1st-order spin-spin coupling
We observe 1st-order NMR spectra when the frequency difference
between the chemical shifts of any given pair of nuclei is much
larger than the value of the coupling constant between them
∆ν/J > 10
and any set of chemically equivalent nuclei is also magnetically
equivalent.
1st-order NMR spectra exhibit a number of simple characteristics:
• Multiplicities that result from coupling reflect the 2nI + 1 rule
(I = nuclear spin quantum number e.g. IH = ½);
• The intensities of spin-spin multiplets correspond to Pascal’s triangle
for I = ½;
• Nuclei with the same chemical shift do not split each other, even
when the coupling constant between them is not zero;
• Spacings between adjacent components of a spin-spin multiplet are
equal to J;
• Spin-spin multiplets are centred on the resonance frequency;
1
2nd-order spin-spin coupling
We observe 2nd-order NMR spectra when the frequency difference
between the chemical shifts of any given pair of nuclei is small
compared to the value of the coupling constant between them
∆ν/J < 10
and/or any set of chemically equivalent nuclei is not magnetically
equivalent.
Nuclei are chemically equivalent if they can be interchanged by a
symmetry operation of the molecule. Nuclei that are interchangeable
by a rotation (Cn) are said to be homotopic. Nuclei related only by a
mirror plane are termed enantiotopic. Chemically equivalent nuclei
are isochronous (same chemical shift) but the converse is not
necessarily true.
Nuclei are magnetically equivalent if they are isochronous and if
all the coupling constants for couplings to any other nucleus are equal
for each nucleus (isogamous coupling).
2
The example spin systems consist of two different magnetically active
nuclei H and F; A = H and X = F
3
Enantiotopic and Diastereotopic Protons
H
Cl
H
H3C
Cl
H
CH3
Enantiotopic protons:
no rotational symmetry but
superimposed by inversion (i)
H
Diastereotopic protons of methylene groups
H2
H
2
H1 H
H
HO2C
H 3C
CO2H
HO
H
chiral molecule
HO
H
1
plane makes the two H1
(H2) protons chemically
equivalent;
CO2H no plane through the
H
achiral molecule
two CH2 groups,
thus the protons of
each CH2 group are
diastereotopic;
Diastereotopic protons can not be placed
into the same chemical environment
4
Staggered Rotamers – non-chiral
Br
Br
H1
H3
Cl
anti
H2
Cl
H4
H3
Br
H1
H4
H2
Cl
H2
H3
H1
H4
gauche
• anti rotamer: H1 and H2 as well as H3 and H4 are
enantiotopic interchanged through a plane of
symmetry;
• all other rotamers incl. gauche: no symmetry, H1 and H2
as well as H3 and H4 are diastereotopic;
• the chemical shifts of H1 and H2 (H3 and H4) for all
rotamers other than anti are not equivalent;
• but rapid rotation gives one chemical shift for H1 and H2
and another for H3 and H4;
5
Staggered Rotamers
– chiral centre next to methylene group
Br
Br
H1
Cl
Cl
H2
Cl
H4
Cl
Br
H1
H4
H2
H2
Cl
Cl
H4
H1
H1 and H2 are not chemically equivalent as they
cannot be interchanged by a symmetry operation;
• no plane, axis or inversion center
• not interchanged by rapid rotation (chemical
environment is always different)
• averaged chemical shift is not identical
6
Spectrum of 1-Chloro-4-nitrobenzene
AA’XX’ spectrum
7
Magnetic Equivalence
If chemical shift equivalent nuclei couple equally to other
nuclei then they are magnetically equivalent!
magnetic equivalent if symmetrically disposed with
respect to each nuclei in the spin system.
NO2
H1
H1'
H1 and H1’ are chemically equivalent and,
thus, have the same chemical shift
but H1 and H1’ couple differently to H2
and H2’;
H2
H2'
J12 J1’2’ = 7-10 Hz, J1’2 J12’ = 1 Hz
Cl
they are magnetically not equivalent and
the AA’XX’ spectrum is complex
8
Aliphatic AA’BB’ Spectrum
9
Aliphatic AMX Spectrum of Styrene
10
Aromatic AA’BB’ Spectrum of 1,2-dichlorobenzene
11
Aliphatic A2B2
Spectrum of
2-Chloroethanol
12
AB spin systems
∆νAB
∆νAB
∆νAB
∆νAB
∆νAB
∆νAB
∆νAB
∆νAB
∆νAB
13
Analysis of AB spin systems
∆νAB = (4C2 – J2)
The ratio of intensities between larger
inner and smaller outer peaks is
(1+J/2C)/(1-J/2C)
14
Geminal couplings
Coupling constants can have positive or negative values and their
determination might aid the analysis of complex spectra. Lone pairs
of electrons, for example, can donate electron density and make 2J
more positive as shown below.
Coupling of magnetically equivalent protons des not appear in the NMR
spectrum but the coupling constants can be determined by
deuteriation or from 13C satellite signals.
Geminal (2J) couplings are usually negative and reach values of up
to 30 Hz. Geminal protons attached to double and triple bonds can
have positive coupling constants.
O
F
H
Cl
H
-21.5
H
H
-3.2 Hz
H
H
-1.3 Hz
H
+42
O
H
O
15
Vicinal Couplings
Vicinal (3J) couplings are often positive and usually reach values of up to 20 Hz.
16
Vicinal couplings (3J) depend on the dihedral angle
H
H
1-6 Hz
H
H
H
0-5 Hz
8-13 Hz
H
Br
Br
H1
Cl
Cl
H2
Cl
H4
Cl
Br
H1
H4
H2
Cl
H2
Cl
H1
H4
17
Vicinal couplings (3J) depend on the dihedral angle
18
Long-Range Couplings
All couplings between protons that are more than 3 bonds apart are called
long-range couplings (4J, 5J, etc.). Their coupling constant can reach values
between 0.5-3 Hz if both sets of protons are connected to the same π-electron
system.
4J
5J
H
t.-Bu
O
H
1.7 Hz
H
N
Br
1.45 Hz
4J
H
H
H
0.9 Hz
CH3
CHO
19