 Karplus equation

A Karplus equation relates a vicinal scalar coupling to molecular torsion, often represented as $J=A{\cos }^2\varphi +B\cos \varphi +C$. Parameters depend on the chemical environment. A mobile molecule gives a population average of couplings, which is generally not the coupling evaluated at its mean angle.

The Karplus equation is a relationship used in chemistry, particularly in the study of nuclear magnetic resonance (NMR) spectroscopy, to describe the correlation between the coupling constant \( J \) of hydrogen atoms and the dihedral angle \( \phi \) between them. It is particularly useful for understanding the coupling observed in aliphatic and aromatic compounds.