Notation for Spin Systems
Capital letters
iiirfMtiliiiiliiiBil
^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 Av [Hz]
Letters separated in the alphabet (A, M, X,...)
large separation of chemical shifts -different nuclei ^H, 31P, 195Pt,...) -same nuclei but Av [Hz] much larger than J !! Av [Hz] depends on B0 !!
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Notation for Spin Systems
^Same letter = same chemical shift (A3, B2, X6, ...
h Cl
Ih Cl
Notation for Spin Systems
^Different letters = different chemical shifts
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> • • •
Notation for Spin Systems
b) Chemical shift equivalence, magnetic INequivalence AA'BB', AA'XX', AA'A"XX'X", ....
Magnetic Inequivalence
AA'BB'
H-P-P-H H
P
Prime vs. Bracket Notation
AA'BB
AA'BXX'
AA'X3X3'
[AB]
[A2B2]
[AX]2B
[AX3]2
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Magnetic Inequivalence
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
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Notation for Spin Systems
HUH
aV2
BB,AA'CC'A"A'"B"B'"
[[ABJ2CJ2
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Notation for Spin Systems
[[A]2B]2
King plane Plane perpendicular to ring
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Notation for Spin Systems
considering isotope shift: A[BC]2DX
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Spin Systems in aH NMR
When separated by more than 3 bonds, the spin systems can be considered separately (with exceptions)
Spin Systems
	3 h	
fac		
AAWXX'X" AB2XY2 3JPH(cis) = 10 - 40 Hz 3JPH(trans) = 80 -150 Hz		
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Spin Systems
13c, 31P
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Spin Systems
Spin Systems
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AB System
The simplest higher-order spin system
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A vAB _ vA - vB =<J(yx - v4 )(v2 - v3) 12
13 _vx - v4
14 v2 - v3
4
AB
— 1.00
- 0.50
0.00
1 r
50
Hz (t1)
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Spin-spin coupling
AB System
AB
AB
A       AvAB B
J
J
Av
AB
'AB
AB
Av
AB
AVab
»1
! AB
Av
>1
Av
<1
marks the chemical shifts
Increasing Frequency
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AB2 Spin System
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ABX Spin System
O
AB part = 2 AB pseudoquartets = 8 lines
X part = 6 lines
AB Part of the ABX Spin System
ABX Spin System
= v2 -vx = v4 -v3 = v6 -v5 = v8 -v7
MJAX + JBX =V12 -V9
JBX ) JBX )
Midp =
)
Midp = 2(
)
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X Part of the ABX Spin System
12 11 10 9
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A
1
JAX + JBX = V12 -V9
N = -j (JAX + JBX)
14
X
n-1-r
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AA'XX' Spin System
4 coupling constants
Both part A and part X feature the same multiplet
symmetrical about vA or vX
with a center of symmetry at vA or vX
K = JAA' + JXX'
M = J AA, - J
AA'
N = JAX + JAX' L = JAX - JAX'
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AA'XX' Spin System
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AA'XX' Spin System
= vi,2 - v3
3,4
= v5 - v6 = v7 - v8
JAA' + JXX<
AA
XX
N K
M = v9 - v10 = v11 - v12 L = V(v6 - v7 )(v5 - v8) = ^/(v9 - v12 )(v10 - v11)
1,2        3,4        5+6+7+8        9+10+11+12 A. = I_YL = v10 -v11 A1       v9 -v12
I5   I8   v6 - v7
- = - = -
I 6    I 7    v 5 -v 8
J      — J
AX AX
AA'X3X3' Spin System
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F3C
F3C ^
F3C
Figure 7. ieF NMR spectra of (CF^BCO (left). [(CF3)3BC(0)OH]" (right) and [(CF^BCO:]:
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i.
Ti
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