COUPLING CONSTANTS DUE TO SPIN - SPIN SPLITTING

The magnitude of the spin - Spin splitting constants between hydrogen nuclei is normally measured in hertz. These values are called coupling constants, J. The coupling between the two groups of protons must be the same because the protons are the same distance apart and are coupling through identical space and bonds. J= line separation in parts per minute x spectrometer frequency in MHz.

RULES GOVERNING FIRST - ORDER SPECTRA :-

The spectra which can be correctly analysed by inspection and direct measurement of coupling constants of multiplets are known as first order spectra. They arise from weakly coupled spin systems.

Rule 1:-

A group of magnetically equivalent protons will split a resonance of an interacting group of protons into n+1 lines. For example, the resonance due to the A protons in an AnXm system will be split into m+1 lines, while the resonance due to the x protons will be split into n+1 lines. More generally, splitting by n nuclei of spin quantum number I, results in 2nI+1 lines. This simply reduce to n+1 for protons where I= 1/2.

Rule 2 :-

The spacing measured in Hz of the lines in the multiplet will be equal to the coupling constant. In the above example all spacings in both parts of the spectrum will be equal to JAx.

Rule 3 :-

The true chemical shift of each group of interacting protons lies in the centre of the multiplet.

Rule 4 :-

The relative intensities of the lines within each multiplet will be in the ratio of the biochemical coefficient of (a+b)ⁿ. This leads to the following numerical relationships :

Number of protons responsible for splitting 

1

2

3

4

5

6

7

Multiplicity 

Doublet (2)

Triplet (3)

Quartet (4)

Quintet (5)

Sextet (6)

Septet (7)

Octet (8)

Relative ratio of intensities in the multiplet

1:1

1:2:1

1:3:3:1

1:4:6:4:1

1:5:10:10:5:1

1:6:15:20:15:6:1

1:7:21:35::35:21:7:1

Clearly, in the case of multiplets the outside components may be lost in the instrumental noise e.g a septet may appear as a quintet.

Rule 5:-

When a group of magnetically equivalent protons interacts with more than one group of protons, it's resonance will take the form of a multiplet of multiplets. Thus the resonance due to the A protons in a system AnMpXm Wil have the multiplicity of (p+1) (m+1). The appropriate coupling constants will control splittings and relative intensities will obey rule 4.

Rule :-

Magnetically equivalent protons don't give rise to splitting, e.g. Any system Aₙ will give rise to a singlet.

Rule 7:-

Spin systems which contain groups of chemically equivalent protons which are not magnetically equivalent can't be analysed by first - order methods.