KNOWPIA
WELCOME TO KNOWPIA

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

where *J* is the ^{3}*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.^{[3]} The relationship may be expressed in a variety of equivalent ways e.g. involving cos^{2} φ rather than cos 2φ —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 ^{3}*J*_{H,H} coupling constants. The superscript "3" indicates that a ^{1}H atom is coupled to another ^{1}H 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.

**^**Minch, M. J. (1994). "Orientational Dependence of Vicinal Proton-Proton NMR Coupling Constants: The Karplus Relationship".*Concepts in Magnetic Resonance*.**6**: 41–56. doi:10.1002/cmr.1820060104.**^**Dalton, Louisa (2003-12-22). "Karplus Equation".*Chemical & Engineering News*.**81**(51): 37. doi:10.1021/cen-v081n036.p037.**^**Karplus, Martin (1959). "Contact Electron-Spin Coupling of Nuclear Magnetic Moments".*J. Chem. Phys.***30**(1): 11–15. Bibcode:1959JChPh..30...11K. doi:10.1063/1.1729860.**^**Karplus, Martin (1963). "Vicinal Proton Coupling in Nuclear Magnetic Resonance".*J. Am. Chem. Soc.***85**(18): 2870–2871. doi:10.1021/ja00901a059.

- Generalized Karplus calculation of proton-proton coupling constants
- Karplus equations app