Karplus equation

The Karplus equation, named after Martin Karplus, describes the correlation between 3J-coupling constants and dihedral torsion angles in nuclear magnetic resonance spectroscopy:[2] where J is the 3J coupling constant,

is the dihedral angle, and A, B, and C are empirically derived parameters whose values depend on the atoms and substituents involved.

[3] The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2φ rather than cos2 φ —these lead to different numerical values of A, B, and C but do not change the nature of the relationship.

[4] The magnitude of these couplings are generally smallest when the torsion angle is close to 90° and largest at angles of 0 and 180°.

This relationship between local geometry and coupling constant is of great value throughout nuclear magnetic resonance spectroscopy and is particularly valuable for determining backbone torsion angles in protein NMR studies.