The simplest molecules that show J coupling contain two spin 1/2 nuclei separated by 1, 2, 3 (occasionally 4 and 5) bonds from each other. If the chemical shift between the protons HAand HX is large compared to the coupling between them (νAX >> JAX), we label them as AX. If the chemical shift is comparable to the coupling between the protons (νAB < 5 JAX),we have an AB system. Some molecules that give AB/AX patterns are shown below (spectra are all at 300 MHz):
· Disubstituted alkenes
· 1,2,3,4- and 1,2,3,5-tetrasubstituted benzenes; polysubstituted furans, pyridines, and other aromatic systems
· Isolated diastereotopic CH2 groups. Exercise: Assign the protons in this spectrum.
· Benzyl, methoxymethyl and related protecting groups in chiral molecules. Exercise: Assign the protons in this spectrum.
Energy Levels of AX and AB Spectra
The four energy levels for an AX system are given in a very straightforward way by the equation below, by substituting the four possible spin combinations of mA and mX (++, +-, -+, --):
E = -(mAνA + mXνX) + mAmXJAX
There are four states: αα, αβ, βα, ββ. We will use the convention: αα is the lowest energy state (α is aligned with the field, m = +½) and ββ is the highest energy state (β is aligned against the field, m = -½). The first term in the equation is the chemical shift part, the second term the coupling part. If the coupling is a small perturbation, then the energy is simply the sum of the two parts. In energy level terms, this means that the energy separation of the αβ and βα states is large compared to J.
AB Spectra
When the energies of the αβ and βα states approach each other, they begin to mix, the αβ state develops some βα character and vice versa (the mixing parameter Q specifies the degree of mixing). The energy of the βα state, instead of ½ (νA-νB), then becomes ½ [(νA-νB)2 + J2]½ (here defined as D)
In addition to these perturbations in energy levels, the probability of the transitions (i.e. line intensities) also varies - the A1 and B2 transitions become weaker and eventually disappear (i.e. they become forbidden), leaving only the A2 and B1 lines, which appear exactly at the chemical shifts of A and B when Δν becomes 0.
Solving an AB pattern:
Graphical method for determining the position of a leaning coupled partner. The point Q is the horizontal projection of the line 2 on the position of line 1, and point P is the projection of the line 1 on the position of line 2. The line through P and Q intersects the baseline at the midpoint between the chemical shifts of A and B (point C) (http://www.ebyte.it/library/docs/kts/KTS isoAB Geometry.html). You can use this method to quickly estimate where a leaning doublet's coupling partner should be, if other peaks obscure the region of interest, or to determine whether you are looking at a leaning doublet, or two unrelated peaks.
How to report an AB quartet.
Journals require that NMR spectra be reported in text format. There are several ways an AB quartet could be reported:
1. Treat the pattern as first order (i.e., as two doublets). This is OK for AB quartets with a large νAB / JAB ratio, say > 4, where the error in chemical shifts caused by simply taking the middle of each doublet is small:
3.68 (d, 1H, J = 10.3 Hz), 3.79 (d, 1H, J = 10.3 Hz)
2. For closely spaced AB quartets (νAB / JAB < 4) the AB character should be explicitly shown, to indicate that the pattern was recognized, and the shifts were calculated correctly. One way is to report the chemical shift of the center of the AB quartet, and ΔδAB and JAB.
2.66 (ABq, 2H, ΔδAB = 0.05, JAB = 12.2 Hz)
A second way is to report the two chemical shifts, and the coupling.
2.63, 2.69 (ABq, 2H, JAB = 12.2 Hz)
Note that the latter two formats not only use less journal space but also contain more information than the "first order" format (1). There is nothing in the first description that specifies that the two doublets are coupled to each other, yet that would be obvious from observing the spectrum.
Shown above is the 60 MHz spectrum of Abel's ketone in CDCl3 solution. There are three sets of protons that one would expect to form AB quartets. Exercise: Identify them on the structure.
The AB quartet at 3.7 δ can be analyzed as follows:
This is a little off because the intensity ratio is not very accurate, but allows proper assignment. You could also use the graphical method illustrated on the previous page.
