CHAPTER 10 Using Nuclear Magnetic Resonance Spectroscopy to Determine Structure

1
CHAPTER 10Using Nuclear Magnetic Resonance
Spectroscopy to Determine Structure
2
Physical and Chemical Tests
10-1
Purification Chromatography Distillation Recry
stallization Comparison to known compounds Melt
ing point Boiling point Many other properties
When the properties of an unknown purified
substance match those in the literature for a
known compound, the identify and structure of the
substance are still not known with certainty.
Many new substances are newly synthesized for the
first time and their properties are not in the
literature.
3
Elemental analysis reveals the gross composition
of the sample. Chemical tests identify the functi
onal groups present. For larger molecules, knowle
dge of the composition and functional groups
present in a substance are not enough to
determine the chemical structure of the
substance, for instance, the alcohol C7H16O
4
Defining Spectroscopy
10-2
Spectroscopy is a technique for analyzing the
structue of molecules, usually based on how they
absorb electromagnetic radiation. Four types are
most often used in organic chemistry.
Nuclear magnetic resonance Spectroscopy (NMR)
Infrared Spectroscopy (IR) Ultraviolet Spectrosco
py (UV) Mass Spectroscopy (MS) NMR spectroscopy
of C and H provides the most detailed information
regarding the atomic connectivity of a molecule
5
Defining Spectroscopy
10-2
Molecules undergo distinctive excitations.
Electromagnetic radiation can be described as a
wave having a wavelength, ?, a frequency, ?, and
a velocity, c.
The speed of light in a vacuum is 3 x 1010 cm s-1
or 3 x 108 m s-1. The units of wavelength must ma
tch those used for the speed of light.
The units of frequency are cycles s-1 (or just
s-1) or Hertz (Hz)
6
Molecules absorb energy in discrete packets of
energy called quanta. A quanta of
electromagnetic radiation is referred to as a
photon. The energy of a photon is determined by t
he frequency of the incident radiation
?E h?
When a photon of energy is absorbed by a
molecule, it causes electronic excitation or
mechanical motion to occur. The electronic excita
tions and motions of a particular molecule are
also quantized so only certain frequencies of
radiation are able to be absorbed.
An analysis of the frequencies of electromagnetic
radiation absorbed by a molecule provides
information about the arrangement of the atoms in
the molecule.
7
The lowest energy state of a molecule is called
the ground state. Absorption of electromagnetic r
adiation causes the molecule to undergo an
excitation, or move to an excited state.
The difference in energy between the excited
state and the ground state must be exactly equal
to the energy of the photon absorbed.
8
Absorption of x-rays results in the promotion of
electrons from inner atomic shells to outer ones
(electronic transitions). This requires x-ray
energies greater than 300 kcal mol-1.
UV and visible absorption excites valence shell
electrons, typically from a filled bonding to an
unfilled antibonding orbital. This involves
energies between 40 and 300 kcal mol-1.
IR absorption causes bond vibration excitation 2
to 10 kcal mol-1 Microwave radiation excites bond
rotations 10-4 kcal mol-1 Radiowaves, in the p
resence of a magnetic field, produces alignment
of nuclear magnetism 10-6 kcal mol-1. This is
the basis of NMR.
9
In this diagram, frequency is specified in units
of wavenumbers, defined as 1/?, which is the
number of waves per centimeter.
Wavenumbers are used to specify energy in
infrared spectroscopy.
10
A spectrometer records the absorption of
radiation

Continuous Wave Spectrometry (CW)
Radiation of a specific wavelength (UV, IR, NMR,
etc.) is generated and passes through a sample.
The frequency of the radiation is continuously
changed and the intensity of the transmitted beam
is detected and recorded. Frequencies that are ab
sorbed by the sample appear as peaks deviating
from a baseline value.
11
Fourier Transform Spectroscopy (FT)
A much faster technique. A pulse of electromagnet
ic radiation covering the entire spectrum under
scrutiny (NMR, UV, IR) is used to obtain the
whole spectrum instantly. The pulse may be applie
d multiple times and the results accumulated and
averaged, which provides for very high
sensitivity. The signal measured is actually the
decay of the absorption event with time. This
signal is then mathematically transformed using a
Fourier transform producing the more familiar
frequency versus absorption plot.
12
Proton Nuclear Magnetic Resonance
10-3
Nuclear spins can be excited by the absorption of
radio waves. Many nuclei can be thought of as spi
nning on their axis, either clockwise or
counterclockwise. One such nucleus is the hydroge
n nucleus 1H. A 1H nucleus is positively charg
ed and its spinning motion generates a magnetic
field. In the presence of an external magnetic fi
eld, H0, the magnetic field of the hydrogen
nucleus can be oriented either with H0 (lower
energy) against H0 (higher energy). These two
states are called ? and ? spin states,
respectively.
13
The difference in energy between the ? and ?
states depends directly on the external magnetic
field strength, H0. 21,150 G 90 MHz 42,300 G
180 MHz 70,500 G 300 MHz The actual energy dif
ference is small. At 300 MHz the energy
difference for a proton is about 3 x 10-5 kcal
mol-1. Because the energy difference is so small
and the equilibrium between the two states is so
fast, the numbers of nuclei in the two states are
nearly equal, however a slight excess will be in
the ? state because of the external magnetic
field. When electromagnetic radiation having the
same energy as energy difference strikes the
nucleus, the electromagnetic radiation is
absorbed and the slight excess of nuclei in the ?
state is reduced.
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Many nuclei undergo magnetic resonance.
In general, nuclei composed of an odd number of
protons (1H and its isotopes, 14N 19F, and 31P)
or an odd number of neutrons (13 C) show magnetic
behavior. If both the proton and neutron counts a
re even (12C or 16O) the nuclei are nonmagnetic.
16
In a hypothetical scan of CH2ClF in a 70,500-G
magnet the following spectrum would be observed
17
High-resolution NMR spectroscopy can
differentiate nuclei of the same element.
In the NMR spectrum of ClCH2OCH3 at 70,500-G from
0 to 300 MHz one peak would be observed for each
element present. Using high-resolution NMR spectr
oscopy the region around each of these peaks can
be expanded and additional spectral details can
be observed.
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Using NMR Spectra to Analyze Molecular Structure
10-4
The position of an NMR absorption of a nucleus is
called its chemical shift. Chemical shifts depend
upon the electron density around a nucleus and
are thus controlled by the structural environment
of the nucleus. The NMR chemical shifts provide i
mportant clues for determining the molecular
structure of a chemical compound.
19
The position of an NMR signal depends on the
electronic environment of the nucleus.
In the high-resolution 1H NMR spectrum of
chloro(methoxy)methane above, two separate
resonance absorptions of hydrogen are observed.
These absorptions reflect the differing
electronic environments of the two types of
hydrogen nuclei present. Electrons in the bonds c
onnecting the hydrogen atoms to the molecule
affect the NMR absorptions.
20
Bound hydrogens are connected to a molecule by
orbitals whose electron density varies
Bond polarity Hybridization of the attached atom
Presence of electron withdrawing/donating
groups The electrons in these orbitals are affect
ed by the external magnetic field, H0, in such a
way as to generate a small local magnetic field,
hlocal, opposing H0.
The total magnetic field seen by the hydrogen
nucleus is the sum of these two fields and is
thus reduced. The hydrogen nucleus is said to be
shielded from H0 by its electron cloud.
21
The degree of shielding of a nucleus depends upon
its surrounding electron density.
Adding electrons increases shielding.
Removing electrons causes deshielding.
Shielding causes a displacement of an NMR peak to
the right in the spectrum (shifted upfield).
Deshielding causes a displacement to the left
(shifted downfield).
22
Chemically equivalent hydrogens in a molecule all
have identical electronic environments and
therefore show NMR peaks at the same position.
In the NMR spectrum of 2,2-dimethyl-a-propanol
there are three different peaks due to
absorptions by Nine equivalent methyl hydrogens
on the butyl group (most shielded)
One hydrogen on the OH Two equivalent methylene h
ydrogens.
23
The chemical shift describes the position of an
NMR peak. Rather than reporting the exact frequen
cy of each resonance in an NMR spectrum, we
measure frequencies relative to an internal
standard, tetramethylsilane, (CH3)4Si.
To remove the effect of differing applied
magnetic fields using different spectrophotomers,
the frequencies relative to tetramethylsilane are
divided by the frequency of the spectrometer.
This yields a field-independent number called the
chemical shift, or d measured in ppm.
24
For (CH3)4Si, d is defined as 0.00.
The spectrum above would be reported as
1H NMR (300 MHz, CDCl3) d 0.89, 1.80, 3.26 ppm
25
Functional groups cause characteristic chemical
shifts.
Each type of hydrogen in a molecule has a
chemical shift which depends upon its chemical
environment
26
The absorptions of alkane hydrogens occur at
relatively high field. Hydrogens close to an elec
tron withdrawing group (halogen or oxygen) are
shifted to relatively lower field (deshielding).
The more electronegative the atom, the more the
deshielded methyl hydrogens are relative to
methane.
27
Multiple substituents exert a cumulative effect
28
The deshielding influence of electron withdrawing
groups dimishes rapidly with distance
29
Hydroxy, mercapto, and amino hydrogens absorb
over a range of frequencies. The absorption peak
of the proton attached to the heteroatom may be
relatively broad. This variability of chemical sh
ift is due to hydrogen bonding and depends upon
Temperature Concentration Presence of H-bonding
species such as water (moisture).
When line broadening is observed, it usually
indicates the presence of OH, SH, or NH2 (NHR)
groups.
30
Tests for Chemical Equivalence
10-5
In general, chemically equivalent protons have
the same chemical shift. To identify chemically e
quivalent nuclei we often have to resort to
symmetry operations to decide on the expected NMR
spectrum for a compound.
31
Tests for Chemical Equivalence
10-5
Molecular symmetry helps establish chemical
equivalence.
Rotational symmetry results in equivalent protons
when the group of protons is rapidly rotating, as
in a methyl group.
32
Conformational interconversion may result in
equivalence on the NMR time scale.
In the case of the rapid rotation of the methyl
group in chloroethane, or the rapid conformation
flip in cyclohexane, the observed chemical shifts
are the averages of the values that would be
observed without the rapid rotation or flip.
33
In the case cyclohexane, the single line in the
NMR spectra at d 1.36 ppm at room temperature
becomes two lines at a temperature of -90o C, one
at d 1.12 ppm for the six axial hydrogens and
one at d 1.60 for the six equatorial
hydrogens. At this temperature the conformational
flip of the benzene is slower than the NMR time
scale. In general, the lifetime of a molecule in
an equilibrium must be on the order of one second
to allow its resolution by NMR.
34
Integration
10-6
Integration reveals the number of hydrogens
responsible for an NMR peak. The area under an NM
R peak is proportional to the number of
equivalent nuclei contributing to the peak.
By comparing peak areas it is possible to
quantitatively estimate the relative numbers of
contributing protons. The areas are obtained by t
he controlling computer and plotted on top of the
regular spectrum by choosing integration mode.
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Chemical shifts and peak integration can be used
to determine structure. Consider the monochlorina
tion of 1-chloropropane
NMR spectroscopy distinguishes all three
isomers 1,1-Dichloropropane Three NMR signals
in the ratio of 321. ? 5.93 ppm (CH), 2.34 pm
(CH2), and 1.01 (CH3). 1,2-Dichloropropane Thre
e NMR signals in the ratio of 321. d 4.17
ppm (CH), 3.68 ppm (CH2), and 1.70 ppm (CH3)
1,3-Dichloropropane Two NMR signals in the
ratio of 21. d 3.71 ppm (CH2Cl) and 2.25
ppm (CH2)
37
Spin-Spin Coupling The Effect of Nonequivalent
Neighboring Hydrogens
10-7
When non-equivalent hydrogen atoms are not
separated by at least one carbon or oxygen atom,
an additional phenomenon called spin-spin
splitting or spin-spin coupling occurs.
Instead of single peaks (singlets), more complex
patterns occur called multiplets (doublets,
triplets or quartets). The number and kind of hyd
rogen atoms directly adjacent to the absorbing
nuclei can be deduced from the multiplicity of
the peak.
38
One neighbor splits the signal of a resonating
nucleus into a doublet. Consider two protons, Ha
and Hb. The population of each of these protons
is very close to 50 ? and 50 ? in the external
magnetic field, H0. This means that in 50 of the
molecules, Ha protons will have Hb protons in
the ? state and in 50 of the molecules Ha
protons will have Hb protons in the ? state.
The total field seen by 50 of the Ha protons
will threefore be slightly greater than H0 and
slightly less than H0 for the other 50 of the
Ha protons. What would have been a singlet NMR pe
ak is now split into a doublet of peaks,
symmetrically displaced from the original peak.
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The chemical shift of the Ha nucleus is reported
as the center of the doublet.
The amount of mutual splitting is equal. The
distance between the individual peaks making up
the doublet is called the coupling constant, J.
Here J is 7 Hz. Coupling constants are independen
t of the field strength of the NMR spectrometer
being used.
41
Spin-spin splitting is usually observed only
between hydrogen atoms bound to the same carbon
(geminal coupling) or to adjacent carbons
(vicinal coupling). Hydrogen nuclei separated by
more than two carbon atoms (1,3 coupling) is
usually negligable.
Finally, equivalent nuclei do not exhibit mutual
spin-spin splitting. Ethane exhibits only a
single line at d 0.85 ppm. Splitting is observe
d only between nuclei with different chemical
shifts.
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Local-field contributions from more than one
hydrogen are additive.
Consider the triplet above. It corresponds to
the methyl protons being split by the methylene
protons. The methylene proton spins will statisti
cally orient in the external magnetic field as
??, ??, ?? and ??. Each methyl proton will see
an increased field 25 of the time (??), no
change 50 of the time (?? and ??), and a
decreased field 25 of the time (??).
44
The integrated intensity of the triplet will be 6
since there are a total of six equivalent methyl
protons.
45
In the case of the methylene protons, the methyl
proton spins will statistically distribute as
???, ???, ???, ???, ???, ???, ???, and ???.
This will result in a 1331 quartet of peaks.
The integrated intensity of the quartet will be
4, corresponding to the 4 equivalent methylene
protons.
46
In many cases, spin-spin splitting is given by
the N1 rule. A simple set of rules Equivalent
nuclei located adjacent to one neighboring
hydrogen resonate as a doublet.
Equivalent nuclei located adjacent to two
hydrogens of a second set of equivalent nuclei
resonate as a triplet. Equivalent nuclei located
adjacent to a set of three equivalent hydrogens
resonate as a quartet.
47
This table illustrates the N1 rule nuclei
having N adjacent equivalent neighbors split into
N1 peaks. The heights of the N1 peaks follow
Pascals triangle.
48
It is important to note that nonequivalent nuclei
split each other. A split in one requires a split
in the other. In addition, the coupling
constants will be the same for each type of
nuclei. Two additional examples
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Spin-Spin Splitting Some Complications
10-8
Complex multiplets sometimes occur when there is
a relatively small difference in d between two
absorptions. The N1 rule may not apply in a dire
ct way if several neighboring hydrogens having
fairly different coupling constants are coupled
to the resonating nucleus. The hydroxy proton may
appear as a single, even if coupled to vicinal
hydrogens.
52
Close-lying peak patterns may give rise to
non-first-order spectra. The intensity patterns i
n many NMR spectra do not follow the idealized
pattern of Pascals triangle but instead are
skewed towards each other. The intensities of the
lines facing each other is slightly larger than
expected. Perfectly symmetrical splittings are ob
served only when the resonant frequency
difference of the two groups of protons is much
larger than the coupling constant between them.
When ?? J the spectra is said to be
first-order. Non-first order spectra assume more
complex shapes and can only be analyzed with the
help of computers. Since the resonant frequency d
ifference increases with higher field strengths
(J remains the same), a complicated spectrum can
be made first order by measuring it a higher
field strengths.
53
Close-lying peak patterns may give rise to
non-first-order spectra. The intensity patterns i
n many NMR spectra do not follow the idealized
pattern of Pascals triangle but instead are
skewed towards each other. The intensities of the
lines facing each other is slightly larger than
expected. Perfectly symmetrical splittings are ob
served only when the resonant frequency
difference of the two groups of protons is much
larger than the coupling constant between them.
When ?? J the spectra is said to be
first-order. Non-first order spectra assume more
complex shapes and can only be analyzed with the
help of computers. Since the resonant frequency d
ifference increases with higher field strengths
(J remains the same), a complicated spectrum can
be made first order by measuring it a higher
field strengths.
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Coupling to nonequivalent neighbors may modify
the simple N1 rule. The spectrum of 1,1,2-trichl
oropropane illustrates the effects of two sets of
non-equivalent neighbors.
56
The Ha proton is split by the Hb proton into a
doublet as expected. This double is at low field
due to the effect of two adjacent chlorine
atoms. The methyl protons are also split by the H
b proton into a doublet as expected. This
doublet is at high field. The Hb proton is split
by both Ha and the methyl protons. In this case
eight lines are observed because Ha and the
methyl protons have different coupling constants
to Hb.
The methyl group splits the Hb resonance into a
quartet (1,3,3,1). Each line of the quartet is
then split into a doublet by the Ha proton
(1,1,3,3,3,3,1,1).
57
In the case of 1-bromopropane, the hydrogens on
C2 are also coupled to two non-equivalent sets of
neighbors. A theoretical analysis of this
resonance would predict as many as 12 lines (a
quartet of triplets). Because the coupling consta
nts are very similar, however, many of the lines
overlap, thus simplifying the pattern.
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Fast proton exchange decouples hydroxy hydrogens.
In the spectra of 2,2-dimethyl-a-propanol, the OH
absorption appears as a single peak and is not
split by the CH2 protons. In addition, the CH2
protons are not split by the OH.
The OH proton is weakly acidic and is rapidly
both between alcohol molecules and to traces of
water on the NMR time scale at room temperature.
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This type of decoupling is called fast proton
exchange. It may be slowed or removed by removal
of traces of water or acid or by cooling.
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Rapid magnetic exchange self-decouples
chlorine, bromine, and iodine nuclei.
Fluorine is the only halogen the exhibits
spin-spin coupling to 1H in a proton NMR
spectra. Chlorine, bromine, and iodine exhibit a
fast internal magnetic equilibration on the NMR
time scale which precludes an adjacent proton
from recognizing them as having different
alignments in the external field.
This is termed self-decoupling, in contrast to
exchange-decoupling as exhibited by the hydroxy
protons.
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Carbon-13 Nuclear Magnetic Resonance
10-9
The NMR spectroscopy of 13C is of greater
potential utility than that of 1H NMR.
The 13C spectra of an organic compound is much
simpler than the 1H spectra because spin-spin
coupling between adjacent carbon atoms and
between carbon and hydrogen atoms can be avoided.
62
Carbon NMR utilizes an isotope in low natural
abundance 13C. Carbon occurs as a mixture of tw
o principle isotopes, 12C (98.89) and 13C
(1.11). Of these, only 13C in active in NMR.
Because of the low abundance of 13C and its
weaker magnetic resonance (1/6000 as strong as
1H), FT NMR is usually used for 13C spectroscopy
because multiple pulsing and signal averaging
allows the accumulation of strong signals than
would otherwise be possible. Carbon-carbon coupli
ng is absent in 13C spectra due to the very low
probability of two 13C nuclei being adjacent to
each other in a single molecule (.0111 x .0111
.0001). 13C-1H coupling is present however the ch
emical shift range of 13C is much greater than
the splittings due to 1H which precludes the
overlapping of adjacent multiplets.
The 13C chemical shifts are reported relative to
an internal standard, usually (CH3)4Si.
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The 13C NMR spectra of bromoethane above exhibits
13C splitting by the methyl and methylene
protons. The 13C peak due to C1 is first split by
its own two hydrogens to produce a triplet.
Each of the triplet peaks is then split into a
quartet by the adjacent protons on the C2
carbon. The 13C peak due to C2 is first split by
its own three hydrogens to produce a quartet.
Each of the quartet peaks is then split into a
triplet by the adjacent protons on the C1 carbon.
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Hydrogen decoupling give single lines.
13C-1H coupling can be completely removed by a
technique called broad-band hydrogen (or proton)
decoupling. In this technique, a strong broad rad
io frequency signal covering the entire resonant
frequency range for hydrogen is simultaneously
applied at the same time as the 13C signal.
The broad band hydrogen signal causes rapid ?-?
flips of the hydrogen nuclei, effecting averaging
their local magnetic field contributions.
Using this technique simplifies the spectra of
bromoethane to two single lines.
65
Proton decoupling is particularily powerful when
analyzing complex molecules because every
magnetically distinct carbon gives only a single
peak. The decoupled 13C spectra of methylcyclohex
ane shows only five peaks, revealing the twofold
symmetry in the structure.
A limitation of FT 13C NMR spectroscopy is that,
due to difficulties in integration, peak
intensities (areas) no longer correspond to the
numbers of nuclei present.
66
Carbon, like hydrogen, has chemical shifts which
depend upon its chemical environment.
Electron withdrawing groups cause deshielding and
the chemical shifts go up in the order primary
67
The numbers of non-equivalent carbons in the
isomers of C7H14 are clearly demonstrated by the
numbers of 13C peaks in their NMR spectra.
68
Advances in FT NMR are greatly aiding structure
elucidation DEPT 13C and 2D-NMR.
Using sophisticated time-dependent pulse
sequences (two-dimensional NMR) it is now
possible to establish coupling (therefore
bonding) between close-lying hydrogens
(homonuclear correlation) or connected carbon and
hydrogen atoms (heteronuclear correlation).
This, in effect, determines the molecular
connectivity of a molecule by measuring the
magnetic effect of neighboring atoms on one
another along a carbon chain.
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On such pulse sequence is the DEPT 13C NMR
spectrum (distortionless enhanced polarization
transfer). DEPT gives information specifying whic
h type of carbon gives rise to a specific signal
in the normal 13C spectrum CH3, CH2, CH, or
Cquaternary. A DEPT experiment consists of three
spectra Normal broad-band decoupled spectra. DE
PT-90 pulse sequence spectra which reveals
signals only of carbons bound to one hydrogen.
DEPT-135 pulse sequence spectra which produces
normal CH3 and CH signals, but negative
absorptions for CH2 and no peaks for quaternary
carbons.
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Limonene DEPT spectra
Spectrum A All 10 lines 6 alkyl C at high
field, 4 alkenyl C at low field.
Spectrum B CH carbons Spectrum C CH carbons,
positive signal CH3 carbons, negative signal CH2
carbons Spectrum A lines Spectrum C lines qua
ternary carbon
71
We can apply 13C NMR spectroscopy to the problem
of the monochlorination of 1-chloropropane.
Both 1,1- and 1,2-dichloropropane should exhibit
three carbon signals each. The groups of three
signals would be spaced differently due to the
different arrangement of chlorine substituents.
1,3-dichloropropane should exhibit only two
carbon signals.
The two deshielded chlorine bearing carbons
assignments in 1,2-dichloropropane can be made
using DEPT data. The signal at 49.5 ppm appears i
nverted in a DEPT-135 spectrum (CH2).
The signal at 55.8 ppm is the only absorption in
a DEPT-90 spectrum
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Important Concepts
10

• NMR Most important spectroscopic tool for
  elucidating organic structures.
  
• Spectroscopy Based on lower energy forms of
  molecules being converted into higher energy
  forms by the absorbion of electromagnetic
  radiation.
• NMR Based On Alignment of the nuclei of certain
  nuclei (ie. 1H and 13C) with (?) and against (?)
  a strong magnetic field.
  
• ? to ? transition affected by radio-frequency
  radiation leading to resonance and characteristic
  absorption spectra.
  
• High magnetic fields lead to higher resonant
  frequencies.
  
• High Resolution NMR Allows differentiation of
  1H and 13C nuclei in different environments.
  
• Spectral positions are measured as the chemical
  shift, d, in ppm from an internal standard (TMS).

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Important Concepts
10

• Chemical Shifts Highly dependent on presence
  (shielding) or absense (deshielding) of electron
  density.
  
• Electron donor substituents shield.
• Electron withdrawing substituents deshield
• Hydrogen bonding or proton exchange result in
  broad peaks.
  
• Chemical Equivalency Equivalent hydrogens or
  carbons have the same chemical shift.
  
• Integration of peak area indicates number of
  contributing hydrogens.
  
• Spin-Spin Splitting
• Pattern determined by number of hydrogen
  neighbors (N1 Rule).
  
• Equivalent hydrogens show no mutual splitting.

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Important Concepts
10

• Non-First-Order Spectra - Complicated patterns
  created when chemical-shift difference between
  coupled hydrogens is comparable to their coupling
  constant.
• Non-Equivalent Neighboring Hydrogens - (N 1)
  rule is applied sequentially.
  
• Carbon NMR Utilizes low abundance 13C nuclei.
  C-C coupling is not observed. C-H coupling can
  be removed by proton decoupling.
  
• DEPT 13C NMR Allows peak assignment to CH3,
  CH2, CH, and quatenary carbons respectively.