When the non-secular term has a negligible contribution compared to secular terms, the spin system is of the first order: The rules of multiplicity of Pascal's binomial apply in this case only.

• In order to detect whether a signal is of the first or second order, the following quantity must be evaluated:
  • Approximation of weakly coupled nuclei: :
    I and J are then written A and X, the spectrum is of the first order
  • If this condition is not respected, the nuclei are said to be strongly coupled
    
    • Changes in the intensity of the lines
    • Changes in the number of lines
    • Spectral analysis requires theoretical calculations
    
    
    Spectral analysis requires the simulation of NMR spectra
    
    Consequences:
    • It is no longer possible to measure J directly (except in the simple case AB)
    • Source of error in the interpretation of the spectra
    • Spectra analysis request calculation
    Possible solution:
    • Analyze the sample with a higher magnetic field
      • Δν depends on B₀
      • J is independent of B₀

Isochrony

• Two nuclei are CHEMICALLY EQUIVALENT, if they have the same chemical environment, that is if geometrically there is at least one element of symmetry (plane, axis, center) between them.
  • If the symmetry element is at least one proper axis of symmetry, the nuclei are said to be homotopic
  • If the symmetry element is strictly an improper axis of symmetry (center, plane, axis of rotation-reflection), the nuclei are called enantiotopes

Isogamy

• Two nuclei are ISOGAMIC if they have the same coupling relationships with any of their neighbors that do not have the same chemical shift.
  Remarks:
  • Two nuclei cannot be isogamic if they are not at least isochronous
  • It makes no sense to test the isogamy of a pair of nuclei if they do not have at least the same chemical environment. Indeed, in this case, they necessarily already have different coupling relationships with a given third party!

Chemical and magnetic equivalence

• Two CHEMICALLY EQUIVALENT nuclei are ISOCHRONOUS
• Two MAGNETICALLY EQUIVALENT nuclei are ISOCHRONOUS & ISOGAMIC
  Corollaries:
  • Two nuclei can therefore be chemically, but not magnetically, equivalent if they are not isogamic.
  • Two magnetically equivalent nuclei are necessarily chemically equivalent

Nomenclature of spin systems

• Nuclei that have no equivalence relations are written with different letters
  Example: AX, AMX…
• Magnetically equivalent nuclei or clusters of nuclei are written with the same letter, indicated by the number of nuclei involved in each group
  Example: A₂, X₂, X₆, A₃X₂, AMX₂, ...
• Chemically equivalent nuclei or clusters of nuclei are written with the same letter, but are differentiated from each other by a typographic character. There are as many characters as there are spins involved in the group considered
  Example: AA’, XX’, AA’KX₃, AA’A ’’A’’’A⁽⁴⁾A⁽⁵⁾A⁽⁶⁾...