1
Four Contributions to the Resonance
Frequency of Nuclei in Matter
 B
1) Shielding, chemical shift
electron distribution around nuclei, induced magnetic field
2) Dipolar interactions
magnetic nuclei distribution, through space interactions, in solids
3) Electric field gradient
distribution of nuclei (positive charge) and electrons (negative charge)
quadrupolar nuclei
4) Scalar coupling
dipolar interactions through electrons in molecules, bonds
ALL TENSORS
2
Nuclear Spin Interactions
Shielding, Chemical shift
3
ν = γ B/2π
4
Chemical Shift Information
• (The presence of an element in the sample)
• Number of signals = number of chemically different atoms
Symmetry of the molecule
• Relative intensity = ratio of atoms – integration
• Position = chemical shielding / shift – electronic
environment, type of bonds, oxidation state,
coordination number
• Multiplicity = connectivity of functional groups, J-coupling
5
Chemical Shift Information
Cl3P
N
C
ClN
PCl3
Cl3P
CH
C
ClN
PCl3
PCl5 + CH3CN
X-ray crystallography 1
H NMR (6.3 ppm, dd 43 and 13 Hz)
The presence of an element in the sample
6
Chemical Shift
1H NMR spectrum
7
Chemical Shift
CH3CH2OH
Chemical shift for a given molecule:
• Number of signals = nonequivalent nuclei
molecular symmetry
• Relative intensity = number of nuclei
• Position in the spectrum = shielding/chemical shift
electronic structure
• Multiplicity = connectivity of atoms and groups
8
Molecular Symmetry
Flow chart for point group determination
Number of signals = nonequivalent nuclei, molecular symmetry
9
Symmetry Elements and Operations
Symbol Element Operation
E Identity Identity No change, (= 1)
i Center of symmetry
(inversion center)
POINT
Inversion Inversion through
the central point
every point x,y,z
translated to -x,-y,-z
Cn
Rotation axis
LINE
True (proper)
rotation
Rotation by an angle
360/n
 Plane of symmetry,
mirror PLANE
Reflection Reflection through
a mirror plane
Sn
Improper axis
Roto-reflection axis
LINE
Improper rotation Rotation by an angle
360/n followed by
reflection through a
mirror plane
10
Inversion Center
NO inversion center
11
s
y
z
x
px
y
z
x
y
z
x
y
z
x
py pz
dxy
dyz dx2 - y2
dz2
x
y
z
dxz
x
y
z
x
y
z
x
y
z
x
y
z
Inversion Center
12
Rotation Axis C2
Rotation by 360/n about Cn brings the
object to an indistinguishable position
from the original
13
Rotation Axis C3
14
Rotation Axis C4
C4
1  C4
2  C4
3  C4
4 = E
F
Xe
F
FF
Cl
Pt
Cl
ClCl
2 H3N
Cu
NH3
NH3H3N
2
15
Rotation Axis C
C5, C6, C7,...................................... C
Linear molecules
16
Plane of Symmetry 
F
B
F
F
CH3
H3C CH3
17
Plane of Symmetry 
h = horizontal plane, perpendicular to principal axis
v = vertical plane, parallel to principal axis, bisects the most atoms
d = dihedral plane, colinear with principal axis, bisecting two C2'
Planar molecules – symmetry plane of the molecule
18
Plane of Symmetry 
19
Improper Axis Sn
S1 = C1  =  S2 = C2  = i
Rotation-reflection = a compound operation, rotation (Cn)
followed by a reflection through a plane perpendicular to the
Cn axis
20
Improper Axis Sn
C
H H
HH
S4
BF3, C6H6
21
Symmetry Elements in a Molecule
Equivalent atoms = exchanged by symmetry operations
F4 = F5 F1 = F2 = F3
22
Chirality
23
Chirality
Condition of chirality: no Sn present in a molecule
S1 = 
S2 = i
C2
24
Chemical Shift
Re
C
O
Si
Ph
Ph
Ph
CH
C
H2
Chemically different atoms
13C NMR
Geometrical difference = chemical difference
3 x t-Bu groups
No C3 axis
Number of signals = nonequivalent nuclei
25
Molecular Symmetry
N
N
1 x Me group signal
C2 axis
26
Chemical Shift
Si
O
Si
O
Si
O
Si
O
O
Si
O Si
O
O
Si
O
O
Si
O
O
R O
R
R
R
R
R
R
Ta
27
Chemical Shift
C
R
C P
P
C
R
P
C
R
R
P
C
P
P C
RR
P
P
P
P
R
R
R
R
28
Chemical Shift
P
Sn Sn
P
Li Li
P
Li Li
P
Sn Sn
P P
O
S
H
W
W
Cl
Cl
Cl
Cl
ClCl
H
Cl
Cl
H
Br
Br
H
Re
Re
O
OO
O
O
O O
S
S
S
O
O
O
O
O
O
O
O
B
N B
N
N B
NB
R
R
R
R
R
RR
R
N
As
P
N
P
N
N
Me
Me
N
As
Me3Si Cl
N
SiMe3
Cl
29
1H NMR (600 MHz, CDCl3, TMS):
3.25 (s, 2H, H-2’ and H-6’),
1.70 (br s, 2H, H-1 and H-3),
1.57 (br s, 2H, H-5 and H-7),
1.55 (br s, 4H, H-4, 8, 9, 10),
1.45 (m, 6H, H-4, 8, 9, 10 and H-6),
1.34 (m, 4H, H-3’ and H-5’),
0.96 ppm (m, 2H, H-4’)
13C NMR (75 MHz, CDCl3, TMS):
102.2 (C-8’=C-2),
80.8 (2C, C-2’ and C-6’),
40.0 (4C, C-4, 8, 9, 10),
39.1 (C-6),
29.2 (2C, C-5 and C-7),
28.7 (2C, C-1 and C-3),
22.3 (2C, C-3’ and C-5’),
20.8 (C-4’),
20.2 ppm (2C, C-1’ and C-7’).
30
Chemical Shift
S
11B NMR
31
Chemical Shift
C
C
C
C
H
C
C
HH
H
H
H
11B NMR
Isomers of B10H10C2H2
32
Chemical Shift
11B NMR
Mono- and Disubstituted B12H12
2- Molecules with
Identical Substituents
33
Chemical Shift
11B NMR
34
Chemical Shift
1
2
34
5
6
7
8
9
10 11
1
2
34
5
6
7
8
9
10 11
11B NMR
35
11B NMR
36
Fullerenes
Icosahedron Truncated icosahedron
37
Chemical Shift
 (13C) = 143 ppm
a
b
c d e
C60
C7
0
38
Chemical Shift
a b
c d
e
a 150.07
c 147.52
b 146.82
d 144.77
e 130.28
 (13C) ppm
39
Geminal Groups
Geminal groups – paired ligands
Y-E-Y: CH2, C(CH3)2, CF2, SiMe2, P(CH3)2, …
40
Prochiral Groups
O
P
O
O
O
S
P
18
O
O
O
S
P
O
O
O
S
P
18
O 17
O
O
pro
pro
pro chiral
pro
pro chiral
pro chiral chiral
Substitution
Symmetry
41
Geminal groups in Prochiral
Groups
CMe Me
X
H
SiMe Me
X
H
CF3
C CF3
O
H
X
PMeO OMe
X
O
CH H
X
PhMe
X
HH C
PMe Me
Ph
M
NMe Me
X
Ph
NMe Me
X
A
X = rest of the molecule
M = transition metal fragment
A = Lewis acid
CMe3Si SiMe3
SiMe Me
42
Chemical Shift Nonequivalence of Geminal
Ligands in Prochiral Groups
X
ClMe C
H
Chiral Group
X
MeMe C
H
Prochiral Group
X
MeMe C
X
C2 Group
Me, Me Homotopic
Equivalent (isochronous)
X
MeMe C
H
No present
Me, Me Enantiotopic
Equivalent (isochronous) in achiral media
Nonequivalent (anisochronous) in chiral
media
Me, Me Diastereotopic
Nonequivalent (anisochronous)
If X is chiral, the paired ligands
in a prochiral group are always
diastereotoppic
X
MeMe C
H

Geminal groups
43
Substitution Test of Geminal Groups
44
Chemical Shift Nonequivalence in
Prochiral Groups
Ir
Cl PMe2
Ph
PhMe2
P CO
Cl
Cl
Ir
PhMe2
P Cl
PhMe2
P Cl
CO
Cl
mer-Cl, trans-P fac-Cl, cis-P
45
Chemical Shift Nonequivalence in
Prochiral Groups
F
Ti
F
Me
F F
Al
Me Me
F
Al
F
Me Me
Me
Ti
46
Chemical Shift Nonequivalence in
Prochiral Groups
P
Al
N
CH2SiMe3
CH2SiMe3
R
Ph
Ph
R = Me
R = 2-butyl
Pyramidal N - Fast inversion on N
47
Chemical Shift Nonequivalence in
Prochiral Groups
R = Et
N
S
N
S
As
R
R = iPr
48
49
50
[4] triangulane
H
H H
H
H H
HH
H H
H
H
51
Prochiral Groups
B
N
CH3
CH3
CH3
Ar
Ar
Ar = mesityl CH3
H3C
CH3
O3S-CF3
1H NMR spectrum
6 CH aromatic signals How many CH2 signals ?
6 CH3 mesityl signals
52
Prochiral Groups
1H NMR spectrum
6 CH aromatic signals
6 CH3 mesityl signals
B
N
CH3
CH3
CH3
Ar
Ar
Ar = mesityl CH3
H3C
CH3
O3S-CF3
Ha
Hb
The methylene hydrogens are diastereotopic
two signals at 3.69 and 4.81 ppm
steric congestion
53
Chemical Shift
Chemical shift for a given molecule:
• Number of signals = nonequivalent nuclei
molecular symmetry
• Relative intensity = number of nuclei
• Position in the spectrum = shielding/chemical shift
electronic structure
• Multiplicity = connectivity of atoms and groups
54
Integration
The area under each signal is proportional to the number
of protons that give rise to that signal
The height of each integration step is proportional to the
area under a specific signal
The integration tells us the relative number of protons
that give rise to each signal, not absolute number
55
Relative Signal Intensity
9 H / 2 H
56
Polyphosphate Chain Length
-24-24-22-22-20-20-18-18-16-16-14-14-12-12-10-10-8-8-6-6-4-4-2-200224466
200.0
1950.3
O
PHO
OH
O P
O
OH
O P
O
OH
OH
n
END
MIDDLE
2222 




 

E
M
E
EM
END
TOTAL
I
I
I
II
P
P
n
57
Relative Signal Intensity
1H NMR spectrum of a mixture of n-propanol and n-butanol
Estimate their ratio