NMR Spectroscopy Primer

This page describes some of the terms and concepts commonly used in NMR spectroscopy (particularly multinuclear NMR), many of which are referred to in other pages, such as:

Quick Jump:  Coupling patterns | Mutual Coupling | Satellites | Decoupling | Berry pseudorotation

Coupling patterns, singlet, doublet, triplet ... multiplets and Pascal's triangle

 

When coupling occurs between different magnetically-active nuclei (I > 0) then characteristic patterns arise. Generally if a nucleus couples with n spin-active nuclei each with a spin-quantum number, I, then (2nI+1) lines will be seen. This equation can be simplified, and often is in organic chemistry applications, if I = 1/2 to (n+1) lines - however we prefer to use the full form of the equation, since that applied in all cases. The relative intensities of the set of lines when I = 1/2 is given by Pascal's triangle (see below). So coupling to 1 spin-1/2 nucleus, such as a proton, or fluorine nucleus would result in the appearance of a doublet (two peaks in the ratio 1:1), coupling to two spin-1/2 nuclei gives a 1:2:1 triplet, while coupling to three equivalent I=1/2 nuclei would give a quartet (four peaks in the ratio 1:3:3:1). You can generate more patterns like this using the j-splitting calculator below.

If I > 1/2 (called "quadrupolar nuclei") then the same 2nI+1 'rule' applies; that is coupling to, for example 3 I=1 nuclei will give a 7-lined pattern. How do you calculate the nmr splitting pattern for qaudrupolar nuclei? The relative intensities of the lines are obtained by extending Pascal's triangle to allow for each nucleus having more than two possible spin-states. There are a number of ways of doing this, including a method called the "sliding window" method, which is used in our pattern generator below:

You can see the effects of coupling using our NMR coupling pattern generator (2nI+1 calculator) below:

Number of nuclei (n) : Nuclear spin (I)

The names of the patterns generated depends on the total number of lines, as listed below:

1 line : singlet
2 lines: doublet
3 lines: triplet
4 lines: quartet
5 lines: quintet (sometimes pentet)
6 lines: sextet
7 lines: septet (sometimes heptet)
8 lines: octet etc...

Mutual Coupling - the 19F and 31P NMR spectra of K[PF6].

 

When you observe the spectrum of one spin-active nucleus which is coupled to one, or more, other spin-active nuclei then the patterns described above occur. This coupling is the same which ever nucleus you observe, so the size of the coupling constant (measured in Hz) is the same which ever spectrum you record. This is because the coupling is mutual - the same for both.

As an example, the spectra below were recorded for a solution of K[PF6] in DMSO. The six fluorines are all equivalent in the [PF6]- anion and so the 31P NMR spectrum consists of a septet. The separation between any adjacent pair of peaks is the P-F coupling constant, in this case 711 Hz. Since all six fluorine nuclei are equivalent they couple to just the phosphorus nucleus to give a doublet, again separated by 711 Hz.

Thus the two nuclei are said to exhibit mutual coupling, that is they couple to each other in the same way. The PF coupling constant labelled as 1J(PF) [where the superscript 1 refers to the 1 bond between the coupling P and F nuclei] is 711 Hz. [Note: coupling constants are always quoted in Hz (which is independent of the spectrometer frequency) not ppm! While the chemical shift is reported in ppm as the position of the centre of the pattern.]

31P NMR spectrum of KPF6, click to expand
The 31P{1H} NMR spectrum of K[PF6]
(click on the spectrum to expand)
19F NMR spectrum of KPF6, click to expand
19F NMR spectrum of K[PF6] (click to expand)

Satellites

 

In the example above both fluorine and phosphorus are 100% spin-active, however this is not the case for all elements. If an element has a spin-active nucleus that is less than 100% abundant then additional peaks are seen either side of the main signal, these are called satellites.

Some of the most frequently observed satellites are found in proton NMR spectra of organic compounds due to coupling arising from the neighbouring 13C nuclei, which are spin-active (I = 1/2) but only 1.1% abundant.

For example, the spectrum shown below is the 1H NMR spectrum of Me3SnCl.

1H NMR spectrum of Me3SnCl, click to expand
The 1H NMR spectrum of Me3SnCl (click on the spectrum to expand)

The spectrum contains one main peak, since all the protons of the three methyl groups are equivalent. Either side of this peak - as shown in the expansion - are some small additional peaks; these are the satellites arising from the presence of non-100% abundant spin-active nuclei.

In this case there are two such nuclei to consider, the 13C, and also the Sn. Starting with the nucleus nearest to the hydrogens, and therefore the most likely to couple with the largest coupling constant, carbon. For most of the molecules (100% - 1.1% = 98.1%) the carbon atom will be a 12C isotope, which is spin-inactive, ie I = 0, so will leave to 2nI+1 (2x1x0+1) peaks, ie a singlet. But, for the 1.1% of molecules where the carbon is 13C, with I=1/2, But, for the 1.1% of molecules that contain 13C coupling will occur to give 2x1x(1/2)+1 = 2 lines, ie a doublet. The chemical shift of the protons attached to 12C and 13C are very similar, so the two peaks of the doublet appear either side of the singlet. The height of these peaks is related to the abundance of 13C, that is the total intensity of the 2 peaks of the doublet is 1.1%, therefore each of the satellite peaks will be 1.1%/2 = 0.55%, while the singlet peak will be of relative intensity 98.9%. These satellites are marked in the spectrum with *, and the coupling constant is measured as the separation between the two satellites, in this case 132 Hz, and since this is a one-bond coupling we can write this as 1J(CH) = 132 Hz.

But what about the more intense peaks that look like doublets either side of the main signal? In fact these are two sets of satellites, one pair separated by 55.4 Hz and another pair with J = 57.8Hz? These arise from low-abundance isotopes of Sn, of which there are two: 117Sn and 119Sn, both of which have I = 1/2, and with approximate relative abundances 7.6 and 8.6%. The same rationale applies here; for 7.6% of the molecules possessing 17Sn a doublet will be observed, for the 8.6% of 119-containing molecules another doublet will be generated, anmd for the remainder of the molecules (100 -7.6 -8.6 = 83.8%) a singlet will be observed.

If you look carefully you will see that the outside of the satellite lines are slightly taller, showing that these come from the 118-Sn containing molecules. So we know that 2J(117SnH) = 55.4 Hz and 2J(119SnH) = 57.8 Hz.

At a slightly more advanced level we could have worked out that the 119Sn-H coupling constant would be greater than that for 117Sn-H, because coupling constants are related (amongst other things, see above) to the degree to which a nucleus is magnetised by an external field - this is called the gyromagnetic (or magnetogyric) ratio. For 117Sn this value is -9.589 x 107 rad T-1s-1; for 119Sn the corresponding value is -10.0138 x 107 rad T-1s-1. Since the value of γ is numerically larger (the sign is unimportant here) for 119Sn in two otherwise identical molecules we expect the coupling constant involving 119Sn to be larger than that for 117Sn. In fact we expect the value for the 119Sn coupling constant to be γ(119Sn)/γ(117Sn) larger, ie -10.0138/-6.589 = 1.0443. So if we multiply the measured 117Sn-H coupling constant (55.4 Hz) by 1.0443 we would calculate the expected 119Sn-H coupling constant as 57.85 Hz!

Satellites can appear in any spectrum, not just proton NMR, but you won't normally see them in a 13C NMR spectrum. (Why?) The spectrum shown below is the 19F NMR spectrum of Hg(CF3)2 which shows mercury satellites. The three peaks arise in a similar way because mercury has a number of different isotopes, one of these 199Hg is spin-active (I=1/2) and 16.8% abundant. So of all the molecules of Hg(CF3)2, 83.2% (100% - 16.8%) will not contain spin-active mercury, and so the six equivalent fluorine nuclei will not couple to any other spin-active nuclei, so a singlet is observed. However, for the 16.8% of molecules containing 199Hg coupling will occur between the 199Hg and 19F nuclei, so a doublet would arise (2nI+1 = 2). The actual spectrum observed is a combination of these two components - a singlet [83.2%] and a doublet [total intensity 16.8%, ie 8.4% each line] with one peak of the doublet either side of the singlet.

19F NMR spectrum of Hg(CF3)2, click to expand
19F NMR spectrum of Hg(CF3)2 (click to expand)
An intense central peak with smaller peaks either side
The derivation of mercury satellites

The 2J(HgF) coupling constant is measured across the doublet, ie from one satellite peak to the other, in this case that is 1253 Hz. We can also check the relative intensities, since the signals due to 199Hg are the outer, weaker peaks, and these add up to 0.0990 + 0.0990. However the intensities of all three peaks corresponds to all of the molecules. So the proportion of spin-active mercury is equal to the sum of the intensities of the satellite peaks divided by the total intensity, ie (0.0990 + 0.0992) / (0.0990 + 0.999 + 0.0992) = 16.5%.

Decoupling

 

It is often useful to remove some of the couplings that might be present in an NMR spectrum to simplify the observed spectra. This is done at the time the data is recorded, and usually is limited to removing coupling to proton nuclei, so is called proton-decoupling. It is denoted by putting the decoupled nucleus in curly brackets, eg 13C{1H}, which means that the carbon NMR spectrum will show no coupling to any of the protons. It is also common to record phosphorus NMR spectra with proton decoupling, ie 31P{1H}, and an example of the difference that this can make is shown below for the phosphorus NMR spectra recorded of (4F-C6H4)3PSe, shown on the spectra.

31P NMR spectrum of (4F-C6H4)3PSe, click to expand
31P NMR spectrum of (4F-C6H4)3PSe (click to expand)
Proton-decoupled phosphorus NMR spectrum of tris(p-fluorophenyl)phosphine selenide, click to expand
31P{1H} NMR spectrum of (4F-C6H4)3PSe (click to expand)

The second spectrum is of the same cimpound, but now recorded as a proton-decoupled spectrum. Because this removes all the coupling between the phosphorus and proton nuclei, the spectrum simplifies to the point where now the selenium satelites are obvious and even the smaller 13C NMR satelites are now visible.

Berry pseudorotation

 

Compared with a number of other spectroscopic techniques NMR spectroscopy is relatively slow, so there is a chance that a molecule may be rearranging more quickly than the rate at which the spectroscopic process is occuring. If this happens then data for a time-averaged structure will be recorded.

Probably the most widely cited, inorganic, examples of such behaviour are the 5-coordinate molecules that adopt a trigonal bipyramidal structure, such as PF5. As shown below (left), these have (in a static structure) two environments, the two axial fluorines (orange) and three equatorial fluorines (blue). However, the 31P NMR spectrum of this molecule, recorded at room temperature, shows a sextet, suggesting that all 5 fluorines are equivalent. This occurs, because the molecule is in motion, via a square-based pyramidal intermediate (picture 2) that gives rise to an averaging, such that the axial and equatorial environments swap over (see picture 3).

trigonal bipyramidal structure adopted by PF5
Starting point, axial fluorine substituents are orange
square-based pyramidal intermediate in Berry pseudororation
The square-based pyramid intermediate
trigonal bipyramidal PF5 structure
Orange substituents are now equatorial

The whole of this process is illustrated below based on a POVRay generated movie. During the motion the two axial (orange) fluorines become equatorial, along with one of the blue atoms, while the other two blue coloured fluorines end up as the two axial substituents. In this way the positions of the fluorine atoms constantly change between being axial and equatorial, ie they become chemically equivalent.

An animation of the Berry pseudorotation that swaps axial and equitorial environments of the five-coordinate PF5 molecule
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