First order or second order spectra
When the nonsecular 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

Analyze the sample with a higher magnetic field
 Δν depends on B_{0}
J is independent of B_{0}
 Approximation of weakly coupled nuclei: :
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 rotationreflection), the nuclei are called enantiotopes
The two nuclei therefore have the same NMR resonance frequency: they are ISOCHRONES
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: A_{2}, X_{2}, X_{6}, A_{3}X_{2}, AMX_{2}, ...  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’KX_{3}, AA’A ’’A’’’A^{(4)}A^{(5)}A^{(6)}...