1
Multiplicity
We’ll start by considering proton (1H) spectra. Recall that a proton in an organic molecule will
give an NMR signal at one particular frequency, which is displayed at corresponding ppm value
in the spectrum. You should be famiar with the concept of coupling, where nearby protons interact with the proton in question, causing splitting of the signal into more than one line.
The rule for predicting the number of lines observed is 2nI + 1, where n is the number of equivalent nuclei, and I is the nuclear spin of the coupling nucleus. For protons, I = ½, and we have the
familiar n + 1 equation describing the splitting of the signal. So for an isolated proton, n = 0 and
we have a singlet (denoted as s). For n = 1, we have a 1:1 doublet (d) where the 1:1 represents the
relative intensities of the lines (Note 1). Continuing onward, when n = 2 we get a triplet (t, 1:2:1),
n = 3 gives a quartet (q, 1:3:3:1) and n = 4 gives a quintet (quintet, 1:4:6:4:1). Higher values of n
are shown in Figure 1 (below) with their descriptions, abbreviations and relative line intensities.
singlet, s
doublet, d, 1:1
triplet, t, 1:2:1
quartet, q, 1:3:3:1
quintet, 1:4:6:4:1
sextet, 1:5:10:10:5:1
septet,
1:6:15:20:15:6:1
octet,
1:7:21:35:35:21:7:1
nonet,
nonet, expanded
1:8:28:56:70:56:28:8:1
Figure 1: The basic multiplets of proton NMR spectroscopy
Unless you do the vertical expansion on a signal with many lines, the outer lines of the multiplet
can easily get lost in the baseline. The nonet (above) is used to show both the “natural” appearance of the signal where the outer lines are barely bumps on the baseline, and the vertical expansion of the signal where the outer lines are clearly visible, and the centre lines are well off the top
of the page.
Different things happen when the protons are not equivalent. Look first at the situation where the
coupled protons are inequivalent, but the coupling constants (J-values) are equal (or nearly so).
This situation defaults to the patterns seen above—you observe the same set of doublets, triplets,
etc. as if all the coupled protons were equivalent. This helps to explain some of the multi-line
splitting patterns seen in the figure. It is difficult to imagine a structure with seven equivalent
protons: but a structure like CHa -CHb(CHc3)2 with Jab = Jbc will give an octet for Hb.
2
For two inequivalent protons with different coupling constants consider proton Hb in the structure
CHa -CHb–CHc (don’t worry about the rest of the bonding), and suppose that Jab > Jbc. The resulting signal is shown in Figure 2 (far left), and is called a doublet of doublets. The larger coupling
constant is measured as the average of the separation between the first and third lines, and the
second and fourth lines. The smaller coupling constant is measured as the average of the separation between the first and second lines, and the third and fourth lines.
This is NOT a quartet!! A doublet of doublets (dd) displays relative line intensities of 1:1:1:1 and
is the result of coupling of the signal to two protons. A quartet displays a relative line intensity of
1:3:3:1 and is the result of coupling to three protons. Don’t confuse the two.
If we take the last structure and add another proton (Hd) coupled to Hb (CHa -CHb–CHcHd) and
make Jab > Jbc > Jbd; the result is a doublet of doublet of doublets (ddd, Figure 2, second from left).
There are eight lines in total, all with equal intensities. Don’t call this an octet. We could add a
fourth coupling proton (giving a dddd) and even a fifth coupling proton (ddddd), but usually at
that point some of the coupling constants are similar and other patterns emerge.
doublet of doublets, doublet of doublet
dd, 1:1:1:1
of doublets, ddd,
1:1:1:1:1:1:1:1
doublet of triplets, triplet of doublets, multiplet, m
dt, 1:2:1:1:2:1
td, 1:1:2:2:1:1
Figure 2: More complex splitting patterns
Let’s go back to the structure CHa -CHb–CHcHd and make two of the coupling constants equal
(or nearly so). Do we get a doublet of triplets (dt) or a triplet of doublets (td)? See Figure 2 (centre
and second from right) for the appearance of the signals. The usual way of reporting the splitting
is to have the larger coupling constant noted first. So a dt (at left) has Jab > Jbc = Jbd, while a td (at
right) has Jab = Jbc > Jbd. More complex splitting can also be seen—remember that methyl groups
can turn a signal into a quartet—but stick with labelling the largest coupling constant first.
In some of the examples above, there was a qualifying statement about the coupling constants
being equal (or nearly so). Equal coupling constants makes things easy, but what about the qualifier “or nearly so”? Recall that the NMR instruments are digital instruments, and that there is a
minimum separation between two consecutive points in the spectrum. Two nearly equal coupling
constants may not be completely resolved by the instrument, and sometimes the signals look as
though the coupling constants are indeed equal.
The other effect of nearly equal coupling constants is that the lines appear to be broadened, and
not clearly resolved into discrete lines. This also occurs with signals where some of the coupling
is weak (i.e. around aromatic rings). If you can’t see or measure the coupling, don’t record it, but
if necessary you could note that the signal is broad rather than sharp.
3
In all of the examples above, the chemical shift value is reported as the centre of the coupling
pattern—i.e. the middle of a doublet, doublet of doublets, or quartet, or the position of the centre
line of a triplet or quintet.
The extreme condition is when a signal has a lot of unresolved (usually small) couplings, there is
overlap between a couple of signals, or there are second order effects. While there is clearly coupling occuring, it’s not possible to distinguish a clear coupling pattern in the signal. This is when
the signal is called a “multiplet” (Note 2), shown on the right of figure 2 and the chemical shift is
reported as occurring over a range rather than the centre of the pattern. The width of the range
gives some idea of the extent of the coupling. A multiplet of this type could be unsymmetrical,
thus reporting the centre of the pattern is wrong. And of course it’s possible to have a doublet of
multiplets, further complicating the situation.
If you are stuck trying to understand the coupling, remember that you can always draw a tree
diagram. If you draw the tree diagram on graph paper, or at least draw the couplings proportionally, the expected pattern should become evident.
Tree diagrams can also be useful when working with nuclei that have I > ½, such as deuterium.
The most common example of deuterium splitting in a signal is seen in 13C spectra. While 13C
spectra are recorded to eliminate C-H coupling in the sample, it’s not (easily) possible to eliminate the C–D coupling in the solvent. When CDCl3 is used, only about 1 % of the carbon in the
solvent is 13C (which must give a signal), but almost all of that 13C is bonded to deuterium and
splitting will be observed. Deuterium has I = 1, and using the 2nI + 1 rule, a triplet with equal
line intensities is expected. See the left hand box of Figure 3, below.
triplet, t, 1:1:1
Tree diagram for
proton in CHD2–
quintet, 1:2:3:2:1
Figure 3: Fun with deuterium coupling
Interesting H–D coupling can be seen when solvents such as acetone-d6 or DMSO-d6 are used.
Deuteration is never 100 %, so some of the methyl groups in solvent have the structure CHD2–.
The tree diagram for the proton signal (CHD2–) showing the expected coupling to deuterium is
shown in the middle of Figure 3, and the simulated quintet is shown on the right. The reason for
the 1:2:3:2:1 line intensities can be seen in the tree diagram.
Notes
1.
2.
The multiplets shown in these notes were simulated in SpinWorks, setting the chemical
shifts and couplings to avoid second-order effects and get the “perfect” line intensities.
This is an unfortuate use of the word “multiplet” as a homonym, because of course a
“doublet” is a multiplet. But it’s only when you are looking at the analysis of a spectrum (chemical shift, multiplicity, coupling, integration, and assignment) and see the term
“multiplet” it means a diffuse signal with no clear coupling observable.
© Peter Marrs, University of Victoria Chemistry 363 NMR Notes, October 2015