Spin System: AB2 Analysis

Contents

This page contains:

1. information on the analysis of an AB₂ spin system and
2. a form to extract coupling constants and chemical shifts from observed frequencies,
3. and simulation using the solution

Analysis of AB₂

• The analysis requires to label the peaks as shown in the picture above (see comments on general features of AB₂ spin systems)

Input Section

Please enter the eight frequencies (in Hz) of the peaks
* in ascending order if A is to lower frequencies of B (as shown in the picture above)
* in descending order if A is to higher frequencies of B
and the frequency SF of the reference compound (in MHz), as well as the desired total width of the simulated spectra in pixels (be reasonable ;-):

f1:	Hz	f2:	Hz	SF:	MHz
f3:	Hz	f4:	Hz	width:	pixel
f5:	Hz	f6:	Hz
f7:	Hz	f8:	Hz

 

Solution:

repeated spacings: JAB + M'+			νA:	9.00 Hz
(ν1 - ν3)	(ν2 - ν4)	(ν5 - ν8)	δA:	0.1500 ppm
-9.00 Hz	-8.90 Hz	-8.80 Hz	vB:	35.50 Hz
repeated spacings: JAB - M'-			δB:	0.5917 ppm
(ν1 - ν2)	(ν3 - ν4)	(ν6 - ν7)	JAB:	7.93 Hz
-6.70 Hz	-6.60 Hz	-6.60 Hz	Δν/J:	3.34

Simulation of AB₂

A	v1 = 0.07 Hz	I1 = 0.5421
	v2 = 6.68 Hz	I2 = 0.7765
	v3 = 9.00 Hz	I3 = 1.0000
	v4 = 15.61 Hz	I4 = 1.6827
B	v5 = 31.85 Hz	I5 = 2.6814
	v6 = 32.53 Hz	I6 = 2.4579
	v7 = 39.15 Hz	I7 = 1.5407
	v8 = 40.79 Hz	I8 = 1.3173
comb.	v9 = 64.32 Hz	I9 = 0.0014
	Δν/J = 3.34	ΣI = 12.0000

left = 70.74 Hz | right = -6.36 Hz
The ticks under the frequency axis mark the chemical shifts of A and B and the position of the combination line

References

1. Garbisch, E. W., Jr., J. Chem. Educ. 1968, 45, 402-416, DOI: 10.1021/ed045p402. The equations for the transition frequencies and intensities look more attractive for an implementation to calculate spectra, but they contain errors. The calculations here use the expressions from [2] and [3].
2. Bernstein, H. J.; Pople, J. A.; Schneider, W. G., Can. J. Chem. 1957, 35, 65-81, DOI: 10.1139/v57-011
3. Bovey, F. A.; Jelinski, L.; Mirau, P. A., Nuclear Magnetic Resonance Spectroscopy, 2nd ed., Academic Press, San Diego, 1988, DOI: 10.1016/C2009-0-21711-9