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5.5A: The source of spin-spin coupling
The 1H-NMR spectra that we have seen so far (of methyl acetate and para-xylene)
are somewhat unusual in the sense that in both of these molecules, each
set of protons generates a single NMR signal. In fact, the 1H-NMR
spectra of most organic molecules contain proton signals that are
'split' into two or more sub-peaks. Rather than being a complication,
however, this splitting behavior actually provides us with more
information about our sample molecule.
Consider the spectrum for
1,1,2-trichloroethane. In this and in many spectra to follow, we show
enlargements of individual signals so that the signal splitting patterns
are recognizable.
The signal at 3.96 ppm, corresponding to the two Ha protons, is split into two subpeaks of equal height (and area) – this is referred to as a doublet. The Hb
signal at 5.76 ppm, on the other hand, is split into three sub-peaks,
with the middle peak higher than the two outside peaks - if we were to
integrate each subpeak, we would see that the area under the middle peak
is twice that of each of the outside peaks. This is called a triplet.
The source of signal splitting is a phenomenon called spin-spin coupling,
a term that describes the magnetic interactions between neighboring,
non-equivalent NMR-active nuclei. In our 1,1,2 trichloromethane example,
the Ha and Hb protons are spin-coupled to each other. Here's how it works, looking first at the Ha signal: in addition to being shielded by nearby valence electrons, each of the Ha protons is also influenced by the small magnetic field generated by Hb next door (remember, each spinning proton is like a tiny magnet). The magnetic moment of Hb will be aligned with B0
in (slightly more than) half of the molecules in the sample, while in
the remaining half of the molecules it will be opposed to B0. The Beff ‘felt’ by Ha is a slightly weaker if Hb is aligned against B0, or slightly stronger if Hb is aligned with B0. In other words, in half of the molecules Ha is shielded by Hb (thus the NMR signal is shifted slightly upfield) and in the other half Ha is deshielded by Hb (and the NMR signal shifted slightly downfield). What would otherwise be a single Ha
peak has been split into two sub-peaks (a doublet), one upfield and one
downfield of the original signal. These ideas an be illustrated by a splitting diagram, as shown below.

Now, let's think about the Hb signal. The magnetic environment experienced by Hb is influenced by the fields of both neighboring Ha protons, which we will call Ha1 and Ha2. There are four possibilities here, each of which is equally probable. First, the magnetic fields of both Ha1 and Ha2 could be aligned with B0, which would deshield Hb, shifting its NMR signal slightly downfield. Second, both the Ha1 and Ha2 magnetic fields could be aligned opposed to B0, which would shield Hb, shifting its resonance signal slightly upfield. Third and fourth, Ha1 could be with B0 and Ha2 opposed, or Ha1 opposed to B0 and Ha2 with B0. In each of the last two cases, the shielding effect of one Ha proton would cancel the deshielding effect of the other, and the chemical shift of Hb would be unchanged.
So in the end, the signal for Hb is a triplet, with the middle peak twice as large as the two outer peaks because there are two ways that Ha1 and Ha2 can cancel each other out.
Now, consider the spectrum for ethyl acetate:
We see an unsplit 'singlet' peak at 1.833 ppm that corresponds to the acetyl (Ha)
hydrogens – this is similar to the signal for the acetate hydrogens in
methyl acetate that we considered earlier. This signal is unsplit
because there are no adjacent hydrogens on the molecule. The signal at
1.055 ppm for the Hc hydrogens is split into a triplet by the two Hb
hydrogens next door. The explanation here is the same as the
explanation for the triplet peak we saw previously for
1,1,2-trichloroethane.
The Hb hydrogens give rise to a quartet signal
at 3.915 ppm – notice that the two middle peaks are taller then the two
outside peaks. This splitting pattern results from the spin-coupling
effect of the three Hc hydrogens next door, and can
be explained by an analysis similar to that which we used to explain the
doublet and triplet patterns.
Exercise 5.6:
a) Explain, using left and right arrows to illustrate the possible combinations of nuclear spin states for the Hc hydrogens, why the Hb signal in ethyl acetate is split into a quartet.
b) The integration ratio of doublets is 1:1, and of triplets is 1:2:1. What is the integration ratio of the Hb quartet in ethyl acetate? (Hint – use the illustration that you drew in part a to answer this question.)
By now, you probably have recognized the pattern which is usually referred to as the n + 1 rule: if a set of hydrogens has n neighboring, non-equivalent hydrogens, it will be split into n + 1 subpeaks. Thus the two Hb hydrogens in ethyl acetate split the Hc signal into a triplet, and the three Hc hydrogens split the Hb
signal into a quartet. This is very useful information if we are
trying to determine the structure of an unknown molecule: if we see a
triplet signal, we know that the corresponding hydrogen or set of
hydrogens has two `neighbors`. When we begin to determine structures of
unknown compounds using 1H-NMR spectral data, it will become more apparent how this kind of information can be used.
Three important points need to be
emphasized here. First, signal splitting only occurs between
non-equivalent hydrogens – in other words, Ha1 in 1,1,2-trichloroethane is not split by Ha2, and vice-versa.
Second, splitting occurs primarily between hydrogens that are separated by three bonds. This is why the Ha hydrogens in ethyl acetate form a singlet– the nearest hydrogen neighbors are five bonds away, too far for coupling to occur.
Occasionally we will see four-bond and
even 5-bond splitting, but in these cases the magnetic influence of one
set of hydrogens on the other set is much more subtle than what we
typically see in three-bond splitting (more details about how we
quantify coupling interactions is provided in section 5.5B). Finally,
splitting is most noticeable with hydrogens bonded to carbon. Hydrogens
that are bonded to heteroatoms (alcohol or amino hydrogens, for
example) are coupled weakly - or not at all - to their neighbors. This
has to do with the fact that these protons exchange rapidly with solvent
or other sample molecules.
Below are a few more examples of chemical shift and splitting pattern information for some relatively simple organic molecules.
Exercise 5.7: How many proton signals would you expect to see in the 1H-NMR
spectrum of triclosan (a common antimicrobial agent found in
detergents)? For each of the proton signals, predict the splitting
pattern. Assume that you see only 3-bond coupling.
Exercise 5.8: Predict the splitting pattern for the 1H-NMR
signals corresponding to the protons at the locations indicated by
arrows (the structure is that of the neurotransmitter serotonin).

5.5B: Coupling constants
Chemists quantify the spin-spin coupling effect using something called the coupling constant, which is abbreviated with the capital letter J.
The coupling constant is simply the difference, expressed in Hz,
between two adjacent sub-peaks in a split signal. For our doublet in
the 1,1,2-trichloroethane spectrum, for example, the two subpeaks are
separated by 6.1 Hz, and thus we write 3Ja-b = 6.1 Hz.
The superscript 3 tells us that this is a
three-bond coupling interaction, and the a-b subscript tells us that we
are talking about coupling between Ha and Hb. Unlike the chemical shift value, the coupling constant, expressed in Hz, is the same regardless of the applied field strength of the NMR magnet.
This is because the strength of the magnetic moment of a neighboring
proton, which is the source of the spin-spin coupling phenomenon, does not depend on the applied field strength.
When we look closely at the triplet
signal in 1,1,2-trichloroethane, we see that the coupling constant - the
`gap` between subpeaks - is 6.1 Hz, the same as for the doublet. This
is an important concept! The coupling constant 3Ja-b quantifies the magnetic interaction between the Ha and Hb hydrogen sets, and this interaction is of the same magnitude in either direction. In other words, Ha influences Hb to the same extent that Hb influences Ha. When looking at more complex NMR spectra, this idea of reciprocal coupling constants can be very helpful in identifying the coupling relationships between proton sets.
Coupling constants between proton sets on neighboring sp3-hybridized carbons is typically in the region of 6-8 Hz. With protons bound to sp2-hybridized
carbons, coupling constants can range from 0 Hz (no coupling at all) to
18 Hz, depending on the bonding arrangement.
For vinylic hydrogens in a trans configuration, we see coupling constants in the range of 3J = 11-18 Hz, while cis hydrogens couple in the 3J
= 6-15 Hz range. The 2-bond coupling between hydrogens bound to the
same alkene carbon (referred to as geminal hydrogens) is very fine,
generally 5 Hz or lower. Ortho hydrogens on a benzene ring couple at 6-10 Hz, while 4-bond coupling of up to 4 Hz is sometimes seen between meta hydrogens.
Fine (2-3 Hz) coupling is often seen between an aldehyde proton and a three-bond neighbor.
Table 4 lists typical constant values.
5.5C: Complex coupling
In all of the examples of spin-spin
coupling that we have seen so far, the observed splitting has resulted
from the coupling of one set of hydrogens to just one neighboring set of hydrogens. When a set of hydrogens is coupled to two or more sets of nonequivalent neighbors, the result is a phenomenon called complex coupling. A good illustration is provided by the 1H-NMR spectrum of methyl acrylate:
First, let's first consider the Hc signal, which is centered at 6.21 ppm. Here is a closer look:
With this enlargement, it becomes evident that the Hc signal is actually composed of four sub-peaks. Why is this? Hc is coupled to both Ha and Hb , but with two different coupling constants. Once again, a splitting diagram can help us to understand what we are seeing. Ha is trans to Hc across the double bond, and splits the Hc signal into a doublet with a coupling constant of 3Jac = 17.4 Hz. In addition, each of these Hc doublet sub-peaks is split again by Hb (geminal coupling) into two more doublets, each with a much smaller coupling constant of 2Jbc = 1.5 Hz.
The result of this `double splitting` is a pattern referred to as a doublet of doublets, abbreviated `dd`.
The signal for Ha at 5.95 ppm is also a doublet of doublets, with coupling constants 3Jac = 17.4 Hz and 3Jab = 6.31 Hz.
The signal for Hb at 5.64 ppm is split into a doublet by Ha, a cis coupling with 3Jab = 10.4 Hz. Each of the resulting sub-peaks is split again by Hc, with the same geminal coupling constant 2Jbc = 1.5 Hz that we saw previously when we looked at the Hc
signal. The overall result is again a doublet of doublets, this time
with the two `sub-doublets` spaced slightly closer due to the smaller
coupling constant for the cis interaction. Here is a blow-up of the actual Hb signal:
Exercise 5.9: Construct a splitting diagram for the Hb signal in the 1H-NMR
spectrum of methyl acrylate. Show the chemical shift value for each
sub-peak, expressed in Hz (assume that the resonance frequency of TMS is
exactly 300 MHz).
When
constructing a splitting diagram to analyze complex coupling patterns,
it is usually easier to show the larger splitting first, followed by the
finer splitting (although the reverse would give the same end result).
When a proton is coupled to two
different neighboring proton sets with identical or very close coupling
constants, the splitting pattern that emerges often appears to follow
the simple `n + 1 rule` of non-complex splitting. In the spectrum of 1,1,3-trichloropropane, for example, we would expect the signal for Hb to be split into a triplet by Ha, and again into doublets by Hc, resulting in a 'triplet of doublets'.
Ha and Hc are not equivalent (their chemical shifts are different), but it turns out that 3Jab is very close to 3Jbc. If we perform a splitting diagram analysis for Hb,
we see that, due to the overlap of sub-peaks, the signal appears to be a
quartet, and for all intents and purposes follows the n + 1 rule.
For similar reasons, the Hc peak in the spectrum of 2-pentanone appears as a sextet, split by the five combined Hb and Hd protons. Technically, this 'sextet' could be considered to be a 'triplet of quartets' with overlapping sub-peaks.
Exercise 5.10: What splitting pattern would you expect for the signal coresponding to Hb in the molecule below? Assume that Jab ~ Jbc. Draw a splitting diagram for this signal, and determine the relative integration values of each subpeak.
In
many cases, it is difficult to fully analyze a complex splitting
pattern. In the spectrum of toluene, for example, if we consider only
3-bond coupling we would expect the signal for Hb to be a doublet, Hd a triplet, and Hc a triplet.
In practice, however, all three aromatic
proton groups have very similar chemical shifts and their signals
overlap substantially, making such detailed analysis difficult. In this
case, we would refer to the aromatic part of the spectrum as a multiplet.
When we start trying to analyze complex
splitting patterns in larger molecules, we gain an appreciation for why
scientists are willing to pay large sums of money (hundreds of thousands
of dollars) for higher-field NMR instruments. Quite simply, the
stronger our magnet is, the more resolution we get in our spectrum. In a
100 MHz instrument (with a magnet of approximately 2.4 Tesla field
strength), the 12 ppm frequency 'window' in which we can observe proton
signals is 1200 Hz wide. In a 500 MHz (~12 Tesla) instrument, however,
the window is 6000 Hz - five times wider. In this sense, NMR
instruments are like digital cameras and HDTVs: better resolution means
more information and clearer pictures (and higher price tags!)
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The basis of spin couplingNuclear magnetic resonance (NMR) signals arise when nuclei absorb a certain radio frequency and are excited from one spin state to another. The exact frequency of electromagnetic radiation that the nucleus absorbs depends on the magnetic environment around the nucleus. This magnetic environment is controlled mostly by the applied field, but is also affected by the magnetic moments of nearby nuclei. Nuclei can be in one of many spin states (Figure 1), giving rise to several possible magnetic environments for the observed nucleus to resonate in. This causes the NMR signal for a nucleus to show up as a multiplet rather than a single peak. Figure 1: The different spin states of a nucleus (I = 1/2) in a magnetic field. These different states increase or decrease the effective magnetic field experienced by a nearby nucleus, allowing for two distinct signals.Figure 1 (Energy States.png)When nuclei have a spin of I = 1/2 (as with protons), they can have two possible magnetic moments and thus split a single expected NMR signal into two signals. When more than one nucleus affects the magnetic environment of the nucleus being examined, complex multiplets form as each nucleus splits the signal into two additional peaks. If those nuclei are magnetically equivalent to each other, then some of the signals overlap to form peaks with different relative intensities. The multiplet pattern can be predicted by Pascal’s triangle (Figure 2), looking at the nth row, where n = number of nuclei equivalent to each other but not equivalent to the one being examined. In this case, the number of peaks in the multiplet is equal to n + 1Figure 2: Pascal’s triangle predicts the number of peaks in a multiplet and their relative intensities.Figure 2 (Pascals Triangle.png)When there is more than one type of nucleus splitting an NMR signal, then the signal changes from a multiplet to a group of multiplets (Figure 3). This is caused by the different coupling constants associated with different types of nuclei. Each nucleus splits the NMR signal by a different width, so the peaks no longer overlap to form peaks with different relative intensities. Figure 3: The splitting tree of different types of multiplets. Figure 3 (Splitting Tree.png)When nuclei have I > 1/2, they have more than two possible magnetic moments and thus split NMR signals into more than two peaks. The number of peaks expected is 2I + 1, corresponding to the number of possible orientations of the magnetic moment. In reality however, some of these peaks may be obscured due to quadrupolar relaxation. As a result, most NMR focuses on I = 1/2 nuclei such as 1H, 13C, and 31P.Multiplets are centered around the chemical shift expected for a nucleus had its signal not been split. The total area of a multiplet corresponds to the number of nuclei resonating at the given frequency.
Spin coupling in moleculesLooking at actual molecules raises questions about which nuclei can cause splitting to occur. First of all, it is important to realize that only nuclei with I ≠ 0 will show up in an NMR spectrum. When I = 0, there is only one possible spin state and obviously the nucleus cannot flip between states. Since the NMR signal is based on the absorption of radio frequency as a nucleus transitions from one spin state to another, I = 0 nuclei do not show up on NMR. In addition, they do not cause splitting of other NMR signals because they only have one possible magnetic moment. This simplifies NMR spectra, in particular of organic and organometallic compounds, greatly, since the majority of carbon atoms are 12C, which have I = 0.For a nucleus to cause splitting, it must be close enough to the nucleus being observed to affect its magnetic environment. The splitting technically occurs through bonds, not through space, so as a general rule, only nuclei separated by three or fewer bonds can split each other. However, even if a nucleus is close enough to another, it may not cause splitting. For splitting to occur, the nuclei must also be non-equivalent. To see how these factors affect real NMR spectra, consider the spectrum for chloroethane (Figure 4)Figure 4: The NMR spectrum for chloroethane. Adapted from A. M. Castillo, L. Patiny, and J. Wist. J. Magn. Reson., 2010, 209, 123.Figure 4 (Fig9.jpg)Notice that in Figure 4 there are two groups of peaks in the spectrum for chloroethane, a triplet and a quartet. These arise from the two different types of I ≠ 0 nuclei in the molecule, the protons on the methyl and methylene groups. The multiplet corresponding to the CH3 protons has a relative integration (peak area) of three (one for each proton) and is split by the two methylene protons (n = 2), which results in n + 1 peaks, i.e., 3 which is a triplet. The multiplet corresponding to the CH2 protons has an integration of two (one for each proton) and is split by the three methyl protons ((n = 3) which results in n + 1 peaks, i.e., 4 which is a quartet. Each group of nuclei splits the other, so in this way, they are coupled.
Coupling constantsThe difference (in Hz) between the peaks of a mulitplet is called the coupling constant. It is particular to the types of nuclei that give rise to the multiplet, and is independent of the field strength of the NMR instrument used. For this reason, the coupling constant is given in Hz, not ppm. The coupling constant for many common pairs of nuclei are known (Table 1), and this can help when interpreting spectra.Table 1: Typical coupling constants for various organic structural types.
Structural type
Coupling constant (Hz)
Fig10.jpg
6 - 8
Fig11.jpg
5 - 7
Fig12.jpg
2 - 12
Fig13.jpg
0.5 - 3
Fig14.jpg
12 - 15
Fig15.jpg
12 - 18
Fig16.jpg
7 - 12
Fig17.jpg
0.5 - 3
Fig18.jpg
3 - 11
Fig19.jpg
2 - 3
Fig20.jpg
ortho = 6 - 9; meta = 1 - 3; para = 0 - 1
Coupling constants are sometimes written nJ to denote the number of bonds (n) between the coupled nuclei. Alternatively, they are written as J(H-H) or JHH to indicate the coupling is between two hydrogen atoms. Thus, a coupling constant between a phosphorous atom and a hydrogen would be written as J(P-H) or JPH. Coupling constants are calculated empirically by measuring the distance between the peaks of a multiplet, and are expressed in Hz.Example 1Coupling constants may be calculated from spectra using frequency or chemical shift data. Consider the spectrum of chloroethane shown in Figure 5 and the frequency of the peaks (collected on a 60 MHz spectrometer) given in Table 2. Figure 5: 1H NMR spectrum of chloroethane. Peak positions for labeled peaks are given in Table 2. Figure 5 (Fig21.jpg)Table 2: Chemical shift in ppm and Hz for all peaks in the 1H NMR spectrum of chloroethane. Peak labels are given in Figure 5.
Peak label
δ (ppm)
ν (Hz)
a
3.7805
226.83
b
3.6628
219.77
c
3.5452
212.71
d
3.4275
205.65
e
1.3646
81.88
f
1.2470
74.82
g
1.1293
67.76
To determine the coupling constant for a multiplet (in this case, the quartet in Figure 5), the difference in frequency (ν) between each peak is calculated and the average of this value provides the coupling constant in Hz. For example using the data from Table 2:
Frequency of peak c - frequency of peak d = 212.71 Hz – 205.65 Hz = 7.06 HzFrequency of peak b - frequency of peak c = 219.77 Hz – 212.71 Hz = 7.06 HzFrequency of peak a - frequency of peak b = 226.83 Hz – 219.77 Hz = 7.06 HzAverage: 7.06 Hz
∴ J(H-H) = 7.06 HzNote: In this case the difference in frequency between each set of peaks is the same and therefore an average determination is not strictly necessary. In fact for 1st order spectra they should be the same. However, in some cases the peak picking programs used will result in small variations, and thus it is necessary to take the trouble to calculate a true average. To determine the coupling constant of the same multiplet using chemical shift data (δ), calculate the difference in ppm between each peak and average the values. Then multiply the chemical shift by the spectrometer field strength (in this case 60 MHz), in order to convert the value from ppm to Hz:Chemical shift of peak c - chemical shift of peak d = 3.5452 ppm – 3.4275 ppm = 0.1177 ppmChemical shift of peak b - chemical shift of peak c = 3.6628 ppm – 3.5452 ppm = 0.1176 ppmChemical shift of peak a - chemical shift of peak b = 3.7805 ppm – 3.6628 ppm = 0.1177 ppmAverage: 0.1176 ppmAverage difference in ppm x frequency of the NMR spectrometer = 0.1176 ppm x 60 MHz = 7.056 Hz∴ J(H-H) = 7.06 HzExercise 1
Calculate the coupling constant for triplet in the spectrum for chloroethane (Figure 5) using the data from Table 2.SolutionUsing frequency data:
Frequency of peak f - frequency of peak g = 74.82 Hz – 67.76 Hz = 7.06 Hz
Frequency of peak e - frequency of peak f = 81.88 Hz – 74.82 Hz = 7.06 Hz
Average = 7.06 Hz
∴ J(H-H) = 7.06 Hz
Alternatively, using chemical shift data:
Chemical shift of peak f - chemical shift of peak g = 1.2470 ppm – 1.1293 ppm = 0.1177 ppm
Chemical shift of peak e - chemical shift of peak f = 1.3646 ppm – 1.2470 ppm = 0.1176 ppm
Average = 0.11765 ppm
0.11765 ppm x 60 MHz = 7.059 Hz
∴ J(H-H) = 7.06 Hz
Notice the coupling constant for this multiplet is the same as that in the example. This is to be expected since the two multiplets are coupled with each other.