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:

νA:	11044.68 Hz	repeated spacings: JAB + M'+
δA:	54.5534 ppm	(ν1 - ν3)	(ν2 - ν4)	(ν5 - ν8)
vB:	11155.41 Hz	-67.64 Hz	-67.86 Hz	-66.81 Hz
δB:	55.1003 ppm	repeated spacings: JAB - M'-
JAB:	56.84 Hz	(ν1 - ν2)	(ν3 - ν4)	(ν6 - ν7)
Δν/J:	1.95	-40.25 Hz	-40.47 Hz	-41.06 Hz

Simulation of AB₂

v1 = 10977.06 Hz	I1 = 0.3596
v2 = 11017.53 Hz	I2 = 0.5161
v3 = 11044.68 Hz	I3 = 1.0000
v4 = 11085.15 Hz	I4 = 2.1304
v5 = 11132.59 Hz	I5 = 3.1242
v6 = 11137.77 Hz	I6 = 2.6404
v7 = 11178.24 Hz	I7 = 1.3535
v8 = 11200.21 Hz	I8 = 0.8696
v9 = 11293.29 Hz	I9 = 0.0062
	ΣI = 12.0000

left = 11324.92 Hz | right = 10945.44 Hz

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