Spin-Spin Interaction or Coupling of NMR Signals

Spin-Spin Interaction or Coupling of NMR Signals

The splitting of nmr signal into 2nI + 1 peaks due to interaction of adjacent nuclear spins under high resolution is called spin-spin interaction. Though signal splits but the area under the curve remains the same. Unlike chemical shift (δ), it is independent of magnetic field. The relative peak intensities are given by coefficients of terms in the expansion of (r + 1)ⁿ:
(r + 1)¹: r + 1 i.e. 1 : 1
(r + 1)²: r² + 2r + 1 i.e. 1 : 2 : 1
(r + 1)³: r³ + 3r² + 3r + 1 i.e. 1 : 3 : 3 : 1
(r + 1)⁴: r⁴ + 4r³ + 6r² + 4r + 1 i.e. 1 : 4 : 6 : 4 : 1
(r + 1)⁵: r⁵ + 5r⁴ + 10r³ + 10r² + 5r + 1 i.e. 1 : 5 : 10 : 10 : 5 : 1
It is not operative beyond three bonds and so, splitting occurs due to neighbouring H atoms and no splitting is caused by protons of the same environment or equivalent protons.
Let us consider ethanol-
CH₃—CH₂—OH
Number of peaks for CH₂ = 2nI+1 = 2 X 3 X ½ + 1 = 4
Number of peaks for CH₃ = 2nI+1 = 2 X 2 X ½ + 1 = 3
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