1
Notation for Spin Systems
Capital letters A, B, C, M, A, X, Y, …….
Same letter = same chemical shift (A3, B2, X6, ….)
Different letters = different chemical shifts
Letters close in the alphabet (A, B, C, …)
J [Hz] of the same magnitude as  [Hz]
Letters separated in the alphabet (A, M, X,…)
large separation of chemical shifts
-different nuclei (1H, 31P, 195Pt,…)
-same nuclei but  [Hz] much larger than J
!! [Hz] depends on B0 !!
2
Notation for Spin Systems
CH2Cl2
A2
H
H Cl
Cl
Same letter = same chemical shift (A3, B2, X6, ….)
3
Notation for Spin Systems
CH2F2 A2X2
Different letters = different chemical shifts
4
Notation for Spin Systems
Two situations:
a) Complete equivalence =
Chemical shift equivalence (isochronous nuclei)
+ magnetic (spin-coupling) equivalence (isotachous)
Magnetic equivalence = each member of one group of
spins is coupled equally to all members of any
other group
A2B2, A2X2,….
5
Notation for Spin Systems
b) Chemical shift equivalence, magnetic INequivalence
AA’BB’, AA’XX’, AA’A’’XX’X’’, ….
P
N
P
N
P
N
F F
F
F F
F
31P & 19F NMR
AA’A”XX’X”X’’’X4X5 [A[X]2]3
6
Magnetic Inequivalence
AA’XX’ A2X2
H P P H H
P
H
P
7
Prime vs. Bracket Notation
AA’BB’ [AB]2
A2B2 [A2B2]
AA’BXX’ [AX]2B
AA’X3X3’ [AX3]2
8
Magnetic Inequivalence
9
Magnetic Inequivalence
10
Bracket Notation
• Square brackets with subscript indicate repeated
symmetry-related magnetically inequivalent groups of
nuclei, e.g. [AB]2
• Square bracket without subscript indicate magnetic
equivalence of isochronous nuclei inside, e.g. [A6]
• Each bracket represents a specific symmetry operation
(see anthracene)
• Append a point group symbol to avoid ambiguity
• Free rotation – apply Mortimer rule = the most
symmetrical conformer
11
Notation for Spin Systems
H H
H
H
H H
H
H
H
H
1H NMR
BB’AA’CC’A’’A’’’B’’B’’’
σV2
σV1
[[AB]2C]2
12
Notation for Spin Systems
[[A]2B]2
B'
B
A
A'
A''
A'''
Ring plane Plane perpendicular to ring
13
Notation for Spin Systems
C
H
H
HH
H
H
13C NMR
considering isotope shift: A[BC]2DX
14
Spin Systems in 1H NMR
When separated by
more than 3 bonds, the
spin systems can be
considered separately
(with exceptions)
15
Spin Systems
P
M
H
P H
HP
H
M
H
P P
HP
fac mer
AA’A’’XX’X’’ AB2XY2
3JPH(cis) = 10 – 40 Hz
3JPH(trans) = 80 – 150 Hz
16
Spin Systems
P
R
N
P
N
R
S
S
Me
S
Me
S
P
R
N
P
N
R
S
S
Me
S
Me
S
1H, 31P
13C, 31P
17
Spin Systems
P
R
N
P
N
S
S
Me
S
Me
S
P
R
N
P
N
S
S
Me
S
Me
S
18
Spin Systems
P
R
N
P
N
S
S
Me
S
Me
S
P
R
N
P
N
S
S
Me
S
Me
SH H H H
1H, 31P
19
AB System
20
AB System
Hz (t1)
50100150200
0.00
0.50
1.00
1.50
32
41
4
3
1
2
3241
4321
))((









I
I
I
I
J
BAAB
AB
JAB JAB
2
1
3
4
The simplest higher-order
spin system
AB
21
AB2 Spin System
A = 3
B = ½ (5 + 7)
JAB = 1/3(1  4 + 6  8)
22
ABX Spin System
H
CC
Br
H
Br
BrBr
AB part = 2 AB pseudoquartets = 8 lines
X part = 6 lines
PP
O
O
13C, 31P1H, 13C
23
AB Part of the ABX Spin System
1
23
4
5
67
8
AB
24
ABX Spin System
NMidp
L
NMidp
L
JJN
JJL
JJ
J
BA
AB
BLUE
AB
BA
AB
RED
AB
BXAX
BXAX
BAAB
BXAX
AB
2
1
2
1
6758
2
1
2
1
2314
2
1
2
1
912
78563412
)(
))((
)(
))((
)(
)(
















25
X Part of the ABX Spin System
9101112
1415
)(2
1
912
BXAX
BXAX
JJN
JJ

 
X
26
AA’XX’ Spin System
4 coupling constants
O
A A'
X'X
JXX'
JAA'
JAX JAX'
Both part A and part X
feature the same multiplet
symmetrical about A or X
Both parts have 12 lines
with a center of symmetry
at A or X
'
'
''
''
AXAX
AXAX
XXAA
XXAA
JJL
JJN
JJM
JJK




27
AA’XX’ Spin System
N
M
K X
1,2 3,4
5
6 7
8
9
10 11
12
28
AA’XX’ Spin System
85
76
7
8
6
5
129
1110
11
12
10
9
121110987654,32,1
'11101298576
''1211109
''8765
'4,32,1
))(())((




















I
I
I
I
I
I
I
I
IIII
JJL
JJM
JJK
JJN
AXAX
XXAA
XXAA
AXAX
29
AA’XnXn’ Spin System
M PP CH3H3C
1H and 31P AA’X3X3’
1H and 31P AA’X9X9’
30
P8O12· 2BH3
31
P8O12· 2BH3
C2h Molecular symmetry
31P Spin system AA’BB’B’’B’’’XX’
Nuclei δ [ppm]
PA: P4, P8 82.65
PB: P2, P3, P6, P7 80.95
PX: P1, P5 70.5
H 0.8
Coupling constants [Hz]
2JAB: J 2-4, J 3-4, J 6-8, J 7-8 29.2
2JBX: J 1-2, J 1-3, J 5-6, J 5-7 24.0
2JAX: J 1-8, J 4-5 11.4
JAH: J 4-H, J 8-H 7.5
P7
P1
O
P2
O
O
P3
O
O
P4
O
P5
O
O
P8
O
O
O
O
P6
H3B
BH3
32
P8O12· 2BH3
33
Coupling Patterns
F3C
B C O
F3C
F3C
34
F3C
B C
O
F3C
F3C
OH
35
36
37
38
39
F3C
B C P
F3C
F3C
MestReNova
40
Simulations of NMR spectra