NMR Spectroscopy and Sterreochemistry

Stereo Chemical Information from coupling constant

Distinction between cis and trans isomers Trans coupling is greater than for cis.

From the value the isomers can be identified as in the following example.

For coupling the two hydrogens must have different chemical shift.
Trans coupling (range :11 to 19 Hz) is greater than cis coupling (range: 5 to 14 Hz).
³J_HH means coupling between two hydrogens separated by a distance of three bonds (vicinal coupling). If it is coupling between hydrogens at the same carbon then it is ²J_HH (geminal coupling)

In some molecules the cis-trans, distinction is made even from the position of the absorption, as in cis and trans stilbenes. In trans case the hydrogens are deshielded by two aromatic rings while in the cis case it is by one ring.

Looking from the front H_b is eclipsed by Ha the angle between the plane containing H_a and H_b is zero (they are in the same plane).
The second conformation has H_b at a different spatial position, they are not in the same plane. The plane containing H_b is 60⁰ to the right of the plane containing H_a. This is the dihedral angle, in the first case the dihedral angle is zero.
In the third case though the two atoms are in the same plane H_b has undergone a rotation of 180⁰ and that is the dihedral angle.
The dihedral angle is used when two are separated by three bonds.
Martin Karplus was the first to study the variation of coupling constant ³J_HH with dihedral angle.
The magnitude of the coupling constant between hydrogens of adjacent carbon atoms depend directly on the dihedral angle.
This magnitude is greatest when this is zero or 180⁰ and smallest when it is 90⁰.
When it is zero side-side overlap of the two C-H bond orbitals will be maximum, when it is 180⁰ back lobes overlap is maximum leading to higher “J”. When it is 60⁰ C-H bond orbitals overlap is at a minimum since they are perpendicular with each other leading to lower “J”.

The information from the above can be used to assign the configuration of the anomeric carbon in cyclic sugars. In the case of α- glucose at the anomeric carbon the equatorial proton is has a chemical shift of δ 5.2 which is down field by 0.5 for the corresponding axial proton in β-glucose.