Nuclear Magnetic Resonance

(NMR) Spectroscopy
Definition of NMR Spectroscopy
Nuclear magnetic resonance spectroscopy:
commonly referred to as NMR, is a technique
which exploits the magnetic properties of
certain nuclei to study physical, chemical, and
biological properties of matter

Compared to mass spectrometry, larger

amounts of sample are needed, but
non-destructive
 NMR History
• 1937 Rabi’s prediction and observation of nuclear magnetic resonance
• 1945 First NMR of solution (Bloch et al for H2O) and solids (Purcell et
al for parafin)!
• 1953 Overhauser NOE (nuclear Overhauser effect)
• 1966 Ernst, Anderson Fourier transform NMR
• 1975 Jeener, Ernst 2D NMR
• 1980 NMR protein structure by Wuthrich
• 1990 3D and 1H/15N/13C Triple resonance
• 1997 Ultra high field (~800 MHz) & TROSY(MW 100K)
 Continuation of NMR History
Nobel prizes
1944 Physics Rabi (Columbia) 1952 Physics Bloch
(Stanford), Purcell (Harvard)
"for his resonance
method for recording
the magnetic
properties of atomic
nuclei"

1991 Chemistry Ernst (ETH) "for their development

of new methods for
"for his contributions to nuclear magnetic
the development of the precision measurements
methodology of high and discoveries in
resolution nuclear connection therewith"
magnetic resonance
(NMR) spectroscopy"
Continuation of NMR History
2002 Chemistry Wüthrich (ETH)

"for his development of nuclear magnetic

resonance spectroscopy for determining the
three-dimensional structure of biological
macromolecules in solution"

2003 Medicine Lauterbur (University of Illinois in

Urbana ), Mansfield (University of Nottingham)

"for their discoveries concerning

magnetic resonance imaging"
 Spin of Nuclei
Fermions : Odd mass nuclei with an odd number of nucleons have
fractional spins.
I = 1/2 ( 1H, 13C, 19F, 31P ), I = 3/2 ( 11B, 33S ) & I = 5/2 ( 17O ).

Bosons : Even mass nuclei with odd numbers of protons and neutrons
have integral spins.

I = 1 ( 2H, 14N )

Even mass nuclei composed of even numbers of protons and neutrons

have zero spin

I = 0 (12C, and 16O, 32S)

Nuclear Magnetic Resonance (nmr)
-the nuclei of some atoms spin: 1H, 13C, 19F, …

-the nuclei of many atoms do not spin: 2H, 12C, 16O, …

-moving charged particles generate a magnetic field (Ö)

-when placed between the poles of a powerful magnet, spinning nuclei will align with or
against the applied field creating an energy difference. Using a fixed radio frequency,
the magnetic field is changed until the ΔE = EEM. When the energies match, the nuclei
can change spin states (resonate) and give off a magnetic signal.

ΔE
Energy How NMR Works
β
E
ER
Flipping Relaxati
on
magnetic field = 14,092 gauss
for 1H v = 60,000,000 Hz (60 MHz)

nmr spectrum

magnetic field à
intensity

10 9 8 7 6 5 4 3 2 1 0

chemical shift (ppm)

1H nuclei are shielded by the magnetic field
produced by the surrounding electrons. The
higher the electron density around the nucleus,
the higher the magnetic field required to cause
resonance.

CH3Cl versus CH4

lower electron higher electron
density density
resonate at lower resonate at higher
applied field applied field

CHCCl3 ??
Information from 1H-nmr spectra:

1. Number of signals: How many different types of

hydrogens in the molecule.
2. Position of signals (chemical shift): What types of
hydrogens.
3. Relative areas under signals (integration): How many
hydrogens of each type.
4. Splitting pattern: How many neighboring hydrogens.
1. Number of signals: How many different types of
hydrogens in the molecule.

Magnetically equivalent hydrogens resonate at the

same applied field.

Magnetically equivalent hydrogens are also chemically

equivalent.

# of signals? CH4 CH3CH3

number of signals?

H3C CH3
C
C
H3C CH3
one
one

CH3

CH3
one
two
 CH3
H3C C CH3 CH3CH2-Br
Br
two
one

CH3CH2CH2-Br CH3CHCH3
Cl
three
two
CH3CHCH2CH3 Cl-CH2CH2CH2-Cl
Br

four two

CH3
CH2Cl

three
2. Position of signals (chemical shift): what
types of hydrogens.
primary 0.9 ppm

secondary 1.3

tertiary 1.5

aromatic 6-8.5 Note: combinations may

greatly influence chemical
allyl 1.7 shifts. For example, the
benzyl hydrogens in
benzyl 2.2-3
benzyl chloride are shifted
chlorides 3-4 H-C-Cl to lower field by the
chlorine and resonate at
bromides 2.5-4 H-C-Br 4.5 ppm.

iodides 2-4 H-C-I

alcohols 3.4-4 H-C-O

alcohols 1-5.5 H-O- (variable)

reference compound = tetramethylsilane (CH3)4Si @ 0.0 ppm

remember: magnetic field à

ß chemical shift

convention: let most upfield signal = a, next most upfield = b, etc.

… c b a tms
toluene

CH3

b a

b a
chemical shifts

H3C CH3
C
a C a
H3C CH3

CH3 a

a b

CH3
a
 a a b
CH3
H3C C CH3 CH3CH2-Br
a Br a

a b c a b a
CH3CH2CH2-Br CH3CHCH3
Cl
 b d c a b a b
CH3CHCH2CH3 Cl-CH2CH2CH2-Cl
Br

a
CH3
CH2Cl
b

c
 Chemically Non Equivalent Protons

Diastereotropic protons

ü Replacement by some arbitrary test group

generates Diastereoisomers
ü Diastereotropic protons can have different
chemical shifts
Br H d 5.3 ppm

C C

d 5.5 ppm
H3 C H
 Enantiotropic protons

ü Are in mirror-image environments

ü Replacement by some arbitrary test
group generates enantiomers
ü Enantiotropic protons have the same
chemical shift
Enantiotropic
protons
H
H
C CH2OH

H3 C

H Cl
Cl H
C CH2OH C CH2OH

R S
H3 C H3 C
3. Integration (relative areas under each signal):
how many hydrogens of each type.

a b c
CH3CH2CH2Br a 3H a:b:c=3:
2:2
b 2H
c 2H

a b a
CH3CHCH3 a 6H a:b=6:1
Cl b 1H
integration

H3C CH3
C
a C a
H3C CH3

a 12 H a 12 H

CH3 a

a b

CH3
a 6H a
a 6H
b 4H
 a a b
CH3
H3C C CH3 CH3CH2-Br
a Br a
a 3H
a 9H b 2H

a b c a b a
CH3CH2CH2-Br CH3CHCH3
Cl
a 3H
b 2H a 6H
c 2H b 1H
 b d c a b a b
CH3CHCH2CH3 Cl-CH2CH2CH2-Cl
Br
a 3H a 2H
b 3H b 4H
c 2H a
d 1H CH3
CH2Cl
b
a 3H
c b 2H
c 4H
 c b a

Integration: measure the height of each “step” in the integration and

then calculate the lowest whole number ratio: a:b:c = 24 mm : 16
mm : 32 mm = 1.5 : 1.0 : 2.0 à 3H : 2H : 4H
If the formula is known ( C8H9OF ), add up all of the “steps” and
divide by the number of hydrogens = (24 + 16 + 32 mm) / 9H = 8.0
mm / Hydrogen. a = 24 mm / 8.0 mm/H à 3 H; b = 16 mm/8.0 mm/
H à 2H; c = 32 mm/8.0 mm/H à 4H.
4. Splitting pattern: how many neighboring hydrogens.
In general, n-equivalent neighboring hydrogens will split a
1H signal into an ( n + 1 ) Pascal pattern.

“neighboring” – no more than three bonds away

n n+1 Pascal pattern:
0 1 1 singlet
1 2 1 1 doublet
2 3 1 2 1 triplet
3 4 1 3 3 1 quartet
4 5 1 4 6 4 1 quintet
note: n must be equivalent neighboring hydrogens to
give rise to a Pascal splitting pattern. If the neighbors
are not equivalent, then you will see a complex pattern
(aka complex multiplet).

note: the alcohol hydrogen –OH usually does not split

neighboring hydrogen signals nor is it split. Normally a
singlet of integration 1 between 1 – 5.5 ppm (variable).
splitting pattern?

H3C CH3
C
a C a
H3C CH3

a 12 H singlet a 12 H singlet

CH3 a

a b

CH3
a 6 H singlet a
a 6 H singlet
b 4 H singlet
 a a b
CH3
H3C C CH3 CH3CH2-Br
a Br a
a 3 H triplet
a 9 H singlet b 2 H quartet

a b c a b a
CH3CH2CH2-Br CH3CHCH3
Cl
a 3 H triplet
b 2 H complex a 6 H doublet
c 2 H triplet b 1 H septet
 b d c a b a b
CH3CHCH2CH3 Cl-CH2CH2CH2-Cl
Br
a 3H triplet a 2 H quintet
b 3H doublet b 4 H triplet
c 2H complex
d 1H complex

a
CH3 a b c
CH2Cl CH3CH2-OH
b
a 3 H triplet
c a 3 H singlet b 2 H quartet
b 2 H singlet c 1 H singlet
c 4 H ~singlet
Information from 1H-nmr spectra:

1. Number of signals: How many different types of

hydrogens in the molecule.
2. Position of signals (chemical shift): What types of
hydrogens.
3. Relative areas under signals (integration): How
many hydrogens of each type.
4. Splitting pattern: How many neighboring
hydrogens.
cyclohexane

a singlet 12H
2,3-dimethyl-2-butene

H3C CH3
C C a singlet
H3C CH3 12H
benzene

a singlet 6H
p-xylene
H3C CH3
a a
b

a singlet 6H
b singlet 4H
tert-butyl bromide

CH3 a singlet 9H
H3C C CH3
Br
ethyl bromide

a b
CH3CH2-Br

a triplet 3H
b quartet 2H
1-bromopropane

a b c
CH3CH2CH2-Br

a triplet 3H
b complex 2H
c triplet 3H
 isopropyl chloride

a b a
CH3CHCH3
Cl

a doublet 6H
b septet 1H
2-bromobutane
b d c a
CH3CHCH2CH3
Br

a triplet 3H
b doublet 3H
c complex 2H
d complex 1H
 o-methylbenzyl chloride

a
CH3 b
CH2Cl

c a singlet 3H
b singlet 2H
c ~ singlet 4H
 ethanol

a c b
CH3CH2-OH

a triplet 3H
b singlet 1H
c quartet 2H
 c
ethylbenzene b a
CH2CH3

a triplet 3H
b quartet 2H
c ~singlet 5H
p-diethylbenzene
a b c b a

CH3CH2 CH2CH3

a triplet 6H
b quartet 4H
c singlet 4H
m-diethylbenzene
o-diethylbenzene
2-bromo-2-methylbutane

b
CH3
b CH3CCH2CH3 a
Br c

a triplet 3H
b singlet 6H
c quartet 2H b&c
overlap
di-n-propylether

a b c c b a
CH3CH2CH2-O-CH2CH2CH3

a triplet 6H
b complex 4H
c triplet 4H
1-propanol

a b d c
CH3CH2CH2-OH

a triplet 3H
b complex 2H
c singlet 1H
d triplet 2H
C11H16

a 9H = 3CH3, no neighbors
9H
c 5H = monosubstituted benzene
b 2H, no neighbors
c b a
CH3
CH2 C CH3
CH3

neopentylbenzene
2H
5H
C4H8Br2

a = 6H, two CH3 with no neighbors

(CH3)2C— 6H

b = CH2, no neighbors & shifted downfield

due to Br

CH3
2H
H3C C CH2
Br Br
C 7H 8O

c = monosubst. benzene
b = CH2
5H
c = OH
OH
H2C

2H

1H
C4H9Br
a doublet 1.04 ppm 6H
b complex 1.95 ppm 1H
c doublet 3.33 ppm 2H

a = two equivalent CH3’s with one neighboring H (b?)

c = CH2 with one neighbor H (also b)

a
CH3 a 6H doublet
CH3CHCH2Br b 1H complex
a b c c 2H doublet
C10H13Cl
a singlet 1.57 ppm 6H
b singlet 3.07 ppm 2H
c singlet 7.27 ppm 5H

a = two-equilalent CH3’s with no neighbors

c = monosubstituted benzene ring
b = CH2

a singlet 6H
a
b CH3 b singlet 2H
c
c singlet 5H
CH2 C CH3
Cl
13C – nmr 13C ~ 1.1% of carbons

1) number of signals: how many different types of carbons

2) splitting: number of hydrogens on the carbon
3) chemical shift: hybridization of carbon sp, sp2, sp3
4) chemical shift: evironment
13C-nmr

2-bromobutane

a c d b
CH3CH2CHCH3
Br
 CHEMICAL SHIFT
• The number and position of signals in NMR spectrum
signifies the number and nature of protons in the molecule.
• Each of these protons will have different electronic
environments and thus they absorb at different applied field
strengths.
• When a molecule is placed in a magnetic field, its electrons
are caused to circulate and thus they produce secondary
magnetic field i.e., induced magnetic field.
• The induced magnetic field can either oppose or reinforce
the applied field.
• If the induced magnetic field opposes the applied field, then the nuclei
in a molecule exert an external force, which shields the nucleus from
the influence of the applied field and the proton is said to be shielded.

• If the induced field reinforces the applied field the proton feels a higher
field strength and thus such a proton is said to be deshielded.

Shielding effect Deshielding effect

• To overcome the shielding effect and to bring the
protons to resonance, greater external field is
required i.e., shielding shifts the absorption upfield
and deshielding shifts the absorption downfield.
• Such shifts (compared with a standard reference) in
the position of NMR absorption which arises due to
the shielding or deshielding of protons in a molecule
by the electrons are called chemical shift.
Measurement of Chemical Shift
• For the measurement or study of chemical shift
Tetramethyl silane(TMS) is taken as a
reference.
• Due to the low electronegativity of silicon the
shielding in TMS is greater than most of the
organic compounds and the chemical shift for
different kinds of protons are measured relative
to it.
• δ and τ scales are commonly used to measure
chemical shift.
q δ scale
• The value of δ is expressed in ppm.
• It can be obtained by using the following
equations,

OR

where,
υS and HS = the resonance frequency of the sample
υR and H R = resonance frequency of the reference.
q τ scale
• The value of τ is expressed as 10 ppm.
i.e., τ = 10- δ
• Shielding and deshielding effects δ value, i.e., greater
the deshielding, larger will be the value of δ and vice-
versa.
• The shielding parameter α can be determined by
using the equation,
H = H0 (1- α)
Where,
H = field felt by the proton,
H0 = applied field strength.
• Most of the chemical shift have δ value between 0
and 10.
 Factors Influencing
Chemical Shift
A.Intra-molecular factors
1. Inductive effect.
2. Vander Waal’s deshielding.
3. Anisotropic effects

B.Intermolecular factors
1. Hydrogen bonding.
2. Temperature.
3. Solvents.
 q Intra-molecular Factors
1. Inductive effect
• The presence of electronegative atoms or groups in a
molecule makes the proton deshielded.
• Higher the electronegativity, greater will be the deshielding
and thus the δ value will also be more.
i.e., F > Cl > Br > I
• E.g. CH 3 -F CH 3 -Cl CH 3 -Br CH 3 -I
δ = 4.26 δ = 3.0 δ = 2.82 δ = 2.16
2. Vander Waal’s deshielding
• The presence of bulky groups in a molecule can cause
deshielding due to the week Vander Waal’s force and give
slightly higher value of δ than expected.
3. Anisotropic effect (space effect)
• Anisotropic effect arises due to the orientation of nuclei
with respect to the applied magnetic field.
• Chemical bonds can set up magnetic field, the effect of this
field on the chemical shift is depend upon the spacial
arrangements.
• π – bonds effects the chemical shift and cause downfield
shift with higher δ value.
• E.g. CH 3 H ― δ H = 0.23 δ C = 2.3
CH 2==CH 2 ― δ H = 5.25 δ C = 123.3
 q Intermolecular factors
1. Hydrogen bonding
• Intra-molecular hydrogen bonding does not show any change
in absorption due to change in concentration.
• While hydrogen atom involved in the intermolecular H-
bonding shares its electrons with two electronegative
elements and as a result it itself deshielded and get higher δ
value.
• E.g. Carboxylic acid dimer and β-diketones.

δ = 9-15 δ = 15.4
Downfield shift No change
2. Temperature
• The resonance position of most signals is little
affected by temperature.
• ― OH, ―NH―, and ―SH protons show upfield
shift at higher temperature
3. Solvents
• The solvents used in NMR spectroscopy should be
chemically inert, magnetically isotropic, devoid of
hydrogen atom and should dissolve the sample to
a reasonable extent.
• E.g. CCl4, CS2, CDCl3 etc.
 Chemical Shift Reagent
• These are the agents used to cause shift in the
NMR spectra.
• The amount of shift depends on,
– Distance between the shift reagent and proton,
– Concentration of shift reagent.
• The advantages of using shift reagents are,
– Gives spectra which are much easier to interpret,
– No chemical manipulation of sample is required,
– More easily obtained.
• Paramagnetic materials can cause chemical
shift, e.g., Lanthanides.
• Complexes of Europium, Erbium, Thallium and
Ytterbium shift resonance to lower field.
• Complexes of Cerium, Neodymium and
Terbium shift resonance to higher field.
• Europium is probably the most
commonly used metal to cause shift in
the NMR spectra.
• Two of its widely used complexes are,

1. Eu(dpm) 3 2. Eu(fod) 3
 REFERENCE STANDARD

1. Tetramethyl Silane (TMS)

CH3
H3C Si CH3
CH3
tetramethylsilane (TMS)

• TMS is the most convenient reference generally

employed in NMR for measuring the position of H1 ,
C13 and Si29.
• The chemical shift of TMS is considered as zero and
all the other chemical shifts are determined relative to
it.
• It has the following characteristics,
⁻ It is chemically inert and miscible with large range
of organic solvents.
⁻ It is highly volatile and can be easily removed to get
back the sample.
⁻ It does not take part in intermolecular association
with the sample.
⁻ Its resonance position is far away from absorption
due to protons in the molecule.
⁻ Its 12 protons are all magnetically equivalent.
2. 3-(trimethyl silyl) propane sulphonate (sodium salts)

• It is used as internal standard for scanning NMR spectra

of water soluble substances in deuterium oxide solvent.
• It has more water solubility than TMS and is commonly
used for protein experiments in water.
• The low electro negativity of the silicon shields the nine
identical methyl protons and show almost lower chemical
shift than naturally occurring organic molecule.
 SPLITTING OF THE
SIGNALS
• Each signals in NMR spectrum represents one kind or
one set of protons in the molecule.
• In certain molecules, instead of a single peak a group of
peaks are observed.
• This phenomena of splitting of proton signals into two or
more sub-peaks are referred as splitting.
• The splitting pattern of a given nucleus can be predicted
by the n+1 rule, where n is the number of protons on
the neighboring carbon.
• The simplest multiplicities are singlet (n =
0), doublets (n = 1 or coupling to just one
proton), triplets (n = 2), quartets (n = 3), quintets (n =
4), sextets (n = 5) and septets (n = 6).
• The theoretical intensity of the
individual lines can be derived from
Pascal's triangle.
 SPIN-SPIN COUPLING
• The source of signal splitting in NMR spectra is a
phenomenon called spin-spin coupling.
• The interactions between the spins of neighboring
magnetic nuclei in a molecule is known as spin-spin
coupling.
• The coupling occurs through bonds by means of slight
impairing of bonding electrons.
• The complexity of the multiplet depends upon the nature
and number of the nearby atoms.
• Chemically equivalent protons do not show spin-spin
coupling due to interaction among themselves. i.e., only
the nonequivalent protons show the property of coupling.
• E.g., 1,1,2-trichloroethane
• Here the Ha and Hb protons are spin-
coupled to each other and therefore it has
been observed that for each kind of
protons we do not get singlet, but a
groups of peaks are observed.

Hb Ha Ha
Cl C C Ha
Cl Cl

Hb
4.05 4.00 3.95 3.90 3.85
5.85 5.80 5.75 5.70 5.65

10 9 8 7 6 5 4 3 2 1 0
PPM (!)
• Coupling may either oppose or reinforce
the field felt by the other molecule.
• E.g., Ethyl bromide (CH3-CH2Br)
– In this molecule the spin of two protons (-CH2-) can couple
with the adjacent methyl group (-CH3) in three different ways,

Reinforcing Not effecting Opposing

 COUPLING CONSTANT
• The spacing of adjacent lines in the multiplet is a direct measure
of the spin-spin coupling and is known as coupling constant (J).
• It is the distance between two adjacent sub-peaks in a split
signal.
• J value is expressed in Hertz(Hz) or in cycles per second(cps).
• For nonequivalent hydrogens on the same sp2
carbon, the J value is usually very small and
are unable to observe.
• But, for nonequivalent hydrogens bonded to
adjacent sp2 carbons, the J is usually large
enough to be observed.
• The leading superscript ( XJ ) indicates the
number of bonds between the coupled nuclei.
• J value is independent of the external field and it
decreases with distance.
• Coupling constants, J vary widely in size, but the
vicinal couplings in acyclic molecules are usually 7 Hz.
• J provides important information in coupling across
double bonds, where trans couplings are always
substantially larger than cis couplings.
 SPIN DECOUPLING

• Coupling causes splitting of signals in NMR

spectra.
• Decoupling is a special technique used in
NMR spectroscopy to avoid the splitting of the
signals by eliminating partially or fully the
observed coupling.
• Which involves the irradiation of a proton with
sufficiently intense radiofrequency energy, so
that it prevents the coupling with the
neighboring proton and gives spectral line as
a singlet.
• Decoupling can help determine structures
of chemical compounds.
• There are two types of decoupling:
– Homonuclear decoupling - the nuclei being irradiated
are the same isotope as the nuclei being observed in the
spectrum.
– Heteronuclear decoupling - the nuclei being irradiated
are of a different isotope than the nuclei being observed
in the spectrum.

• E.g., 3-amino-acroleine
• Selective irradiation of M reduces the
AMX spin system to AX : two dublets,
A-X coupling constant can be
determined
• Selective irradiation of X reduces the
AMX spin system to AM: two dublets,
A-M coupling constant can be
determined
 Effects of Coupling and Decoupling in NMR
spectra
• The identification of coupled protons in spectra are too
complex because they show so many signals.

• Decoupling is used to simplify a complex NMR spectrum.

• It is possible to irradiate (decouple) each coupled protons in

the molecule to produce the spectrum with less complexity.

• Decoupling causes the multiplet to collapse to a doublet or

singlet and give spectra which are easy to interpret.

• In this way the full coupling relationship can be established

and much information can be collected about the connection
between alkanes, alkenes and alkynes .
• E.g., Furfural

• It is a complex compound because Ha, Hb and Hc

appear as four lines in the spectrum due to
coupling effects.
• The effects of strong decoupling eliminates
the coupling of Ha with Hb and Hc as a
result each multiplet collapse into doublet.
 ISOTOPIC NUCLEI
• An isotope can be defined as the atoms with the same
number of protons but have a different number of neutrons or
the elements with the same atomic number but different
mass number.

• Any nucleus with an odd atomic number or odd mass number

will have a nuclear magnetic resonance.

• In addition to hydrogen, there are several other nuclei which

have magnetic movements and can be studied by NMR
spectroscopy.

• E.g., 1H, 13C, 19F, 15N, 11B, 31P, etc.

• CARBON-13

• 13C was difficult to study because it gives rise to extremely weak

signals in NMR spectra.

• It can be studied by using Fourier Transform method.

• Principle behind 13C NMR are exactly similar to those of Proton

NMR, but the scale of observed chemical shift and coupling is
greater for 13C NMR.

• 13C shift range varies from 0-250 ppm.

• FLUORINE-19

• Fluorine with an atomic number of 9 has a magnetic

momentum of 2.6285,can be studied by NMR
spectroscopy by the same technique as PMR.
• This technique is commonly used for study of fluorinated
aliphatic and aromatic compounds.
• The range of chemical shift for aromatic fluorine atoms
are five times greater than the total range of proton shift in
PMR.
• The fluorine absorption is sensitive to the environment
• PHOSPHOROUS -31

• It shows magnetic property similar to hydrogen and

fluorine isotopes.
• It exhibits sharp NMR peaks with chemical shifts
extending over range of 700ppm.
• A quantitative analysis of these isotopes are studied
out by Colson and Marr, they found out that 31P
resonance shift are very large.
• BORON -11

• The 11B spectra has been extensively used to analyse

the complex boron hydrides
• The chemical shift ranges very large
• It has 2 naturally occuring isotopes (11B and 10B).
• 11B is used mainly in studies of NMR.
• NITROGEN -15

• 15N
yields sharp lines in NMR spectra but is very
insensitive.
• 15N experiments gives narrow lines and has a larger
chemical shift range.
• IUPAC recommends CHNO as the chemical shift
standard for nitrogen isotope nucleides.
 Angular Momentum
A spinning charge generates a magnetic field, the resulting
spin-magnet has a magnetic moment (µ) proportional to the
spin I

magnetic moment µ = γ p
where γ is the gyromagnetic ratio,
and it is a constant for a given nucleus

µ = γ p = γ I ( I + 1)h / 2π When I=0, µ=0

** There is no spin for nuclei with I=0

“Right Hand Rule”

determines the direction of the magnetic field

around a current-carrying wire and vice-
versa
 Energy Differentiation
In the presence of an external magnetic field (B0), two spin states exist, +1/2 and -1/2
(For I=1/2).
The magnetic moment of the lower energy +1/2 state is aligned with the external field,
and that of the higher energy -1/2 spin state is opposed to the external field.

Aligned against
the applied field

Aligned with
the applied field
 Energy Differentiation

Difference in energy between the two states is given by:

ΔE = γ h Bo / 2π

where:
Bo – external magnetic field
h – Planck’s constant
γ – gyromagnetic ratio

When the energy of the photon matches the energy difference between the two spin
states , an absorption of energy occurs. We call that phenomenon Resonance

ΔE = hυ = γhBo / 2π
So, υ = γ Bo / 2π
 Larmor Precession
Spinning particle precesses about the
external field axis with an angular
frequency known as the Larmor frequency

ωL = γ B o

When radio frequency energy matching

the Larmor frequency is introduced at a
right angle to the external field, it would
cause a transition between the two energy
levels of the spin. In other world, the
precessing nucleus will absorb energy and
the magnetic moment will flip to its I =
_1/2 state
γ- Values for some nuclei
Isotope Net Spin γ / MHz T-1 Abundance / %
1H 1/2 42.58 99.98
2H 1 6.54 0.015
3H 1/2 45.41 0.0
31P 1/2 17.25 100.0
23Na 3/2 11.27 100.0
14N 1 3.08 99.63
15N 1/2 4.31 0.37
13C 1/2 10.71 1.108
19F 1/2 40.08 100.0
Schematic NMR Spectrometer
 Fourier transformation and the
NMR spectrum

Fourier
RF Pulse transform

The Fourier transform (FT) is

a computational method for
analyzing the frequencies
present in an oscillating signal
The NMR spectrum
 1H NMR and 13C NMR Spectrum

1H NMR spectra

δ ppm

Down field High field

13C NMR spectra

δ ppm
 Chemical Shift-δ
When an atom is placed in a magnetic field, its electrons
circulate about the direction of the applied magnetic
field. This circulation causes a small magnetic field at
the nucleus which opposes the externally applied field

The magnetic field at the nucleus (the effective field)

is therefore generally less than the applied field by a
fraction :
B = Β0 (1-σ), So υ = γ B0 (1-σ) / 2π
 Chemical Shift-δ
The electron density around each nucleus in a molecule varies according to the
types of nuclei and bonds in the molecule. The opposing field and therefore the
effective field at each nucleus will vary. This is called the chemical shift
phenomenon.
As we can tell from ν = γ B0 (1-σ) / 2π , the greater the value of Bo, the greater the
frequency difference.
This relationship could make it difficult to compare NMR spectra taken on
spectrometers operating at different field strengths.

The term chemical shift was developed to avoid this problem. The chemical shift
of a nucleus is the difference between the resonance frequency of the nucleus and a
standard, relative to the standard. This quantity is reported in ppm and given the
symbol delta.

δ = (ν - νref) x106 / νref

 Standard for Chemical Shift
In NMR spectroscopy, the standard is often tetramethylsilane, Si(CH3)4,
abbreviated TMS.

Tetramethyl silane (TMS) is used as reference because it is soluble in most organic

solvents, is inert, volatile, and has 12 equivalent 1H and 4 equivalent 13C. TMS
signal is set to 0
 Shielding and Deshielding
A nucleus is said to be shielded when
electrons around the nucleus circulates
in a magnetic field and create a
secondary induced magnetic field which
opposes the applied field .

Trends in chemical shift are explained

based on the degree of shielding or
deshielding , e.g. of deshielding effect
 Chemical Shift-δ

Chemical shift depends on :

• Electronegativity of nearby atoms

• Hybridization of adjacent atoms

• diamagnetic effects

• paramagnetic effects

• solvent effect
 Spin-Spin Coupling
Spin-spin coupling:

The coupling of the intrinsic angular momentum of different

particles. Such coupling between pairs of nuclear spins is an
important feature of nuclear magnetic resonance (NMR) spectroscopy
as it can provide detailed information about the structure and
conformation of molecules. Spin-spin coupling between nuclear spin
and electronic spin is responsible for hyperfine structure in atomic
spectra.
 J-Coupling
J-coupling:

also called indirect spin-spin coupling, is the coupling between two nuclear spins due
to the influence of bonding electrons on the magnetic field running between the two
nuclei. J-coupling provides information about dihedral angles, which can be
estimated using the Karplus equation. It is an important observable effect in 1D
NMR spectroscopy.

The coupling constant, J (usually in frequency units, Hz) is a measure of the interaction between
a pair of nuclei
 1H-NMR

• 1H experiencing the same chemical environment or chemical shift are called

equivalent hydrogens.

• 1H experiencing different environment or having different chemical shifts

are nonequivalent hydrogens.
Chemical Shift - 1H-NMR
 1H Chemical shifts
Type of Chemical Type of Chemical
Hydrogen Shift (δ) Hydrogen Shift (δ)
(C H 3 ) 4 S i 0 (by definition) O
RC H 3 0.8-1.0 RC O C H 3 3.7-3.9
RC H 2 R 1.2-1.4 O
R 3 CH 1.4-1.7 RC O C H 2 R 4.1-4.7
R 2 C=C RC H R 2 1.6-2.6 RC H 2 I 3.1-3.3
RC C H 2.0-3.0 RC H 2 Br 3.4-3.6
A rC H 3 2.2-2.5 RC H 2 Cl 3.6-3.8
A rC H 2 R 2.3-2.8 RC H 2 F 4.4-4.5
RO H 0.5-6.0 A rO H 4.5-4.7
RC H 2 OH 3.4-4.0 R 2 C=C H 2 4.6-5.0
RC H 2 OR 3.3-4.0 R 2 C=C HR 5.0-5.7
R 2 NH 0.5-5.0 A rH 6.5-8.5
O O
RC C H 3 2.1-2.3 RC H 9.5-10.1
O O
RC C H 2 R 2.2-2.6 RC O H 10-13
Factors to Affect 1H Chemical Shift
Chemical shift : (1) electronegativity of nearby atoms, (2) hybridization of
adjacent atoms, and (3) diamagnetic effects

Electronegativity

Electroneg- Chemical
CH3-X ativity of X Shift (δ)
CH3F 4.0 4.26
CH3OH 3.5 3.47
CH3Cl 3.1 3.05
CH3Br 2.8 2.68
CH3I 2.5 2.16
(CH3) 4C 2.1 0.86
(CH3) 4Si 1.8 0.00
Hybridization of adjacent atoms

Type of Hydrogen Name of Chemical

(R = alkyl) Hydrogen Shift (δ)
RCH3 , R2 CH2 , R3 CH Alkyl 0.8 - 1.7
R2 C=C(R)CHR2 Allylic 1.6 - 2.6
RC CH Acetylenic 2.0 - 3.0
R2 C=CHR, R2 C=CH2 Vinylic 4.6 - 5.7
RCHO Aldehydic 9.5-10.1
Carbon-Carbon Triple Bond Effect
A carbon-carbon triple bond shields an acetylenic hydrogen and shifts its
signal to lower frequency (to the right) to a smaller value

Chemical
Type of H Name Shift (δ)
RCH3 Alkyl 0.8- 1.0
RC CH Acetylenic 2.0 - 3.0
R2 C=CH2 Vinylic 4.6 - 5.7
 Carbon-Carbon Double Bond Effect
Magnetic induction in the p bond of a carbon-carbon double bond deshields
vinylic hydrogens and shifts their signal higher frequency
 Aromatic Effect
The magnetic field induced by circulation of p electrons in an aromatic ring deshields
the hydrogens on the ring and shifts their signal to higher frequency
 Signal Splitting for 1H

Peak:
The units into which an NMR signal is split; doublet, triplet, quartet,
multiplet, etc.

Signal splitting:
Splitting of an NMR signal into a set of peaks by the influence of
neighboring nonequivalent hydrogens.

(n + 1) rule:
If a hydrogen has n hydrogens nonequivalent to it but equivalent
among themselves on the same or adjacent atom(s), its 1H-NMR
signal is split into (n + 1) peaks.
 Pascal’s triangle
The relative peak intensities for
multiplet peaks arising from J-
coupling of a 1H to N equivalent
1H can be determined using Pascal’s

triangle:
 Coupling constant

Coupling constant (J):

The separation on an NMR
spectrum (in hertz) between
adjacent peaks in a
multiplet.
 13C-NMR Spectroscopy
Organic compounds contain carbon. Unfortunately, the C-12
nucleus does not have a nuclear spin, but the C-13 nucleus does due
to the presence of an unpaired neucarbon-1tron. C-13 nuclei make
up approximately 1% of the carbon nuclei on earth. Therefore, 13C
NMR will be much less sensitive than 1HNMR NMR
 13C-NMR Spectroscopy
The presence of spin-spin coupling between a 13C nucleus and
the nuclei of 1H atoms bonded to the 13C, splits the carbon-13
peaks and causes an even poorer signal-to-noise ratio

Each nonequivalent 13C gives a different signal

A 13C signal is split by the 1H bonded to it according to the
(n + 1) rule.
Coupling constants of 100-250 Hz are common, which
means that there is often significant overlap between
signals, and splitting patterns can be very difficult to
determine.

The most common mode of operation of a 13C-NMR

spectrometer is a proton-decoupled mode.
 Decoupling
proton-decoupled mode,
a sample is irradiated with two different radiofrequencies. One to
excite all 13C nuclei, a second to cause all protons in the molecule
to undergo rapid transitions between their nuclear spin states.

On the time scale of a 13C-NMR spectrum, each proton is in an

average or effectively constant nuclear spin state, with the result
that 1H-13C spin-spin interactions are not observed and they are
decoupled.
 Chemical Shift - 13C-NMR

Characteristic Carbon NMR Chemical Shifts (ppm)

(CH3)4Si = TMS = 0.00 ppm (singlet) CDCl3 (solvent) = 77.0 ppm (triplet)

RCH3 0 – 40 RCH2Cl 35 – 80 benzene ring 110 – 160

RCH2R 15 – 55 R3COH 40 – 80 C=O ester 160 – 180

R3CH 20 – 60 R3COR 40 - 80 C=O amide 165 – 180

RCH2I 0 – 40 RC≡CR 65 – 85 C=O carboxylic acid 175 – 185

RCH2Br 25 - 65 R2C=CR2 100 - 150 C=O aldehyde, ketone 180 – 210

Trends
•RCH3 < R2CH2 < R3CH
•Electronegative atoms cause downfield shift
•Pi bonds cause downfield shift
•C=O 160-210 ppm
 13C-NMR: Integration
1H-NMR: Integration reveals relative number of hydrogens per signal

13C-NMR: Integration reveals relative number of carbons per signal

•Rarely useful due to slow relaxation time for 13C

time for nucleus to relax from

excited spin state to ground state
Interpreting NMR Spectra
Alkanes
1H-NMR signals appear in the range of 0.8-1.7.
13C-NMR signals appear in the considerably wider

range of 10-60.

Alkenes
1H-NMR signals appear in the range 4.6-5.7.
1H-NMR coupling constants are generally larger for

trans-vinylic hydrogens (J= 11-18 Hz) compared with

cis-vinylic hydrogens (J= 5-10 Hz).
13C-NMR signals for sp2 hybridized carbons appear in

the range 100-160, which is to higher frequency from

the signals of sp3 hybridized carbons.
 Interpreting NMR Spectra
Alcohols
1H-NMR O-H chemical shift often appears in the range 3.0-4.0, but
may be as low as 0.5.
1H-NMR chemical shifts of hydrogens on the carbon bearing the -OH
group are deshielded by the electron-withdrawing inductive effect of
the oxygen and appear in the range 3.0-4.0.

Ethers
A distinctive feature in the 1H-NMR spectra of ethers is the chemical
shift, 3.3-4.0, of hydrogens on the carbons bonded to the ether
oxygen.
b

b
a
a
 Interpreting NMR Spectra
Aldehydes and ketones
1H-NMR: aldehyde hydrogens appear at 9.5-10.1.
1H-NMR: a-hydrogens of aldehydes and ketones appear at 2.2-2.6.
13C-NMR: carbonyl carbons appear at 180-215.

Amines
1H-NMR: amine hydrogens appear at 0.5-5.0 depending on
conditions.
 b
a c
c

a b c
b c
a

a
1H NMR isobutyraldehyde b

1H NMR Methyl ethyl ketone

 Interpreting NMR Spectra
Carboxylic acids
1H-NMR: carboxyl hydrogens appear at 10-13 ppm, higher than most
other types of hydrogens.
13C-NMR: carboxyl carbons in acids and esters appear at 160-180

ppm.

b
c a
a

c b
 NMR = Nuclear Magnetic Resonance

Physical Principles:
Some (but not all) nuclei, such as 1H, 13C, 19F, 31P have nuclear spin.
A spinning charge creates a magnetic moment, so these nuclei can be
thought of as tiny magnets.
If we place these nuclei in a magnetic field, they can line up with or against
the field by spinning clockwise or counter clockwise.
N N

N α- spin state, S β- spin state,

favorable, unfavorable,
lower energy higher energy
S N
S S

A spinning nucleus with it's magnetic field A spinning nucleus with it's magnetic field
aligned with the magnetic field of a magnet aligned against the magnetic field of a magnet
Alignment with the magnetic field (called α) is lower energy than against the
magnetic field (called β). How much lower it is depends on the strength of
the magnetic field
Note that for nuclei that don’t have spin, such as 12C, there is no difference
in energy between alignments in a magnetic field since they are not
magnets. As such, we can’t do NMR spectroscopy on 12C.
 NMR: Basic Experimental Principles

Imagine placing a molecule, for example, CH4, in a magnetic field.

We can probe the energy difference of the α- and β- state of the protons by
irradiating them with EM radiation of just the right energy.
In a magnet of 7.05 Tesla, it takes EM radiation of about 300 MHz (radio
waves).
So, if we bombard the molecule with 300 MHz radio waves, the protons will
absorb that energy and we can measure that absorbance.
In a magnet of 11.75 Tesla, it takes EM radiation of about 500 MHz (stronger
magnet means greater energy difference between
at no magnetic field, the α- and β- state of the
β proton spin state
protons) there is no difference beteen (higher energy )
α- and β- states.
Graphical relationship between
magnetic field (Bo) and frequency (ν) E ΔE = h x 300 MHz ΔE = h x 500 MHz

for 1 H NMR absorptions

α proton spin state
(lower energy)

0T 7.05 T 11 .75 T

Bo

But there’s a problem. If two researchers want to compare their data using
magnets of different strengths, they have to adjust for that difference. That’s
a pain, so, data is instead reported using the “chemical shift” scale as
 The Chemical Shift (Also Called δ) Scale

Here’s how it works. We decide on a sample we’ll use to standardize our

instruments. We take an NMR of that standard and measure its absorbance
frequency. We then measure the frequency of our sample and subtract its
frequency from that of the standard. We then then divide by the frequency
of the standard. This gives a number called the “chemical shift,” also called
δ, which does not depend on the magnetic field strength. Why not? Let’s
look at two examples.
Imagine that we have a magnet where our standard absorbs at 300,000,000
Hz (300 megahertz), and our sample absorbs at 300,000,300 Hz. The
difference is 300 Hz, so we take 300/300,000,000 = 1/1,000,000 and call
that 1 part per million (or 1 PPM). Now lets examine the same sample in a
stronger magnetic field where the reference comes at 500,000,000 Hz, or
500 megahertz. The frequency of our sample will increase proportionally,
and will come at 500,000,500 Hz. The difference is now 500 Hz, but we
divide by 500,000,000 (500/500,000,000 = 1/1,000,000, = 1 PPM).
It’s brilliant.
Of course, we don’t do any of this, it’s all done automatically by the NMR
machine.
Even more brilliant.
 The Chemical Shift of Different Protons

NMR would not be very valuable if all protons absorbed at the same
frequency. You’d see a signal that indicates the presence of hydrogens in
your sample, but any fool knows there’s hydrogen in organic molecules.
What makes it useful is that different protons usually appear at different
chemical shifts (δ). So, we can distinguish one kind of proton from another.
Why do different protons appear at different δ? There are several reasons,
one of which is shielding. The electrons in a bond shield the nuclei from the
magnetic field. So, if there is more electron density around a proton, it sees
a slightly lower magnetic field, less electron density means it sees a higher
magnetic field: This represents the electron density of a C-H bond. How much electron
Z density is on the proton depends on what else is attached to the carbon. If Z
C H is an elelctronegative atom, the carbon becomes electron deficient and pulls
some of the electron density away from the H. if Z is an electron donating
group, more electron density ends up on the H.

How do the electrons shield the magnetic field? By moving. A moving

charge creates a magnetic field, and the field created by the moving
electrons opposes the magnetic field of our NMR machine. It’s not a huge
effect, but it’s enough to enable us to distinguish between different protons
in our sample.
 The Hard Part - Interpreting Spectra

Learning how an NMR machine works is straightforward. What is less

straightforward is learning how to use the data we get from an NMR machine
(the spectrum of ethyl acetate is shown below). That’s because each NMR
spectrum is a puzzle, and there’s no single fact that you simply have to
memorize to solve these spectra. You have to consider lots of pieces of data
and come up with a structure that fits all the data. What kinds of data do we
get from NMR spectra? For 1H NMR, there are three kinds each of which we
will consider each ofshift
1) Chemical these separately:
data - tells us what kinds of protons we have.
2) Integrals - tells us the ratio of each kind of proton in our sample.
3) 1H - 1H coupling - tells us about protons that are near other protons.
 Chemical Shift Data

As previously mentioned, different kinds of protons typically come at different

chemical shifts. Shown below is a chart of where some common kinds of
protons appear in the δ scale. Note that most protons appear between 0 and
10 ppm. The reference, tetramethylsilane (TMS) appears at 0 ppm, and
aldehydes appear near 10 ppm. There is a page in your lab handout with
more precise values for this chart.
Note that these are typical values and that there are lots of exceptions!
R
NH
R
OH

Ph R H
Me
OH
(R) TMS = Me Si Me
HO CH3 Ph CH3 Me
R R
R O R R
O
Cl NR2 O
H H H OCH3 CH3 CH3 CH3
R CH3
TMS

10 9 8 7 6 5 4 3 2 1 0
Downfield region δ pp m Upfield region
of the spectrum of the spectrum
 Integrals

Integrals tell us the ratio of each kind of proton. They are lines, the heights
of which are proportional to the intensity of the signal. Consider ethyl
acetate. There are three kinds of protons in this molecule, the CH3 next to
the carbonyl, the CH2 next to the O and the CH3 next to the CH2. The ratio
of the signals arising from each of these kinds of protons should be 3 to 2 to
3, respectively. So, if we look at the height of the integrals they should be 3
to 2 to 3. With this information, we can know which is the CH2 signal (it’s the
smallest one), but to distinguish the other two, we have to be able to predict
their chemical shifts. The chart on the previous page allows us to make that
assignment (the CH3 next to the C=O should appear at ~ 2 PPM, while the
other CH3 should be at ~ 1 PPM).
3H'S
O

O CH3 O
O
H H 3C O
O H
3H'S

2 H'S
 1H
- 1H Coupling
You’ll notice in the spectra that we’ve seen that the signals don’t appear as
single lines, sometimes they appear as multiple lines. This is due to 1H - 1H
coupling (also called spin-spin splitting or J-coupling). Here’s how it works:
Imagine we have a molecule which contains a proton (let’s call it HA)
attached to a carbon, and that this carbon is attached to another carbon
which also contains a proton (let’s call it HB). It turns out that HA feels the
presence of HB. Recall that these protons are tiny little magnets, that can be
oriented either with or against the magnetic field of the NMR machine. When
the field created by HB reinforces the magnetic field of the NMR machine
(B0 ) HA feels a slightly stronger field, but when the field created by HB
opposes B0, HA feels a slightly weaker field. So, we see two signals for HA
depending on the alignment of HB. The same is true for HB, it can feel either
a slightly stronger or weaker field due to HA’s presence. So, rather than see
a single line for each of these protons, we see two lines for each.
For this line, H B is lined up For this line, H B is lined up
with the magnetic field against the magnetic field
(adds to the overall (subtracts from the overall
magnetic field, so the line magnetic field, so the line
comes at higher frequency) comes at lower frequency) HA HB

C C
HA HB
HA is split into two lines because HB is split into two lines because
it feels the magnetic field of H B. it feels the magnetic field of H A.
 More 1H - 1H Coupling
What happens when there is more than one proton splitting a neighboring
proton? We get more lines. Consider the molecule below where we have
two protons on one carbon and one proton on another.

Note that the signal produced

by HA + HA' is twice the size
of that produced by HB

HA HB

HA' C C
HA + HA' HB
HA and H A' appear at the same HB is split into three lines
chemical shift because they are because it feels the magnetic
in identical environments field of HA and HA'
They are also split into two lines
(called a doublet) because they
feel the magnetic field of HB.
 Why are There Three Lines for HB?

HB feels the splitting of both HA and HA’. So, let’s imagine starting with HB as
a single line, then let’s “turn on” the coupling from HA and HA’ one at a time:

HB If uncoupled, H B would appear as a

single t whe re the dashed line indicates
the chemical shift of the sin glet.

Now, let's "turn on" HB - HA coupling. This splits

the single line into two lines
HA HB
Now, let's "turn on" HB - HA' coupling. This
splits each of the two new lines into two lines,
HA' C C
bu t notice how the two lines in the middle
overlap. Overall, we then have three lines.

Because the two lines in the middle overlap, that line is twice as big as the
lines on the outside. More neighboring protons leads to more lines as shown
on the next slide.
 Splitting Patterns with Multiple Neighboring
Protons
If a proton has n neighboring protons that are equivalent, that proton will be
split into n+1 lines. So, if we have four equivalent neighbors, we will have
five lines, six equivalent neighbors… well, you can do the math. The lines
will not be of equal intensity, rather their intensity will be given by Pascal’s
triangle as shown below.relative intensities
no . of neighbors pa ttern example
0 1 singlet (s)

H H
1 1 1 do ublet (d)
C C
H H
2 1 2 1 triplet (t) C C H
H H

3 1 3 3 1 qu artet (q) C C H
H H H H

4 1 4 6 4 1 pe ntet C C C H

H H H H

5 1 5 10 10 5 1 sextet H C C C H
H H H H

6 1 6 15 20 15 6 1 septe t H C C C H
H H

We keep emphasizing that this pattern only holds for when the neighboring
protons are equivalent. Why is that? The answer is two slides away.
 More About Coupling
Earlier we said that protons couple to each other because they feel the
magnetic field of the neighboring protons. While this is true, the
mechanism by which they feel this field is complicated and is beyond the
scope of this class (they don’t just feel it through space, it’s transmitted
through the electrons in the bonds). It turns out that when two protons
appear at the same chemical shift, they do not split each other. So, in
EtBr, we have a CH3 next to a CH2, and each proton of the CH3 group is
only coupled to the protons of the CH2 group, not the other CH3 protons
because all the CH3 protons come at the same chemical shift.
The blue protons all come H H
The red protons both come
at the same chemical shift H C C Br at the same chemical shift
and do not split each other H H and do not split each other

H H
H H H C C Br
H C C Br H H
H H
 Not all Couplings are Equal
When protons couple to each other, they do so with a certain intensity. This
is called the “coupling constant.” Coupling constants can vary from 0 Hz
(which means that the protons are not coupled, even though they are
neighbors) to 16 Hz. Typically, they are around 7 Hz, but many molecules
contain coupling constants that vary significantly from that. So, what
happens when a molecule contains a proton which is coupled to two
different protons with different coupling constants? We get a different
pattern as described in the diagram below.

So, if the protons are not equivalent, they can have different coupling
constants and the resulting pattern will not be a triplet, but a “doublet of
doublets.” Sometimes, nonequivalent protons can be on the same carbon
 Coupling Constants in Alkenes
Coupling constants in alkenes can also differ depending on whether the
protons are cis or trans to each other. Note that in a terminal alkene (i.e., an
alkene at the end of a carbon chain), the cis and trans protons are NOT
equivalent. One is on the same side as the substituent, the other is on the
opposite side. The coupling of trans protons to each other is typically very
large, around 16 Hz, while the coupling of cis protons, while still large, is a
little smaller, around 12 Hz. This leads to the pattern shown below, and an
example of a molecule with this splitting pattern is shown on the next slide.
HA If uncoupled, HA would appear as a
single t where the dashed line indicates

12 Hz coupling 16 Hz Now, let's "turn on" HA - HX coupling. This splits

HA the single line into two lines that are 16 Hz appart

HM
12 Hz Now, let's "turn on" HA - HM coupling. This
12 Hz
splits each of the two new lines into two lines
16 Hz coupling that are 12 Hz appart for a total of four lin es
HX

There are other times when protons on the same carbon are nonequivalent,
which we’ll see later.
 H HO
HO CH3
A molecule with a terminal alkene
H

H
HO
HO
CH3
H H
H HO

H
H H HO HO
H
H

A molecule with a nine line splitting pattern

Me
OH
OH
Me

Nine lines, you just can't

Me
see two of them because
OH they are so small.
Me
H H Me
Me
OH H
Me OH
Me
3. Nuclear Magnetic Resonance
- NMR results from resonant absorption of
electromagnetic energy by a nucleus (mostly protons)
changing its spin orientation
- The resonance frequency depends on the chemical
environment of the nucleus giving a specific finger
print of particular groups (NMR spectroscopy)
- NMR is nondestructive and contact free
- Modern variants of NMR provide 3D structural
resolution of (not too large) proteins in solution
- NMR tomography (Magnetic resonance imaging,
MRI) is the most advanced and powerful imaging tool
154
Some history of NMR
1946 Principle of solid state NMR
(Bloch, Purcell)

1950 Resonance frequency depends

on chemical environment (Proctor, Yu)

1953 Overhauser effect

1956 First NMR spectra of protein
(Ribonuclease)

1965 Fourier Transform

spectroscopy (Ernst)
155
1973 Imaging tomography
(Mansfield)

1985 First protein structure (bovine

pancreatic trypsin inhibitor) in solution
(Wüthrich)

156
By now: More than 150 protein structures
(M < 60 000)

BPTI

Bound water

Protein dynamics 157

Functional MRI

158
 3.1 Principle of Nuclear Magnetic Resonance
Many (but not all) nuclei have a spin
(I). Quantum mechanically I can
have 2I+1 orientations in an
external magnetic field B.

This spin is associated with a

magnetic moment

gI: nuclear g-factor

159
Since biomatter is made of H,C,N and O, these are
the most relevant nuclei for biological NMR

160
 Mechanical (classical) model
B0 || z
Spinning top with magnetic
moment µL and angular
momentum I precesses with Larmor precession
frequency ωL under torque D α of µL around B0
B1
y
x Larmor precession
around B1
Torque on magnetic moment
µL in B0

The precession frequency is independent of α and equals the Larmor frequency

Application of a horizontal magnetic field B1 which
rotates at ωL:
In the frame rotating with µL the orientation of B1 relative to µL is constant

Additional precession of µL around B1 at frequency 161

Quantum mechanical description
The magnetic moment orients in a magnetic field B0. Different orientations
correspond to different energies
I = 1/2 1H, 13C, 31P
E
B0 mI = 1/2
gI = 5.58 B0
γ = 42.576 MHz/T mI = - 1/2

E When photons
I=1 2H, 14N,
B0 mI = 1 with frequency
ωL are absorbed
0 B0
a transition from
-1 the lower to the
upper level
23Na, E occurs. Selection
I = 3/2 mI = 3/2
B0 rule ΔmI = 1
1/2
B0
-1/2
- 3/2
162
 Bulk magnetization
A sample contains many nuclei (typically N ~ 1017 or higher). In
zero field all spin orientations are equivalent. The bulk
magnetization (I.e. is the sum of all m’s) is very small and
fluctuates around M=0.

At finite fields B0 (and finite temperature) the occupation of

states at different energies E obeys Boltzmann statistics exp(-
E/kBT) – thermal equilibrium is assumed. For I=1/2 the spin
state “parallel” to B0 has lower energy E1 than the “ antiparallel”
state with energy E2.

Therefore there is a net magnetization along the z-axis.

However since ΔE = E2 – E1 is much smaller than kBT the
magnetization is far from saturation.
163
The number of spins in state 1,2 is

Thus the population imbalance is

Which yields a bulk magnetization

with

The average magnetization in x,y vanishes because the

precessions of individual spins are uncorrelated. 164
The application of a pulse of duration t changes the average
angle of the magnetization by a certain angle (c.f. the
mechanical model or a change in population densities), given
by:
ϑ
t (ϑ ) =
γ B1
Thus a pulse of duration τ =2π/4 ω1 gives a change in angle of
π/2 – pulse I.e. the magnetization is flipped into the xy plane.
Mx and My now oscillate with ωL.
If M is flipped out of equilibrium (out of the z-direction) by a
B1- pulse, it will relax back to Mz into thermal equilibrium.
This occurs because of magnetic interaction of µ with the
environment (atoms, eventually in crystalline lattice) and is
characterized by the so–called longitudinal (or spin-lattice)
165
relaxation time T1.
This relaxation is described by a set of rate equations for the
transitions between the states
dnα
= W (nβ − nβ0 ) − W (nα − nα0 )
dt
dnβ 0 0
= W (nα − nα ) − W (nβ − nβ )
dt
Which yields a simple exponential relaxation of the
magnetization in the z-direction

166
The amplitudes of Mx and My decay with another relaxation
time T2 called spin-spin relaxation time. This relaxation
originates from inhomogeneity of B0 . It is described by
another phenomenological equation

y y

x
x

Immediately later
after π/2 pulse
167
To be complete, the precession in the static field has to be
taken into account as well, which is described by the Bloch
equations

One can detect the transverse

magnetization Mx or My by a pick
up coil where a current I(t) is
induced by the oscillating
transverse magnetization. The
width of the FT of I(t) provides a
measurement of T2 (Method of
free induction decay) 168
3.2 Classical NMR experiments

Absorption
signal

169
600 MHz Proton NMR Spectrometer

High frequency NMR

spectrometers require very
strong magnetic fields, which are
produced using super-cooled
coils (T = 4.2K, liquid He). The
superconducting coils are
surrounded by a giant vessel
containing liquid N2.

B0
k He
N2

170
B1
3.3 Chemical shift
The external field B0 is changed (reduced in amplitude) due to local field -σB0
generated by the diamagnetic currents induced by B0 in the electron system near
the nucleus. s is the shielding constant (diamagnetic susceptibility)

The shielding depends on the orientation

of B0 with respect to the molecules (e.g.
benzene ring) near the nucleus. σ is a
tensor. If the rotational motion of the
molecules is fast compared to 1/ωL the
precessing spin I sees an effective (time Motional narrowing! 13CNMR
averaged ) field Bloc. If the rotation is free spectrum of liquid
(like in most simple liquids) the anisotropy benzene
of the shielding is averaged out, σ
becomes a number. The NMR lines are
very narrow.
NB. In solids or large proteins in viscous
environment where motions are strongly
hindered or slowed down, the NMR lines 171
are significantly broader.
Usual measure: Frequency
shift of sample (1) relative to
some reference sample (2);
unit: ppm

Origin of chemical shift: =

shielding of B0 172
Examples: 13C NMR
Benzene C6H6

All 6 carbons are identical

same chemical shift, one line

Toluene C6H5-CH3

5 different types of
C-atoms, 5 lines
173
1H-NMR of ethyl alcohol, CH3CH2OH
Three types of protons

CH3 OH

CH2
175
Typical chemical shifts Reference Tetramethylsilane Si (CH3) 4
Has very narrow line

Chemical shifts are frequently used in chemistry and biology to

determine amount of specific groups in sample (quantitative
176
spectroscopy)
177