Spin System: ABX Analysis | AB Part

Contents

This page contains:

1. information on the analysis of the AB part of an ABX spin system and
2. a form to extract coupling constants and chemical shifts from observed frequencies,
3. and simulations using both solutions, especially the resulting X parts

Analysis of AB-part

• The AB part of an ABX spin system consists of up to 8 peaks.
• The AB part can be broken down into two AB subspectra, corresponding to the two spin states of the X nucleus.
• The AB part is not necessarily symmetric about the center of gravity of the AB part (see figure above).
• The analysis gives |J_AB|, J_AX, J_BX, and δ_AB. Only if the A and B nuclei are at least moderately tightly coupled will the relative signs of J_AX and J_BX affect the spectrum.
• For the analysis, one needs to identify the two AB subspectra (see figure above):
  1. one should find J_AB four times in the spectrum (property of repeated spacings);
  2. the intensities should correspond to the intensity sum rule:
     I1' = I4', I1'' = I4'', I2' = I3', I2'' = I3''
• In general, the analysis of the AB part yields two solutions, but both solutions differ in the intensities in the X part.

Input Section

Please enter the eight frequencies (in Hz) of the peaks in descending order 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

Now assign the index number of the peaks to the transitions of the two AB sub spectra:

1':		1'':
2':		2'':
3':		3'':
4':		4'':

 

Input Data
first AB spectrum:	v1' = 44.67	v2' = -105.61	v3' = -603.37	v4' = -753.64
second AB spectrum:	v1'' = -857.45	v2'' = -1007.72	v3'' = -1023.91	v4'' = -1174.18
JAB (std. dev.):	150.27 (0.00) Hz

Solution 1:

fo':	-354.49			fo'':	-1015.82
D':	630.37			D'':	71.61
vA':	-39.30	vB':	-669.67	vA'':	-980.01	vB'':	-1051.62
JAX:	940.71 Hz			JBX:	381.95 Hz
vA:	-509.66 Hz	δA:	-5.0333 ppm	vB:	-860.65 Hz	δB:	-8.4997 ppm

Solution 2:

fo':	-354.49			fo'':	-1015.82
D':	630.37			D'':	71.61
vA':	-39.30	vB':	-669.67	vA'':	-1051.62	vB'':	-980.01
JAX:	1012.32 Hz			JBX:	310.34 Hz
vA:	-545.46 Hz	δA:	-5.3869 ppm	vB:	-824.84 Hz	δB:	-8.1461 ppm

Simulation of ABX, Solution 1

vA: -509.66 Hz | δA: -5.0333 ppm || vB: -860.65 Hz | δB: -8.4997 ppm   first AB spectrum (red): v1' = 44.67 | v2' = -105.61 | v3' = -603.37 | v4' = -753.64 I1' = 0.7681 | I2' = 1.2319 | I3' = 1.2319 | I4' = 0.7681   second AB spectrum (blue): v1'' = -857.45 | v2'' = -1007.72 | v3'' = -1023.91 | v4'' = -1174.18 I1'' = 0.0973 | I2'' = 1.9027 | I3'' = 1.9027 | I4'' = 0.0973	X part (magenta): v10 = 407.25 I10 = 0.1861 v11 = 661.33 I11 = 1.0000 v12 = 240.79 I12 = 0.8139 v13 = -240.79 I13 = 0.8139 v14 = -661.33 I14 = 1.0000 v15 = -407.25 I15 = 0.1861

Simulation of ABX, Solution 2

vA: -545.46 Hz | δA: -5.3869 ppm || vB: -824.84 Hz | δB: -8.1461 ppm   first AB spectrum (red): v1' = 44.67 | v2' = -105.61 | v3' = -603.37 | v4' = -753.64 I1' = 0.7681 | I2' = 1.2319 | I3' = 1.2319 | I4' = 0.7681   second AB spectrum (blue): v1'' = -857.45 | v2'' = -1007.72 | v3'' = -1023.91 | v4'' = -1174.18 I1'' = 0.0973 | I2'' = 1.9027 | I3'' = 1.9027 | I4'' = 0.0973	X part (magenta): v10 = 407.25 I10 = 0.6046 v11 = 661.33 I11 = 1.0000 v12 = 240.79 I12 = 0.3954 v13 = -240.79 I13 = 0.3954 v14 = -661.33 I14 = 1.0000 v15 = -407.25 I15 = 0.6046

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.