-
I n this chapter, we concentrate on absorption of
radio-frequency radiation bynuclei and the resulting transitions
between energy levels, better known asnuclear magnetic resonance
(NMR) spectroscopy. Felix Bloch and EdwardPurcell, both of the
United States, first detected the phenomenon of nuclear mag-netic
resonance in 1946. They shared the 1952 Nobel Prize for physics.
Nuclearmagnetic resonance (NMR) spectroscopy was developed in the
late 1950s and,within a decade, became the single most important
technique available to chem-ists for the determination of molecular
structure. Nuclear magnetic resonancespectroscopy gives us
information about the number and types of atoms in a mol-ecule: for
example, about hydrogens using IH-NMR spectroscopy, and about
car-bons using 13C-NMR spectroscopy. It can also give us
substantial information aboutthe connectivity of the atoms and, in
many cases, can allow determination of thestructure of a molecule
with no additional information.
13.1 Nuclear Spin StatesYou are already familiar from general
chemistry with the conceRts that q) an elec-tron has a spin quantum
number of t, with allowed values of +t and -2' and that(2) a moving
charge has an associated magnetic field. In effect, an electron
be-haves as if it is a tiny bar magnet and has a magnetic moment.
The same effectholds for certain atomic nuclei.
Any atomic nucleus that has an odd mass number, an odd atomic
number, orboth, also has a spin and a resulting nuclear magnetic
moment. The allowed nuclearspin states are determined by the spin
quantum number, 1, of the nucleus. A nucleuswith spin quantum
number I has 21 + 1 spin states. Our focus in this chapter ison
nuclei of IH and 13C, isotopes of the two elements most common to
organiccompounds. Each has a nuclear spin quantum number of t and
therefore has 2(t)+ 1 = 2 allowed spin states. Quantum numbers and
allowed nuclear spin states for
Magnetic resonance imagingis a useful medical diagnostictool.
Inset: a model of methylacetate. For a lH-NMR spec-trum of methyl
acetate. seeFigure 13.5.
OUTLINE13.1 Nuclear Spin States13.2 Orientation of Nuclear
Spins in an AppliedMagnetic Field
13.3 Nuclear Magnetic"Resonance"
13.4 An NMR Spectrometer13.5 Equivalent Hydrogens13.6 Signal
Areas13.7 Chemical Shift13.8 Signal Splitting and the
en + 1) Rule13.9 The Origins of Signal
Splitting13.10 Stereochemistry and
Topicity13.11 13C-NMR13.12 Interpretation of NMR
Spectra~ How To Solve NMR Spectral
Problems
Online homework for thischapter may be assignedin Organic
OWL.
13.1 Nuclear Spin States 477
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Table 13.1 Spin Quantum Numbers and Allowed Nuclear Spin States
forSelected Isotopes of Elements Common to Organic Compounds
Element 10 2JI 12C 13C 14N 15N 160 19N 31p 32S
Nuclear spin1 1 1 1 1quantum number (1)"2 1 0 "2 1 "2 0 "2 "2
0
Number ofspin states 2 3 1 2 3 2 1 2 2 1
these nuclei and those ofother elements common to organic
compounds are shown inTable 13.1. Note that 12e, 160, and 32S each
have a spin quantum number of zero andonly one allowed nuclear spin
state; these nuclei are inactive in NMR spectroscopy.
13.2 Orientation of Nuclear Spins in anApplied Magnetic
Field
Note: the 51 unit for magneticfield strength is the tesla 1TI.A
unit still in common use,however, is the gauss (G). Valuesof T and
G are related by theequation 1 T = 104 G.
Within a sample containing IH and 13e atoms, the orientations of
the nuclear mag-netic moments associated with their nuclear spins
are completely random. Whenplaced between the poles of a powerful
magnet of field strength .80, however, inter-actions between the
nuclear spins and the applied magnetic field are quantized, withthe
result that only certain orientations of nuclear magnetic moments
are allowed.For IH and 13e nuclei, only two orientations are
allowed as illustrated in Figure 13.1.By convention, nuclei with
spin +~ are aligned with the applied magnetic field andare in the
lower energy state; nuclei with spin -~ are aligned against the
appliedmagnetic field and are in the higher energy state.
The most important NMR physical concept from the point of view
of molecularstructure determination is that the difference in
energy between nuclear spin statesfor a given nucleus is
proportional to the strength of the magnetic field experiencedby
that nucleus (Figure 13.2). We will come back to this concept
several times inthis chapter. At an applied field strength of 7.05
T, which is readily available withpresent-day superconducting
electromagnets, the difference in energy between nu-clear spin
states for IH is approximately 0.120 J (0.0286 cal)/mol
(corresponding toelectromagnetic radiation of 300 MHz). At 7.05 T,
the energy difference in nuclearspin states for 13e nuclei is
approximately 0.030J (0.00715 cal) Imol (correspondingto radiation
of 75 MHz). Advanced commercial instruments now operate at
fieldsmore than three times this value; the operating frequencies
are proportional to thefield. Sensitivities are more than
proportionally higher!
To put these values for nuclear spin energy levels in
perspective, energies fortransitions between vibrational energy
levels observed in infrared (IR) spectros-copy are 8 to 63 kJ (2 to
15 kcal) Imol. Those between electronic energy levelsin
ultraviolet-visible spectroscopy are 167 to 585 kJ (40 to 140
kcal)/mol. Nucleartransitions involve only small energies, on the
order of a few hundredths ofa calorie!
Figure 13.1IH and 13C nuclei with spin +~are aligned with the
appliedmagnetic field, Eo, and are inthe lower spin energy
state;those with spin -~ are alignedagainst the applied
magneticfield and are in the higherspin energy state.
Higherenergy state
Lowerenergy state t
Spin -t(aligned againstthe applied field)
Spin +t(aligned withthe applied field)
478 Chapter 13 Nuclear Magnetic Resonance Spectroscopy
-
L0.120llm~
~I__.~~t:::=======-.:1=-.1Q~ I
0.0239llmol
-
Spin -t(aligned against theapplied field)
Spin +t(aligned with theapplied field)
Figure 13.2The energy differencebetween the allowed nuclearspin
states increases linearlywith applied field strength.Values shown
here are forIH nuclei.
1.41 T
Example 13.1
Eo (Tesla)7.05 T
Calculate the ratio of nuclei in the higher spin state to those
in the lower spinstate, Nh/~, for IH at 25C in an applied field
strength of 7.05 T.SolutionUse the equation given in Section 2.6B
for the relationship between the difference inenergy states and
equilibrium constant. In this problem, this relationship has the
form
dCo = - RTln Nt,No,
The difference in energy between the higher and lower nuclear
spin states inan applied field of 7.05 T is approximately 0.120
J/mol, and the temperature is25 + 273 = 298 K. Substituting these
values in this equation gives
In Nt, = -dGo = -0.120Jmol-1 = -4.843 X 10-5No, RT 8.314JK I'mol
I X 298K
Nh = 09999516 = 1.000000No,' 1.000048
From this calculation, we determine that, for every 1,000,000
hydrogen atoms in thehigher energy state in this applied field,
there are 1,000,048 in the lower energy state.The excess population
of the lower energy state under these conditions is only 48
permillion! What is important about this number is that the
strength of an NMR signal isproportional to the population
difference. As you will see, the greater this differencein
populations, the stronger the signal will be, because more spins
are flipping.
Problem 13.1Calculate the ratio of nuclei in the higher spin
state to those in the lower spinstate, Nh/~, for 13C at 25C in an
applied field strength of 7.05 T. The differencein energy between
the higher and lower nuclear spin states in this applied field
isapproximately 0.030J (0.00715 cal) Imol.
13.3 Nuclear Magnetic "Resonance"As we have seen, when nuclei
with spin quantum number t are placed in anapplied magnetic field,
a small majority of nuclear spins are aligned with theapplied field
in the lower energy state. When nuclei in the lower energy spin
stateare irradiated with a radio frequency of the appropriate
energy, they absorb theenergy, and nuclear spins flip from the
lower energy state to the higher energystate, the only other
allowed spin state.
13.2 Nuclear Magnetic "Resonance" 479
-
Resonance in NMR spectroscopyThe absorption of
electromagneticradiation by a precessing nucleusand the resulting
"flip" of its nu-clear spin from the lower energystate to the
higher energy state.SignalA recording in an NMR spectrumofa nuclear
magnetic resonance.
Diamagnetic current in NMRThe circulation of electrondensity in
a molecule in anapplied magnetic field.
To visualize the mechanism by which a spinning nucleus absorbs
energy andthe meaning of resonance in this context, think of the
nucleus as if it were reallyspinning. When an applied field of
strength Bo is turned on, the nucleus becomesaligned with the
applied field in an allowed spin energy state. The nucleus
thenbegins to precess as shown in Figure 13.3(a) and traces out a
cone-shaped surfacein much the same manner as a spinning top or
gyroscope traces out a cone-shapedsurface as it precesses in the
earth's gravitational field. We can express the rate ofprecession
as a frequency in hertz.
If the precessing nucleus is irradiated with electromagnetic
radiation at exactlythe precession frequency, then the two
frequencies couple, energy is absorbed, andthe nuclear spin "flips'
from spin state +i (with the applied field) to spin state
-i(against the applied field) as illustrated in Figure 13.3(b). For
lH in an applied mag-netic field of 7.05 T, the frequency of
precession is approximately 300 MHz. ForlSC in the same field, it
is approximately 75 MHz. Resonance in this context is theabsorption
of electromagnetic radiation by a precessing nucleus and the
resultingflip of its nuclear spin from the lower energy state to
the higher energy state. Thespectrometer detects this absorption of
electromagnetic radiation and records it as asignal. The process is
quantized, so that only electromagnetic radiation of preciselythe
correct frequency causes a nuclear spin to flip. Electromagnetic
radiation of afrequency that is too low or too high is not
absorbed.
Ifwe were dealing with lH nuclei isolated from all other atoms
and electrons,any combination of applied field and electromagnetic
radiation that produces asignal for one hydrogen nucleus would
produce a signal for all hydrogen nuclei.In other words, hydrogens
would be indistinguishable. Hydrogens in an organicmolecule,
however, are not isolated; they are surrounded by electron
density.
A key physical principle for NMR is that circulating electrons
induce a magneticfield. This is the principle behind electromagnets
and electric motors. The directionof electron movement dictates the
orientation of the induced magnetic field. Ofequal importance to
NMR, the converse is also true. An applied magnetic field in-duces
electrons to circulate, and the orientation of the field dictates
the direction ofcirculation. You will learn more details of these
relationships in your physics classes.The important point for our
purposes is that an applied magnetic field induces theelectron
density in a molecule to circulate. The spin states of underlying
nuclei are,in turn, influenced to a small but measurable degree by
the magnetic field createdby the induced electron density
circulation. The circulation of electron density in amolecule in an
applied magnetic field is called a diamagnetic current
It turns out that a molecule's u-bonding electron density is
induced to circu-late in a direction that creates a small magnetic
field that directly upposes the appliedmagnetic field. As a result
of the opposing magnetic fields, the nuclei within thecirculating
electron density experience a magnetic field that is slightly
smoJJ.er thanthe actual applied field. In other words, nuclei
underneath circulating u-bonding
Figure 13.3The origin of nuclear mag-netic "resonance." (a)
Preces-sion of a spinning nucleus inan applied magnetic field.(b)
Absorption ofelectromag-netic radiation occurs whenthe frequency of
radiationis equal to the frequency ofprecession.
B"Axis of precession~
Orbit of precession..-/
El ~radi'ectrornagneuc aUonof same frequency asprecession
frequency
Axis of nuclear spin;spin +t
absorption of ~n~rgy;th~ nuclear spin flips
Bo
I
(b)
480 Chapter 13 Nuclear Magnetic Resonance Spectroscopy
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Table 13.3 The Effect of Hybridizationon Chemical Shift
Type of Hydrogen(R = alkyl)
RCH3, ~CH2' R3CH~C=C(R)CHR2RC=CH
~C=CHR,R2C=CH2RCHO
Name ofHydrogen
AlkylAllylicAcetylenicVinylicAldehydic
ChemicalShift 6
0.8-1.71.6-2.62.0-3.04.6-5.79.5-10.1
of the explanation for the greater deshielding of vinylic
hydrogens compared withalkyl hydrogens lies in the hybridization of
carbon. Because a u-bonding orbitalof an sf-hybridized carbon has
more s-character than a u-bonding orbital of ansp"-hybridized
carbon (33% compared with 25%), an sf-hybridized carbon atomis more
electronegative. Vinylic hydrogens are deshielded by this
electronegativ-ity effect and their nuclei resonate farther
downfield relative to alkyl hydrogens.Similarly, signals for
acetylene and aldehyde hydrogens also appear farther down-field
compared with alkyl hydrogens.
However, differences in chemical shifts of vinylic and
acetylenic hydrogenscannot be accounted for on the basis of the
hybridization of carbon alone. If thechemical shift ofvinylic
hydrogens (a 4.6-5.7) were caused entirely by the hybrid-ization of
carbon, then the chemical shift of acetylenic hydrogens should be
evengreater than that of vinylic hydrogens. Yet the chemical shift
of acetylenic hydro-gens is only a2.0 to 3.0. It seems that either
the chemical shift of acetylenic hydro-gens is abnormally small or
the chemical shift of vinylic hydrogens is abnormallylarge. In
either case, another factor must be contributing to the magnitude
of thechemical shift. Theoretical and experimental evidence suggest
that the chemicalshifts of hydrogens bonded to 7T-bonded carbons
are influenced not only by therelative electronegativities of the
sf- and sjrhybridized carbon atoms but also bymagnetic induction
from 7T bonds.
c. Diamagnetic Effects from TT BondsTo understand the influence
of 7T bonds on the chemical shift of an acetylenichydrogen, imagine
that the carbon-carbon triple bond is oriented as shown inFigure
13.9 with respect to the applied field. Because of magnetic
induction, theapplied field induces a circulation of the 7T
electrons, which in turn produces aninduced magnetic field. Given
the geometry of an alkyne and the cylindrical na-ture of its 7T
electron cloud, the induced magnetic field is shielding in the
vicinity
Figure 13.9A magnetic field inducedin the 7T bonds of a
carbon-carbon triple bond shields anacetylenic hydrogen and
shiftsits signal upfield.
Induced flow ofelectrons in the 7Tsystem of an alkyne
Induced local magneticIt ~~field of the 7T electrons
is against the applied fieldat the hydrogen atoms;it requires
lower frequency
V radiation to bring anacetylenic hydrogen~ nucleus into
resonance.488 Chapter 13 Nuclear Magnetic Resonance
Spectroscopy
-
Induced circulationof 1T electrons inan alkene
Applied field, Bo
~ Induced local magnetic~ field of the 1T electrons
reinforces the applied fieldat the hydrogen atoms;it requires
higher frequencyradiation to bring a vinylichydrogen nucleus
intoresonance.
Figure 13.10A magnetic field inducedin the 1T bond of a
carbon-carbon double bond deshieldsvinylic hydrogens and
shiftstheir signals downfield.
of the acetylenic hydrogen. Therefore, lower frequency
electromagnetic radiationis required to make an acetylenic hydrogen
nucleus resonate; the local magneticfield induced in the 'TT' bonds
shifts the signal of an acetylenic hydrogen upfield toa smaller 8
value.
The effect of the induced circulation of 'TT' electrons on a
vinylic hydrogen(Figure 13.10) is opposite to that on an acetylenic
hydrogen. The direction ofthe induced magnetic field in the 'TT'
bond of a carbon-carbon double bond isparallel to the applied field
in the region of the vinylic hydrogens. The inducedmagnetic field
deshields vinylic hydrogens and, thus, shifts their signal
downfieldto a larger 8 value. The presence of the 'TT' electrons in
the carbonyl group has asimilar effect on the chemical shift of the
hydrogen of an aldehyde group.
The effects of the 'TT' electrons in benzene are even more
dramatic than in al-kenes. All six hydrogens of benzene are
equivalent, and its IH-NMR spectrum is asharp singlet at 87.27.
Hydrogens bonded to a substituted benzene ring appear inthe region
8 6.5 to 8.5. Few other hydrogens absorb in this region; thus, aryl
hy-drogens are quite easily identifiable by their distinctive
chemical shifts, as much as2 ppm higher than comparably substituted
alkenes.
That aryl hydrogens absorb even farther downfield than vinylic
hydrogens isaccounted for by the existence of a ring current, a
special property of aromaticrings (Figure 13.11). When the plane of
an aromatic ring tumbles in an appliedmagnetic field, the applied
field causes the 'TT' electrons to circulate around thering, giving
rise to the so-called ring current. This induced ring current has
as-sociated with it a magnetic field that opposes the applied field
in the middle ofthe ring but reinforces the applied field on the
outside of the ring. Thus, giventhe position of aromatic hydrogens
relative to the induced ring current, theyare deshielded and come
into resonance at a larger chemical shift.
Ring currentAn applied magnetic field causesthe 1T electrons of
an aromaticring to circulate, giving rise to theso-called ring
current and an asso-ciated magnetic field that opposesthe applied
field in the middle ofthe ring but reinforces the appliedfield on
the outside of the ring.
Inducedcirculation of1T electrons ina benzene ring
Induced local magnetic field of
iW the circulating 1T electrons/ reinforces the applied fieldat
the hydrogen atoms; it~_....- requires higher frequencyradiation to
bring aromatic"'\''';+-'f''~ hydrogen nuclei inID ~on~re
Applied field
Figure 13.11The magnetic field inducedby circulation of 7T
electronsin an aromatic ring deshieldsthe hydrogens of the
aromaticring and shifts their signaldownfield.
13.7 Chemical Shift 489
-
ChemicalConnections
Magnetic Resonance Imaging
The NMR phenomenon was discovered and explainedby physicists in
the 1950s and by the 1960s, it had be-come an invaluable analytical
tool for chemists. By theearly 1970s, scientists realized that
imaging of parts ofthe body using NMR could be a valuable addition
to di-agnostic medicine. Because the term "nuclear
magneticresonance" sounds to many people as if the techniquemight
involve radioactive material, health care person-nel call the
technique magnetic resonance imaging(MRI). MRI has become so
important, that in 2003, theNobel Prize for medicine or physiology
was awarded toPaul Lauterbur and Peter Mansfield for their
discover-ies that led to practical MRI.
The body contains several nuclei that, in principle,could be
used for MRI. Of these, hydrogens, most ofwhich come from the
hydrogens of water, triglycerides(Section 26.1), and membrane
phospholipids (Section26.5) give the most useful signals.
Phosphorus MRI isalso used in diagnostic medicine.
Computer-enhanced MRI scan ofa normal human brainwith pituitary
gland highlighted.
Recall that in NMR spectroscopy, energy in theform of
radio-frequency radiation is absorbed by nucleiin the sample.
Relaxation time is a characteristic timeat which excited nuclei
give up this energy and relax totheir ground state.
In 1971, it was discovered that relaxation of waterin certain
cancerous tumors takes much longer thanthe relaxation of water in
normal cells. Thus, if a relax-ation image of the body could be
obtained, it might bepossible to identify tumors at an early stage.
Subsequentwork demonstrated that many tumors can be identifiedin
this way. Another important application of MRI is inthe examination
of the brain and spinal cord. Whiteand gray matter are easily
distinguished by MRI, whichis useful in the study of such diseases
as multiple sclero-sis. Magnetic resonance imaging and x-ray
imaging are,in many cases, complementary. The hard, outer layerof
bone is essentially invisible to MRI but shows up ex-tremely well
in x-ray images, whereas soft tissue is nearlytransparent to x-rays
but shows up in MRI.
The key to any medical imaging technique is toknow which part of
the body gives rise to which sig-nal. In MRI, spatial information
is encoded usingmagnetic field gradients. Recall that a linear
relation-ship exists between the frequency at which a
nucleusresonates and the intensity of the magnetic field. InIH-NMR
spectroscopy, we use a homogeneous mag-netic field, in which all
equivalent hydrogens absorbat the same radio frequency and have the
same chem-ical shift. In MRI, the patient is placed in a
magneticfield gradient that can be varied from place to
place.Nuclei in the weaker magnetic field gradient absorbat a lower
frequency. Nuclei elsewhere in the strongermagnetic field absorb at
a higher frequency. In a mag-netic field gradient, a correlation
exists between theabsorption frequency of a nucleus and its
position inspace. A gradient along a single axis images a plane.Two
mutually perpendicular gradients image a linesegment, and three
mutually perpendicular gradientsimage a point. In practice, more
complicated proce-dures are used to obtain magnetic resonance
images,but they are all based on the idea of magnetic
fieldgradients.
13.10 Stereochemistry and Topicity 501
-
13.9 Calculate the index of hydrogen deficiency of these
compounds.
~,->-L,~ Online homework for this chapter may be assigned in
Organic OWL. indicates problems assignable in OWL.Red numbers
indicate applied problems.
Interpretation of lH-NMR and 13C-NMR Spectra13.10 Complete the
following table. Which nucleus requires the least energy to flip
its
spin at this applied field? Which nucleus requires the most
energy?
(b) Ascorbic acid (vitamin C), C6Hs0 6(d) Urea, CH4N20(f)
Dopamine, CsH u N02
Applied Field Radio Frequency EnergyNucleus (tesla, T) (MHz)
O/mol)
IH 7.05 30013C 7.05 75.519F 7.05 282
(a) Aspirin, C9Hs0 4(c) Pyridine, CsHsN(e) Cholesterol,
C27H460
Section 13.11 13C-NMR 13C-NMR is like 1H-NMR, except the nuclear
spins of13C nuclei are being analyzed.
- 13C-NMR spectra are commonly recorded in a hydrogen-decoupled
instrumen-tal mode. In this mode, all 13C signals appear as
singlets.
- The number of different signals in a 13C-NMR spectrum tell you
how manynonequivalent carbon atoms are in a molecule.
- 13C-NMR chemical shifts tell you what kind of carbon atoms are
present.
Section 13.12 Interpretation of NMR Spectra Four important types
of structural information can be obtained from a IH-NMR
spectrum.- From the number of signals, we can determine the
number of sets of equiva-
lent hydrogens.- From the integration of signal areas, we can
determine the relative numbers of
hydrogens in each set.- From the chemical shift of each signal,
we can derive information about the
chemical environment of the hydrogens in each set.- From the
splitting pattern of each signal, we can derive information about
the
number and chemical equivalency of hydrogens on the same and
adjacent car-bon atoms, in other words the connectivities between
different groups on themolecule.
Molecules in which substitution produces diastereomers are
called diastereotopic.- Diastereotopic atoms are nonequivalent in
all environments so they have dif-
ferent chemical shifts. These differences can lead to complex
splitting of thesgnals of diastereotopic H atoms, especially those
adjacent to a chiral center.
13.11 The natural abundance of 13C is only 1.1 %. Furthermore,
its sensitivity in NMRspectroscopy (a measure of the energy
difference between a spin aligned with oragainst an applied
magnetic field) is only 1.6% that of IH. What are the relative
sig-nal intensities expected for the IH-NMR and 13C-NMR spectra of
the same sampleof Si(CH3)4?
Problems:13.09, 13.12-13.13,13.15-13.24, 13.28
Problems: 13.8, 13.27
PROBLEMS
512 Chapter 13 Nuclear Magnetic Resonance Spectroscopy
Assignable in OWL
-
Ha = 1.0 ppmHb = 3.0 ppmHe = 6.0 ppmlab = 5.0 Hzlbc = 8.0 Hzlac
= 1.0 Hz
13.27 The 13C-NMR spectrum of 3-methyl-2-butanol shows signals
at 0 17.88 (CH3), 18.16(CH3), 20.01 (CH3), 35.04 (carbon-3), and
72.75 (carbon-2). Account for the factthat each methyl group in
this molecule gives a different signal.
13.28 Sketch the NMR spectrum you would expect from a partial
molecule with the follow-ing parameters.
Ascaridole
13.25 The percent s-character of carbon participating in a C-H
bond can be establishedby measuring the 13C-1H coupling constant
and using the relationship
Percent s-character = 0.2le3C - IH)The 13C-1H coupling constant
observed for methane, for example, is 125 Hz, whichgives 25%
s-character, the value expected for an sj/' hybridized carbon
atom.(a) Calculate the expected 13C-1H coupling constant in
ethylene and acetylene.(b) In cyclopropane, the 13C-1H coupling
constant is 160 Hz. What is the hybridiza-
tion of carbon in cyclopropane?
13.26 Ascaridole is a natural product that has been used to
treat intestinal worms. Explainwhy the two methyls on the isopropyl
group in ascaridole appear in its IH-NMR spec-trum as four lines of
equal intensity, with two sets of two each separated by 7 Hz.
Assignable in OWL Problems 519