Karplus equation
Encyclopedia
The Karplus equation, named after Martin Karplus
, describes the correlation between 3J-coupling
constants and dihedral torsion angles
in nuclear magnetic resonance spectroscopy:
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. The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2 φ rather than cos2φ —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
). 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 back bone torsion angles in protein NMR studies.
Martin Karplus
Martin Karplus is an Austrian-born American theoretical chemist. He has been Theodore William Richards Professor of Chemistry at Harvard University since 1979...
, describes the correlation between 3J-coupling
J-coupling
J-coupling is the coupling between two nuclear spins due to the influence of bonding electrons on the magnetic field running between the two nuclei. J-coupling contains information about dihedral angles, which can be estimated using the Karplus equation...
constants and dihedral torsion angles
Dihedral angle
In geometry, a dihedral or torsion angle is the angle between two planes.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection...
in nuclear magnetic resonance spectroscopy:
where J is the 3J coupling constant,
is the dihedral angleDihedral angle
In geometry, a dihedral or torsion angle is the angle between two planes.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection...
, 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 φ rather than cos2φ —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
Vicinal (chemistry)
In chemistry vicinal stands for any two functional groups bonded to two adjacent carbon atoms. For example the molecule 2,3-dibromobutane carries two vicinal bromine atoms and 1,3-dibromobutane does not....
). 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
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
spectroscopy and is particularly valuable for determining back bone torsion angles in protein NMR studies.