text: The Karplus equation, named after Martin Karplus, describes the correlation between J-coupling constants and dihedral torsion angles in nuclear magnetic resonance spectroscopy:
  where J is the J coupling constant,  is the dihedral angle, and A, B, and C are empirically derived parameters whose values depend on the atoms and substituents involved. The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2&phi; rather than cos &phi; —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 J coupling constants.  The superscript "3" indicates that a H atom is coupled to another H atom three bonds away, via H-C-C-H bonds.  (Such hydrogens bonded to neighbouring carbon atoms are termed vicinal). 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.