Field Dependence of a Simple Spin System

With the recent re-emergence of low-field NMR spectrometers at proton frequencies of 40, 60, 80 and 100 MHz, many younger NMR users (who have grown up with high-field spectrometers) are encountering more and more second-order spectra. These spectra are observed when the frequency difference between signals is comparable to the coupling between them.  On a 600 MHz spectrometer, 1 ppm in a ¹H spectrum = 600 Hz while on a 60 MHz spectrometer, 1 ppm in a ¹H spectrum is only 60 Hz.  Unlike frequency differences between signals (in Hz) which depend on the field strength, the coupling between signals (in Hz) is field invariant. Easily interpreted first-order spectra on high-field instruments can be information rich but much more complicated second-order spectra on low-field instruments.  The figure below shows simulated ¹H NMR spectra of a fictitious isolated ethyl group as a function of field strength.  The difference in chemical shift between the -CH₃ and -CH₂- signals is 0.5 ppm and the ³J_H-H  coupling constant is 10 Hz.  The spectra are plotted on a ppm scale on the left and on a Hz scale on the right.  At higher fields, one immediately recognizes the familiar triplet and quartet.  At lower fields, the spectra are much more complicated.  The signals are closer to one another (in Hz) and therefore have more second-order character as the frequency difference between signals becomes comparable to the coupling between them.