We have discussed how the chemical shift of an NMR absorption is affected by the magnetic field Be produced by the circulation of neighboring electrons. Now we wish to examine how the magnetic field produced by neighboring nuclei Bn affects the appearance of the 1H NMR absorption. The effect occurs through the interaction of nuclear spins with bonding electron spins rather than through space. Let's first consider the absorption of a hydrogen nucleus labeled A with only one neighboring hydrogen nucleus in a vicinal position labeled X. Let's also assume that HA and HX have significantly different chemical shifts.
HX will have approximately equal probability of existing in either the low energy alpha state or high energy beta state. Again because of the small energy difference between the low and high energy states, the high energy state is easily populated from thermal energy. For those molecules in which HX exists in the low energy state, about half the molecules in the sample, its magnetic field Bn will subtract from the magnetic field Bo-Be and for those molecules in which HX exists in the higher energy state, again about half the molecules, its magnetic field Bn will add to Bo-Be.
Note: whether Bn for a particular spin state adds to or subtracts from Bo is a function of the number of intervening bonds; this phenomenon doesn't usually affect the appearance of the signal and will not be explained here but results from the mechanism of coupling involving interaction of nuclear spins with electron spins. For the example of vicinal coupling (3 intervening bonds), the Bn field is negative for HX in the alpha spin state; for geminal coupling Bn is positive for HX in the alpha spin state. Geminal coupling occurs between protons of different chemical shift bonded to the same carbon (2 intervening bonds); it will be discussed later.
As a consequence of the Bn field in a vicinal system, at fixed external magnetic field Bo, a lower frequency will be required to achieve resonance for those molecules which have HX in the state than for those molecules which have HX in the state. The NMR signal for HA will appear as a two line pattern as shown in Figure 16. We say the HX splits the absorption HA into a doublet and the two protons are coupled to each other. The intensity of the two lines will be equal since the probability of HX existing in the or states is approximately equal. The chemical shift, which is defined as the position of resonance in the absence of coupling, is the center of the doublet. Just as HX splits the signal of HA into a doublet, HA splits the signal of HX into a doublet. The overall splitting pattern consisting of two doublets is call an AX pattern. The splitting of HA by HX is diagramed in Figure 16.
When the molecule bears two equivalent vicinal protons, four possibilities exist for their combined magnetic fields: both are in spin states, one is in the spin state and one in the spin state, and vice versa, or both in the spin state. These four possibilities have about equal probability, and the appearance of the NMR signal is a 3-line pattern, a triplet (Figure 17), with intensities 1:2:1 because the effect of and are the same. With one adjacent proton in the spin state and the other in the spin state, the effect of the Bn field becomes zero, and the center line of the triplet is the position of the chemical shift. The two HX protons split the HA signal into a triplet and the HA proton splits the two HX protons into a doublet. The overall splitting pattern consisting of a triplet and a doublet is called an AX2 pattern.
Three chemical shift equivalent vicinal protons HX split the absorption of HA into a quartet with intensity pattern 1:3:3:1 as shown in Figure 10. The chemical shift is the center of the quartet. The three HX protons split the HA signal into a quartet and the HA proton splits the signal for the three HX protons into a doublet. The overall splitting pattern consisting of a quartet and a doublet is called an AX3 pattern.
The spacing between the lines of a doublet, triplet or quartet is called the coupling constant. It is given the symbol J and is measured in units of Hertz (cycles per second). The magnitude of the coupling constant can be calculated by multiplying the separation of the lines in units (ppm) by the resonance frequency of the spectrometer in megaHertz.
J Hz = ppm x MHz (typically 300, 400, or 500 MHz)
In general, N neighboring protons with the same coupling constant J will split the absorbance of a proton or set of equivalent protons into N+1 lines. Note that the splitting pattern observed for a particular proton or set of equivalent protons is not due to anything inherent to that nucleus but due to the influence of the neighboring protons. The relative intensity ratios are given by Pascal's triangle as shown in Figure 18.
Because of the mechanism of J coupling, the magnitude is field independent: coupling constants in Hertz will be the same whether the spectrum is measured at 300 MHz or 500 MHz. Coupling constants range in magnitude from 0 to 20 Hz. Observable coupling will generally occur between hydrogen nuclei that are separated by no more than three sigma bonds.
H-C-H, two sigma bonds or geminal coupling
H-C-C-H, three sigma bonds or vicinal coupling
Coupling is never observed between chemical shift equivalent nuclei, be it from symmetry or by accident, not because the Bn field disappears but because spin transitions that would reveal the coupling are forbidden by symmetry. The role of symmetry in forbidding spectral transitions is of general importance in spectroscopy but is beyond the scope of this discussion. The magnitude of the coupling constant also provides structural information; for example, trans-alkenes show larger vicinal coupling than cis-alkenes. Sometimes, coupling is not observed between protons on heteroatoms such as the OH proton of an alcohol and adjacent protons on carbon. In this case the absence of coupling results from rapid exchange of the OH protons via an acid base mechanism; because of rapid exchange the identity of the spin state, or , of the acidic proton is lost. Examples of coupling constants J are shown in Figure 12.
The example of geminal coupling of protons on a saturated carbon requires a structure in which the protons have different chemical shifts. This commonly occurs in a chiral molecule with a tetrahedral stereocenter adjacent to the methylene group as shown in the following compounds with stereocenters labeled with an asterisk. The geminal protons are labeled HA and HB rather than HA and HX because they have similar chemical shifts (A and B are close in the alphabet). Coupling between the geminal protons is independent of optical activity and rotation about single bonds. The hydrogens HA and HB are said to be diastereotopic hydrogens because if alternately each one is replaced with a deuterium atom, the resulting two structures are diastereomers (stereoisomers that aren't mirror images).
Now let's examine the 1H NMR spectrum of methyl propanoate (methyl propionate). Notice that hydrogen atoms of the methyl group bonded to oxygen appear as a singlet at 3.6 ppm. They are chemical shift equivalent and hence, do not couple with each other. The chemical shift results from the deshielding effect of the strongly electronegative oxygen atom. The resonance for the methylene protons appear as a quartet at 2.3 ppm. The splitting is caused by the three chemical shift equivalent protons on the adjacent methyl group. The methylene protons do not split each other since they are also chemical shift equivalent. The methyl protons appear at 1.1 ppm and are split into a triplet by the adjacent methylene protons. The coupling constant for the methyl triplet and the methylene quartet is 7 Hz. The overall splitting pattern consisting of a three-proton triplet and a two-proton quartet is called an A3X2 pattern.
next section: Spin-spin splitting and coupling - More complex 1H NMR splitting
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