Che 440/540
Proton Nuclear Magnetic Resonance (NMR) Spectroscopy
Fundamental NMR Equations
Number of energy levels = 2I + 1
I = the spin quantum number (1/2 for 1H and 13C)
Therefore, there are two possible spin states for these nuclei.
E = h;
h = Planck’s constant,
 = resonant frequency, Hz
 = Bo/2
Bo = applied magnetic field
 = gyromagnetic ratio (unique for each NMR active nucleus)
E = hBo/2
Characteristics of Some NMR Active Nuclei
Natural %
Spin (I)
Abundance
Isotope
Magnetic
Magnetogyric
Moment (μ)* Ratio (γ)†
1H
99.9844
1/2
2.7927
26,753
2H
0.0156
1
0.8574
4,107
11B
81.17
3/2
2.6880
--
13C
1.108
1/2
0.7022
6,728
17O
0.037
5/2
-1.8930
-3,628
19F
100.0
1/2
2.6273
25,179
29Si
4.700
1/2
-0.5555
-5,319
31P
100.0
1/2
1.1305
10,840
* μ in units of nuclear magnetons = 5.05078•10-27 JT-1
† γ in units of 107 rad T-1 sec-1
Nuclear Spins in the Absence and Presence of a Magnetic Field
no magnetic field present
Bo
Slide by Joanna LeFevre
magnetic field present
 spin state
 spin state
(slight excess)
N/N = e-E/kT
For a 300 MHz instrument, N/N = 1,000,000/1,000,048.
Therefore, for every two million nuclei, there are only 48
excess nuclei in the  spin state!! Therefore NMR is an
inherently insensitive technique.
http://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/nmr1.htm
A spinning gyroscope
in a gravitational field
I = +1/2
A spinning charge
in a magnetic field
magnetic moment, μ
I = -1/2
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Net Macroscopic Magnetization of a Sample in an External Magnetic Field Bo
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Excitation by RF Energy and Subsequent Relaxation
T1 = spin-lattice relaxation time; establishes the z axis equilibrium. T1’s
are usually short (<1 sec) in 1H NMR. They can be quite long (>1 min) in 13C NMR.
T2 = spin-spin relaxation time; causes a decrease in magnetization in the x-y plane.
For a good magnet, T2 = 1-2 sec.
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Generation and Fourier Transformation (FT)
of a Free Induction Decay (FID) Pattern
Complex summation wave (FID)
Four different frequencies
Fourier
transformation
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse
Free Induction Decay (FID) Signal:
A Decaying Cosine Curve
5 Hz signal
Assume T2 = 2 sec
It = Ioe-t/T2
~35% of signal remains after 2 sec.
0
1
2
3
4
5
seconds
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#pulse
Portion of the FID of Betulin
H
H
OH
H
HO
0.02
0.02
0.04
0.04
0.06
0.06
Time (sec)
0.08
0.08
H
0.10
0.1
1H
Spectrum of Betulin after Fourier Transformation
H
H
OH
H
HO
5.0
4.5
H
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Presentation of NMR Data
 = chemical shift (Hz) – shift of tetramethyl silane (TMS; 0 Hz) = ppm
spectrometer frequency (MHz)
For example, in CH2Cl2 a sharp
singlet occurs at 1,590 Hz using a
300 MHz spectrometer frequency.
The chemical shift is:
(1,590 – 0) Hz = 5.3 ppm
300 MHz
Shielding vs Deshielding
CH3
ClCH2
C CH2Cl
CH3
Downfield
Increasing deshielding
Increasing shielding, Bo
Upfield
Compound, CH3X
CH3F
CH3OH
CH3Cl
CH3Br
CH3I
CH4
(CH3)4Si
X
F
O
Cl
Br
I
H
Si
Electronegativity of X
4.0
3.5
3.1
2.8
2.5
2.1
1.8
Chemical shift,  / ppm
4.26
3.4
3.05
2.68
2.16
0.23
0
Electronegative groups attached to the C-H system decrease the electron density around
the protons, and there is less shielding (i.e. deshielding) so the chemical shift increases.
These effects are cumulative, so the presence of more electronegative
groups produce more deshielding and therefore, larger chemical shifts.
Compound
 / ppm
CH4
CH3Cl
CH2Cl2
CHCl3
0.23
3.05
5.30
7.27
Anisotropic Shielding and Deshielding
http://www.chem.ucalgary.ca/courses/351/Carey/Useful/nmr1.gif&imgrefurl
1H
NMR Spectrum of 4-Methylbezaldehyde
CH3
H
H
O
deshielded
protons
H
Chemical Shifts of Various Protons
R
R
NH
OH
R
Ph
Me
OH
(R)
HO CH3
R
TMS = Me
Ph CH3
R
R
O
O
R
NR2 O
Cl
H
H
H
R
OCH3
H
CH3
CH3
Si Me
Me
R
CH3
CH3
TMS
10
9
Dow nfie ldregion
of the spectrum
8
7
6
5
ppm
4
3
2
http://orgchem.colorado.edu/hndbksupport/nmrtheory/NMRtutorial.html
1
0
Upfie ld region
of the spectrum
Integrations: Relative Numbers of Protons
O
H3C
CH3
O
3
CH3
CH3
1
1H
NMR Spectrum of Isopentyl Acetate
CH3
H3C
O
O
CH3
6H
2H
1H
3H
2H
Spin-Spin Splitting: The n+1 rule in Vicinal Coupling (HA-C-C-HB)
Equivalent nuclei do not couple each other.
The number of lines in a multiplet is determined by the number of
equivalent protons on neighboring atoms plus one, i.e. the n + 1 rule
The distance between the peaks is called the coupling constant (3J).
The coupling constant is not dependent on the applied field strength.
B
A
B
B
JAB = 7 Hz
JAB = 7 Hz
The Origin of Spin-Spin Splitting
CH3
CH2 OH
http://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/nmr1.htm
Some Common Splitting Patterns
Condition for Applying the n+1 Rule
HA HB HA'
C
C
C
If JHA-HB = JHA’-HB then the n+1 rule
applies and HB appears as a 1:2:1 triplet.
However, if the relevant J values are not the same, the splitting is more complex.
Example: Cis and Trans Coupling in a Carbon-Carbon Double Bond
HA
12 Hz
HX
O
16 Hz
HM
HA
HX
O
HM
CH2CH2Cl
The Karplus Relationship
The vicinal coupling constant (3J) is dependent upon the dihedral angle, .
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Menthol
CH3
H1
CH3
H3C
OH
H3C
CH3
H6(eq)
HO
H2(ax)
H6(ax)
CH3
H1
3.70
3.60
3.50
3.40
3.30
3.20
3.10
Some Alkene Splitting Patterns
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Typical 1H-1H Coupling Constants
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm
First-Order Coupling
The splitting pattern shown below displays the ideal or
"First-Order" arrangement of lines. This is usually observed
if the spin-coupled nuclei have very different chemical shifts.
The condition that must be met is /J > 6. Consider ethyl acetate.
HA = 1.26 ppm x 90 Hz/ppm = 113.4 Hz
HC = 4.11 ppm x 90 Hz/ppm = 369.9 Hz
/J = (369.9 – 113.4)Hz/7.2 Hz = 35.6
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Second-Order Coupling
However, if the ratio of Δν to J decreases to less than 10
a significant distortion of the expected pattern will take place.
First-order
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Example of a Second-Order Coupling Pattern
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Magnetic Non-equivalence
H(A) and H(B) are magnetically non-equivalent.
H(A) and H(A)* couple differently to H(B) [and to H(B*)].
*
*
Para and Meta-Disubstituted Benzene Rings
NO 2
NO2
Cl
Cl
Mono-Substituted Benzene Ring
Increasing the field strength leads to greater dispersion of signals.
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm#nmr12b
Chemical Shift Equivalence
H’s are homotopic:
Related by a 180o rotational axis, Cn.
They have the same chemical shift.
H
C
H
Chemical Shift Equivalence
H’s are enantiotopic:
Related by a mirror plane, .
They have the same chemical shift.
H
C NH2
H
Chemical Shift Equivalence
HA and HB are diastereotopic: They are not related by a rotational axis or a
mirror plane. They have different chemical shifts, and they split each other.
HB
H
C
HA
NH2
CO 2H
Homotopic Methyl Groups
These methyls are homotopic: they are
related by a 180o rotational axis, Cn.
They have the same chemical shift.
CH3
Cl
Cl
CH3
Enantiotopic Methyl Groups
These methyls are enantiotopic:
They are related by a mirror plane, .
They have the same chemical shift.
CH3
HO
CH3
Diastereotopic Methyl Groups
These methyls are diastereotopic: They are not related by a
rotational axis or a mirror plane. They have different chemical shifts.
Notice that a chiral center* is present.
H CH3
CH3O
C
H
OH CH3
Compare with isopentyl acetate
(enantiotopic methyls)
O
H3CCOCH2CH2
CH3
H
CH3
For the following molecules label any groups that
are homotopic, enantiotopic, or diastereotopic.
O
H3C
Br
CH3
Br
CH3
O
OH
CH3
OCCH3
HO
N
H
OCH3
NOE Difference Spectra of Pamoic Acid
NOE
Hd
He
Hc
CO2H
Hb
OH
NOE
Ha
Hd
CH2
OH
CO2H
Ha
http://www.cis.rit.edu/class/schp740/docu/avance/noediff.pdf
NOE Difference Spectrum of Betulin
Hcis
Htrans
NOE
H3C
H
OH
NOE difference spectrum
normal spectrum
4.90
4.80
4.70
4.60
4.50
4.40
Pople Notation: Describes sets of spins
If /J > 8, the pattern is called AX (i.e. ethyl acetate).
CH3CO2CH2CH3:
A3X2
A3
X2
If /J < 8, the pattern is called AB (i.e. 2-chloroacrylonitrile)
A
H
CN
H
Cl
B
Three weakly coupled sets are designated AMX; (i.e. styrene)
HX
M
HA
HM
X
A
AA’XX’ pattern
CO 2H
Cl
AA’BB’ pattern
*
*
A compound whose 1H NMR spectrum appears below has a molecular
formula of C7H14O2. The IR spectrum shows a strong absorbance at
1739 cm-1. Suggest a structure for this compound.
23 mm
23 mm
15 mm
15 mm
15 mm
15 mm