnetic
radiation (n in Hz) causes spin flip transitions
provided the resonance condition is satisfied:

hn

¼ _gB

0

¼ m

z

b

B

0

½1

where h is Planck’s constant (6.62608

 10

 34

J s),

_ ¼ h=ð2_Þ, b is the nuclear Bohr magneton (eh/
4pm

p

¼ 5.0508  10

 27

J T

 1

) and m

z

is the z-com-

ponent of the total moment

¼ O[I(I þ 1)]m

z

. The nu-

clear magnetogyric ratio (g in rad s

 1

T

 1

) is an

exquisitely sensitive discriminator between elements
and also of the immediate electronic environment of
each nucleus. Tables list values of m in units of b
according to different conventions. For protons, the
values are 5.5854 with m

¼ g_; 2.7927 with m

z

¼ g_I

for the z-component of spin I; or 4.8372 with
m

¼ g_O [I(I þ 1)] for the total magnetic moment.

The common information obtainable from an

NMR spectrum is summarized in Table 1 and illus-
trated with the proton NMR spectrum of ethanol
(CH

3

CH

2

OH) (Figure 1). The horizontal axis, which

gives the ‘chemical shift’ of the signal, is a linear
frequency scale in hertz, which is almost always
converted to the dimensionless d scale (ppm) with
tetramethylsilane (TMS) as reference at d

¼ 0.000.

The d scale is independent of magnetic field stren-
gth and so is transferable from spectrometer to
spectrometer. It is defined as

d

i

¼ Dn

i

=n

ref

½2

where n

ref

is the absolute resonance frequency of

TMS (e.g., 200.010078 MHz in a field of 4.70 T) and
Dn

i

¼ n

i

 n

ref

is the difference between the frequency

of the nucleus of interest (n

i

) and n

ref

. The vertical

axis is a linear relative intensity scale that is generally
proportional to the number of nuclei in the resonant

NMR SPECTROSCOPY

/ Principles

211