Spin System: AA'X Analysis | X Part

Contents

This page contains:

1. information on the analysis of the X part of an AA'X spin system and
2. a form to extract coupling constants and chemical shifts from observed frequencies,
3. and, as a cross check, simulations of the X part using the solutions.

Analysis of X-Part

• The X part of an AA'X spin system can be derived from the X part of an ABX system and consists of up to 5 peaks.
• Characteristic are the two so-called N lines, peaks 11 and 14 in the figure above. Together, they account for 50% of the intensity of the X part. Their spacing corresponds to the sum of the J_AX and J_A'X coupling constants.
• The central peaks 12 and 13 are degenerate in the AA'X case, and are labeled "inner" peaks in the figure, I_i; together with peaks 10 and 15, the "outer" peaks I_o, they account for the other 50% of intensity.
• If all five peaks can be observed, the analysis gives J_AX, J_A'X, and |J_AA'|. The coupling constant |J_AA'| is hard to get otherwise, hence this spin system can be quite attractive. The relative signs of J_AX and J_A'X can also be determined.
• The outer peaks can be outside or inside the N lines. If J_AA' is much greater than the other two coupling constants, they will lie far outside the N lines and may be too weak to be detected. The spectrum will appear deceptively simple then, and look like a "triplet". First-order analysis will result in wrong couplings. A correct analysis will only yield N.
• There can also be cases where the inner lines become weak and may disappear into the noise. The spectrum may then appear deceptively simple as a "doublet of doublet". First-order analysis will result in wrong couplings.

Input Section

Please assign and enter the five frequencies (in Hz) and intensities (in arbitrary units) of the peaks and the frequency SF of the reference compound (in MHz), as well as the desired total width of the simluated spectra in pixels (be reasonable ;-):

f10:	Hz	I10:
f11:	Hz	I11:
f12:	Hz	I12:
f14:	Hz	I14:
f15:	Hz	I15:
SF:	MHz	width:	pixel

 

Analysis and Simulation of AA'X, X Part

Input Data
ν10 =	70.29 Hz	I10 =	0.23
ν11 =	38.53 Hz	I11 =	0.26
ν12 =	-11.83 Hz	I12 =	0.03
ν14 =	-63.92 Hz	I14 =	0.26
ν15 =	-95.89 Hz	I15 =	0.23
δ =	-0.13 ppm	Ii =	0.01
so =	166.18 Hz	Io =	0.23
N =	102.45 Hz	IN =	0.26
J(AX) =	131.90 Hz
J(A'X) =	-29.45 Hz
J(AA') =	19.90 Hz

Simulation of AA'X, X part

 

ν10 =	70.53 Hz	I10 =	0.2357	plot limits:
ν11 =	38.66 Hz	I11 =	0.2500	high frequency:	87.14
ν12, ν13 =	-12.57 Hz	I12+I13 =	0.0287	low frequency:	-112.27
ν14 =	-63.79 Hz	I14 =	0.2500
ν15 =	-95.66 Hz	I15 =	0.2357

 

References

1. Günther, H. NMR-Spektroskopie, Eine Einführung. Georg Thieme Verlag, Stuttgart, 1973.
2. Garbisch, E. W., Jr., J. Chem. Educ. 1968, 45, 402–416, DOI: 10.1021/ed045p402.
3. Dischler, B. Angew. Chem. 1966, 78, 653–663, DOI: 10.1002/ange.19660781302;
   Angew. Chem. Int. Ed. Engl. 1966, 5, 623–633, DOI: 10.1002/anie.196606231.