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, [math]\displaystyle{ \phi }[/math] 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.
The relationship is used for 3JH,H coupling constants. The superscript "3" indicates that a 1H atom is coupled to another 1H atom three bonds away, via H-C-C-H bonds. (Such hydrogens bonded to neighbouring carbon atoms are termed vicinal).[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.
![]() | Original source: https://en.wikipedia.org/wiki/Karplus equation.
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