Information-Rich 13C Satellites

Seemingly simple NMR spectra often contain much more information than one might think.  For example, the ¹H NMR spectrum of 1,4-dioxane is primarily a singlet from which one obtains only an isotropic ¹H chemical shift value.  There is however much more information available in the spectrum which is often not recognized or used.  The ¹H NMR spectrum of a naturally occurring sample of 1,4-dioxane is the weighted sum of the ¹H spectra of all possible isotopomers.  It is the dominant tetra-¹²C isotopomer that gives rise to the singlet but since ¹³C (spin I = 1/2) is 1.1% naturally abundant, one expects to observe also the mono-¹³C isotopomer.  The di-, tri- and tetra-¹³C isotopomers are very rare and can be neglected.  The symmetry in the mono-¹³C isotopomer is lost compared to the tetra-¹²C isotopomer and one obtains a complex second-order spectrum, part of which can be represented by an AA'BB'X spin system.  The spectrum of the AA'BB'X spin system depends on many more parameters than just the isotropic ¹H chemical shift.   This is illustrated in the figure below.

The bottom panel of the figure is the measured 300 MHz ¹H NMR spectrum of 1,4-dioxane with an exaggerated vertical scale to accentuate the ¹³C satellites resulting from the protons color coded in pink in the mono-¹³C isotopomer.  The large central region of the spectrum is the result of all the protons color coded in yellow from both the tetra-¹²C and mono-¹³C isotopomers.   A simulation of this second-order spectrum was calculated from the parameters below and is shown in the top panel of the figure. 

Any isotope shifts in the ¹H frequencies due to ¹³C vs ¹²C bonding were neglected in the simulation.  The fit of the simulation to the ¹³C satellites is particularly sensitive to ¹J_C-Ha,  ¹J_C-Hb,  ³J_Ha-Hc,  ³J_Ha-Hd, ³J_Hb-Hc and ³J_Hb-Hd and much less sensitive to  ²J_C-Hc,  ²J_C-Hd,  ²J_Ha-Hb and  ²J_Hc-Hd.  A fit of the simulation to the experimental spectrum produces estimates for all of the coupling constants in the AA'BB'X spin system - much more information than a single ¹H isotropic chemical shift!