HOW TO CALCULATE COUPLING CONSTANTS IN NMR

The signals of protons, which have other magnetically inequivalent protons at geminal or vicinal positions are split because of spin-spin coupling between these neighboring protons. The splitting of the signal can be measured by calculating the coupling constant of the concerned signal. Coupling constant is a constant value, independent of the magnetic field strength and it mostly depends upon the extent of interaction between two proton systems. Denoted by “J”, the values of coupling constants are calculated in Hz.

Following is how we can calculate the coupling constant for a signal. Generally, the coupling constant can be calculated from the chemical shift values, as well as from the frequency data, if available.

DOUBLET

The coupling constant for doublet is calculated simply by taking the difference of the two peaks.

From Chemical shift

0.864-0.849 = 0.015 x 500 =7.5 Hz (Where, 500 is the instrument frequency, i.e., 500 MHz)

                                                                          

From frequency

The corresponding frequencies for these two peaks are 432.093 and 424.875 Hz. Simply take the difference of the two frequencies, you will get the coupling constant

                                                         432.093 – 424.875 = 7.218 Hz

TRIPLET

Triplet has three peaks. We can take difference of any of the two peaks because the proton couples equally with both the neighboring protons.

So, 3.5857 – 3.5684 = 0.0173 x 500 = 8.65 Hz     and    3.5684 – 3.5510 = 0.0174 x 500 = 8.7 Hz

OR

1793.309 – 1784.653 = 8.656 Hz     and     1784.653 – 1775.984 = 8.669 Hz

In either case, we get almost the same values.

QUARTET

The coupling constant for quartet is calculated just like triplet. Taking difference of any two consecutive peaks will give the J value for quartet.

DOUBLE DOUBLET

A double doublet has two coupling constants because it has two doublets. The coupling tree of the signal is quite helpful in identifying the peaks which will be used for calculation of the coupling constants in this case.

We have four lines in this tree. The two coupling constants are denoted as J1 and J2. Its quite simple to calculate J2 by taking difference of the line 1 and 2 or line 3 and 4. J1 is the coupling constant for the two blue line in the tree which are in fact not visible in the spectrum. But if you look at this tree closely, you will find that the difference between line 1 and 3 or 2 and 4 is actually equal to the difference between the two blue lines, which in fact is J1.

J1 => 2.837 – 2.808 = 0.029 x 500 = 14.5 Hz     or    2.825 – 2.796 = 0.029 x 500 = 14.5 Hz

J2 => 2.837 – 2.825 = 0.012 x 500 = 6 Hz    or    2.808 – 2.796 = 0.012 x 500 = 6 Hz