5-HMR-14 A2X2 and AA'XX' Patterns
In A2X2 and A2B2 patterns the two A nuclei and the two X (B) nuclei are magnetically equivalent: they have the same chemical shift by symmetry, and each A proton is coupled equally to the two X (or B) protons. True A2X2 patterns are quite rare. Both the A and X protons are identical triplets.
An example of an A2X2 patterns is shown below. Note that the methyne protons signals are a little broader than the CH2, presumably there is a small long-range coupling to the MeO protons.
More complicated patterns are seen when the chemical shift difference approaches or is smaller than the JAB coupling. However, both A2B2 and AA'BB' always give centrosymmetric patters (A2 part mirror image of the B2 part).
AA'XX' and AA'BB' spectra are much more common. Here each A proton is coupled differently to the B and B' protons (or X, X' nuclei). Some molecules with such patterns are:
Such molecules give inherently second-order multiplets. Only if the JAB coupling is identical to the JAB' coupling by accident does the system become A2B2 or A2X2, and a first order pattern is seen (if νAB is large enough).
AA'XX' spectra consist of two identical half spectra, one for AA' and one for XX', each a maximum of 10 lines, each symmetrical about its midpoint, νA and νX, respectively. See example B below. The appearance of the spectrum is defined by four coupling constants: JAA', JXX', JAX and JAX'. The spectrum is sensitive to the relative signs of JAX and JAX', but not to the relative signs of JAA' and JXX'. The relationship between these, and the directly measurable values K, L, M, and N are given below and in the graphic.
Each half-spectrum consists of a 1:1 doublet with a separation of N (intensity 50% of the half spectrum), and two ab quartets, each with "normal" intensity ratios and νab = |L|. One has apparent couplings (Jab) of |K| and the other of |M|, as indicated. Unfortunately, K and M cannot be distinguished, the relative signs of JAA' and JXX' are not known, nor is it known which number obtained is JAA' and which is JXX'. It is also not known which coupling is JAX and which is JAX', but the relative signs of JAX and JAX' can be determined: if |N| is larger than |L|, signs are the same. Thus the 19F and 1H spectra of 1,1-difluoroethylene (B) are identical, so it is not possible to distinguish which coupling is 2JFF and which is 2JHH, nor can one tell which is the cis JHF and which is trans JHF. This would have to be done using information about such couplings obtained from compounds where the assignments are not ambiguous.
Solving an AA'XX' Pattern. If all 10 lines are visible, and can be assigned to the large doublet and the two ab quartets, the process is straighforward, as shown for the solution of the 19F NMR spectrum of 1,1-difluoroethylene below:
1. Determine N from the doublet separation (35.3 Hz).
2. Measure K (41.2 and 41.4 Hz) and M (31.7, 32.0 Hz) from the appropriate line separation ("J" of the two ab quartets).
3. Calculate L - it is the "δab" of each of the ab quartets. For the K quartet we get: SQRT[(276.2-181.3)(235.0-222.7)] = 33.8 Hz, for the M quartet: SQRT[(268.1-189.8)(236.4-221.8)] = 34.2 Hz
4. Calculate JAA' and JXX' by summing and subtracting K and M: JAA' = (K+M)/2 = (41.3+31.8)/2 = 36.5 Hz; JXX' = (K-M)/2 = (41.3-31.8)/2 = 4.7 Hz. Because we do not know which ab quartet is K, and which M, we do not know the relative signs of JAA' and JXX', nor do we know which coupling is which.
5. Calculate JAX and JAX' by summing and subtracting L and N: JAX = (N+L)/2 = (35.3+34.0)/2 = 34.7 Hz, JAX' = (N-L)/2 = (35.3-34.0)/2 = 0.7 Hz. Again, we do not know which coupling is which, but the relative signs can be determined: if |N| is larger than |L|, the signs are the same, as in this case.
Special Cases of AA'XX' patterns: Unfortunately a large fraction of AA'XX' patterns are missing lines, which means that some or all of the coupling constants may be indeterminate. Below are summarized several common (and some less common) situations where a reduced number of lines is seen.
In the situation where JAX = JAX' (i.e. L = 0, A2X2) the spectrum collapses to a triplet. In other words, the effective "chemical shift" of each of the ab quartets is zero, and thus each gives a single line at νA. This is more or less the situation with many acyclic compounds of the X-CH2-CH2-Y type, provided that X and Y are not too large, but cause very different chemical shifts. See example C.
In cases where JXX' is zero, both ab quartets will have the same Jab (M = K) and will be identical, leaving only 6 lines. This is nearly the case for situations like symmetrical o-disubstituted benzenes or 1,4-disubstituted butadienes, where JAA' is a 3-bond coupling, and JXX' a 5-bond coupling. In these situations L is small (i.e.JAX is close to JAX') and the central lines of the K and M quartets will likely be superimposed, whereas the small outer lines may be distinct -- the outer lines are separated by just under twice the value of JXX', the inner lines by just a fraction of JXX'.
If the signs of JAX and JAX' are different the N lines will be relatively close together. This is the case for AA'XX' patterns of the AA' vicinal type, where JAB is a geminal coupling, hence negative, and JAB' is vicinal, and hence positive. In the limit, if JAX = -JAX' then the N lines can collapse to a singlet.
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