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

The nuclear spin of two protons of CH₂ group can have three possible orientations that may affect the resonance frequencies of protons of CH₃ group.

Orientation	I	Peak Intensity
↑↓	+1	1
↑↓  ↑↓	0	2
↑↓	−1	1

The nuclear spin of CH₃ protons interacts with I = +1, 0, −1 and thus splits into three peaks in the peak height i.e. intensity ratio 1 : 2 : 1.
The nuclear spin of three protons CH₃ group can have four possible orientations that may affect the resonance frequencies of protons of CH₂ group.

Orientation	I	Peak Intensity
↑↑↑	+ 3/2	1
↓↑↑   ↑↓↑   ↑↑↓	+ 1/2	3
↑↓↓   ↑↓↑   ↓↓↑	−1/2	3
↓↓↓	−3/2	1

The nuclear spin of CH₂ protons interacts with the nuclear spin of CH₃ protons and thus CH₂ signal splits into four peaks in the intensity ratio 1 : 3 : 3 : 1. The O—H peak does not split due to the presence of 0-atom (I = 0) between C and H atoms.The ¹H nmr spectrum for ethanol under high and low resolution is shown as-

Q. Explain spin-spin interaction of nmr signals with suitable example.