# How to predict a COSY NMR spectra for an AMX spin system?

Does anyone know how to draw (predict) a hypothetical COSY NMR spectra for AMX spin system (the spin of A M X nuclei is 1/2)?

An AMX spin system represents three nuclei coupled to each other, with their signals separated by a large chemical shifts compared to the coupling between them (such that $\Delta \delta >> 3J$). This system is said to be first-order, and the A, M and X signals are each a doublet of doublets, and the couplings can be extracted by inspection.

The simple COSY spectrum of this will show the three core signals along the diagonal, with cross peaks appearing for all signals ie each signal will have two cross peaks. Below is a (very basic) schematic for an AMX COSY. The appearance of the cross peaks will depend on the type of COSY experiment you are running, such as a COSY-45 or COSY-dqf etc, but this should give you the general picture for what you are asking.

• Thank you for your answer! I get the concept. But how would the signals of A, M and X look if the spin of M and X nuclei is 1 (and the spin of A remains 1/2)? They wouldn't be doublet of doublets, right?
– Mark
Jan 13, 2014 at 21:19
• The quick answer as a comment (ask a new question if you need further clarification): Remember that splitting is described by the formula 2nI+1. For the system of A (n=1, I=1/2) M (n=1, I=1/2) and X (n=1, I=1/2), you would have the spectrum appearing as A: 9 line multiplet (9 lines of equal intensity which some describe as a triplet of triplets), and M and X each a 6 line multiplet (6 lines of equal intensity, which some describe as a doublet of triplets). The actual appearance though will depend on the coupling constants as you may get overlap of some of the lines.
– long
Jan 14, 2014 at 1:47