NMR signals are ordinarily characterized by three variables: chemical shift, spin–spin coupling, and relaxation time.
Chemical shift The energy difference Δ
E between nuclear spin states is proportional to the magnetic field (
Zeeman effect). Δ
E is also sensitive to the electronic environment of the nucleus, giving rise to what is known as the chemical shift, δ. The simplest types of NMR graphs are plots of the different chemical shifts of the nuclei being studied in the molecule. The value of δ is often expressed in terms of "shielding": shielded nuclei have higher Δ
E. The range of δ values is called the dispersion. It is rather small for 1H signals, but much larger for other nuclei. NMR signals are reported relative to a reference signal, usually that of TMS (
tetramethylsilane). Additionally, since the distribution of NMR signals is field-dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. The chemical shift provides structural information. The conversion of chemical shifts (and J's, see below) is called
assigning the spectrum. For diamagnetic organic compounds, assignments of 1H and 13C NMR spectra are extremely sophisticated because of the large databases and easy computational tools. In general, chemical shifts for protons are highly predictable, since the shifts are primarily determined by shielding effects (electron density). The chemical shifts for many heavier nuclei are more strongly influenced by other factors, including
excited states ("paramagnetic" contribution to shielding tensor). This paramagnetic contribution, which is unrelated to
paramagnetism) not only disrupts trends in chemical shifts, which complicates assignments, but it also gives rise to very large chemical shift ranges. For example, most 1H NMR signals for most organic compounds are within 15 ppm. For 31P NMR, the range is hundreds of ppm. In
paramagnetic NMR spectroscopy, the samples are paramagnetic, i.e. they contain unpaired electrons. The paramagnetism gives rise to very diverse chemical shifts. In 1H NMR spectroscopy, the chemical shift range can span up to thousands of ppm. 3 peak has three times the area of the OH peak. Similarly the CH2 peak would be twice the area of the OH peak but only 2/3 the area of the CH3 peak. Software allows analysis of signal intensity of peaks, which under conditions of optimal relaxation, correlate with the number of protons of that type. Analysis of signal intensity is done by
integration—the mathematical process that calculates the area under a curve. The analyst must integrate the peak and not measure its height because the peaks also have
width—and thus its size is dependent on its area not its height. However, it should be mentioned that the number of protons, or any other observed nucleus, is only proportional to the intensity, or the integral, of the NMR signal in the very simplest one-dimensional NMR experiments. In more elaborate experiments, for instance, experiments typically used to obtain
carbon-13 NMR spectra, the integral of the signals depends on the relaxation rate of the nucleus, and its scalar and dipolar coupling constants. Very often these factors are poorly known - therefore, the integral of the NMR signal is very difficult to interpret in more complicated NMR experiments.-->
J-coupling Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling, or scalar coupling (a special case of
spin–spin coupling), between NMR active nuclei. This coupling arises from the interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive. This coupling provides detailed insight into the connectivity of atoms in a molecule. The multiplicity of the splitting is an effect of the spins of the nuclei that are coupled and the number of such nuclei involved in the coupling. Coupling to
n equivalent spin-1/2 nuclei splits the signal into a
n + 1 multiplet with intensity ratios following
Pascal's triangle as described in the table. Coupling to additional spins leads to further splittings of each component of the multiplet, e.g. coupling to two different spin-1/2 nuclei with significantly different coupling constants leads to a
doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect on the NMR spectra, and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings.
Long-range couplings over more than three bonds can often be observed in
cyclic and
aromatic compounds, leading to more complex splitting patterns. plotted as signal intensity vs.
chemical shift. There are three different types of
H atoms in ethanol regarding NMR: the hydrogen (H) on the
−OH group is not coupling with the other H atoms and appears as a singlet, but the
CH3− and the
−CH2− hydrogens are coupling with each other, resulting in a triplet and quartet respectively. For example, in the proton spectrum for ethanol, the CH3 group is split into a
triplet with an intensity ratio of 1:2:1 by the two neighboring CH2 protons. Similarly, the CH2 is split into a
quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH3 protons. In principle, the two CH2 protons would also be split again into a
doublet to form a
doublet of quartets by the hydroxyl proton, but intermolecular exchange of the acidic hydroxyl proton often results in a loss of coupling information. Coupling to any spin-1/2 nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than 1/2 because the
spin quantum number has more than two possible values. For instance, coupling to deuterium (a spin-1 nucleus) splits the signal into a
1:1:1 triplet because the spin 1 has three spin states. Similarly, a spin-3/2 nucleus such as 35Cl splits a signal into a
1:1:1:1 quartet and so on. Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number of
neighboring NMR active nuclei within the molecule. In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling is often the only way to distinguish different nuclei. The magnitude of the coupling (the coupling constant
J) is an effect of how strongly the nuclei are coupled to each other. For simple cases, this is an effect of the bonding distance between the nuclei, the magnetic moment of the nuclei, and the dihedral angle between them.
Second-order (or strong) coupling with
chemical shift in ppm on the horizontal axis. Each magnetically inequivalent proton has a characteristic shift, and couplings to other protons appear as splitting of the peaks into multiplets: e.g. peak
a, because of the three magnetically equivalent protons in methyl group
a, couple to one adjacent proton (
e) and thus appears as a doublet. The above description assumes that the coupling constant is small in comparison with the difference in NMR frequencies between the inequivalent spins. If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved). Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in the background noise, although the integrated area under the peaks remains constant. In most high-field NMR, however, the distortions are usually modest, and the characteristic distortions (
roofing) can in fact help to identify related peaks. Some of these patterns can be analyzed with the
method published by
John Pople, though it has limited scope. Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower-frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above. Furthermore, as in the figure to the right, J-coupling can be used to identify ortho-meta-para substitution of a ring. Ortho coupling is the strongest at 15 Hz, Meta follows with an average of 2 Hz, and finally para coupling is usually insignificant for studies.
Magnetic inequivalence More subtle effects can occur if chemically equivalent spins (i.e., nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins. Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent. For example, the 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair. Magnetic inequivalence can lead to highly complex spectra, which can only be analyzed by computational modeling. Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while conformational averaging about C−C bonds in flexible molecules tends to equalize the couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence. == Correlation spectroscopy ==