Navigation menu

First order or second order spectra

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: (Vi - Vj) / Jij
    • Approximation of weakly coupled nuclei: : |Vi - Vj| >> |Jij|
      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

      • 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


  • 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
The two nuclei therefore have the same NMR resonance frequency: they are ISOCHRONES


  • Two nuclei are ISOGAMIC if they have the same coupling relationships with any of their neighbors that do not have the same chemical shift.
    • 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 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)...
Next page
Previous page