CH303.5
Today:
Non-first-order spectra
Magnetic inequivalence
Non-first-order NMR spectra
If δA - δB ≤ JAB, the NMR spectrum will not be first order (note the use of adjacent
letters of the alphabet in this case). Non-first-order NMR spectra are typically
complex and require computer simulation for the determination of the chemical
shifts and coupling constants.
Non-f irst order AB system
Figure on the right illustrates how an AB
system is going to appear in NMR
spectra depending on δA - δB. As the
difference becomes small, so the outer
lines of the resonances of A and B
become small.
“Roof effect”
A
B
-20 -10 0 10 20 Hz
2
Non-first-order AB2 spectra.
Example: 1,2,2-trichloroethane
The chemical shifts and coupling
constants in a first-order AM2 spin
system can be directly measured from
the spectra. The non-first-order AB2
spectra are characterized by splittings
that do not correspond to coupling
constants, by distorted intensities, by
chemical shifts that are not at the
M2
A
5.77
3J
AM = 6 Hz
3.99
200 MHz
5.82
5.34
4.86
4.38
3.90
4.31
3.75
60 MHz
6.00
5.44
4.87
B2
resonances’ midpoints, and by
resonance multiplicities that do not
follow the n+1 rule.
A
20 MHz
6.50
5.75
5.00
4.25
3.50
3
Non-first-order ABC spectra.
Example: Methylacrylate
5.84
H
H
6.34
6.13
H
3.76
O
O
The following are examples of AMX
(first-order) and ABC (non-first-order)
spin systems. The ABC spectra have
a complicated appearance. Such
patterns often require computer
simulation to determine the chemicals
shifts and coupling constants.
4
Non-first-order ABX spectra.
Example:
A particularly subtle example of
non-first order complexity occurs
in an ABX spectrum when δA and
δB are very close and JAX is zero.
With no coupling to A, the X part
should be a simple doublet from
coupling to B (which is the case in
an AMX system). Since A and B
are closely coupled, the spin
states of A and B are mixed, and
the X resonance appears split by
the B spins. This phenomenon
has been termed virtual coupling.
5
Magnetic equivalence
The nuclei are said to be chemically equivalent when they have the same
environments. It is important to distinguish chemical equivalence from magnetic
equivalence.
Two nuclei are magnetically equivalent if they are identically coupled with other
spins in the molecule.
Here are examples of chemically AND magnetically equivalent protons:
X
J AX
A
A
J AX
A
X
X
A
2
J AX
2 2
6
Magnetic inequivalence
Here are examples of chemically equivalent AND magnetically inequivalent
protons.
Note that 3JAX ≠ 4JA’X in the first example and 3JAX(cis) ≠ 3JA’X(trans) in the second.
Except when there are certain fortuitous combinations of the coupling constants,
spectra of magnetically inequivalent nuclei can never be first-order!
7
Examples of magnetic inequivalence
Example: 90 MHz 1H NMR spectrum of 1,1-difluoroethene in CDCl3.
AA' part
AA'XX'
4.4
4.0
3.6
3.2 ppm
Example: 300 MHz 1H NMR spectrum of p-chloronitrobenzene in CDCl3.
NO2
HA
HA'
HB
HB'
Cl
8
Examples of magnetic inequivalence
Example: 300 MHz 1H NMR spectrum of o-dichlorobenzene in CDCl3.
Cl
HA
Cl
HB
HA'
HB'
Example: 300 MHz 1H NMR spectrum of 2-phenyl-1,3-dioxolane in CDCl3.
HB'
H
HA'B HA
O
H
O
Ph
9
Virtual coupling in non-first-order spectra
An AA'M2M'2 spin system normally
gives a non-first-order NMR
spectrum. The appearance,
however, depends on the coupling
constants. The first spectrum on
the right was calculated with 3JAA'
= 100 Hz and looks deceptively
simple. The M2M'2 part appears as
a triplet (often called virtual triplet).
The multiplicity may suggest an
A2M4 system - which is not the
case.
M2M'2
5.20
3J
3
AM = JA'M' = 6.6 Hz
4J
4
AM' = JA'M = 0 Hz
AA'
5.95
3J
6.25
5.91
100 Hz
5.57
3J
6.25
AA' =
5.91
5.24
4.90
5.24
4.90
AA' = 40 Hz
5.57
Only when 3JAA' is small the true
complexity is revealed.
3J
6.25
5.91
AA' = 15 Hz
5.57
10
5.24
4.90