For the ABX spectrum shown in Fig. 12.27 the frequencies of the lines, relative to some arbitrary

Question:

For the ABX spectrum shown in Fig. 12.27 the frequencies of the lines, relative to some arbitrary origin, are given in the following table.

(a) From the AB part, pick out the lines which correspond to the two subspectra. In doing this it is useful to remember that in an AB pattern: (i) the separation between the two low-frequency lines, and the separation between the two high-frequency lines, is JAB; (ii) the two outer lines have the same intensity as one another, as do the two inner lines. In addition the same splitting by JAB occurs in both subspectra.

(c) You should now have four effective Larmor frequencies, two for each subspectrum: let us call these u1 and u2 for the first subspectrum, and u3 and u4 for the second subspectrum. The problem is that at this stage there is no way of knowing which pair of these frequencies correspond to u0,A± and which pair correspond to uo,B±. There are basically two distinct
possibilities: (1) v1 and v3 are v0,A±» and v2 and v4 are vo.B±; (2) v1 and v4 are vo,A±, and v2 and v3 are v0,B±- In the first case it does not matter whether v1 or v3 is v0.A+, and so on for the other combinations.
Make a choice corresponding to (1) and hence find values for v0,A, v0,B) J AX and JBX (the signs of the coupling constants should be retained). Then make a choice corresponding to (2) and hence find a second set of parameters.
(d) The only way of distinguishing between the two choices is to compute the form of the X part of the spectrum. Assuming that v is -1000 Hz do this for both possibilities and, by comparing your result with Fig. 12.27 on the previous page, determine which possibility is the correct one.