Graph of the Karplus relation JHH(φ) = 12 cos^2φ - cosφ+2 obtained for ethane derivatives [1]
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.
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.
^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.
^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.
The Karplusequation, named after Martin Karplus, describes the correlation between 3J-coupling constants and dihedral torsion angles in nuclear magnetic...
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...
academic Karplus-Strong string synthesis Martin Karplus (born 1930), American theoretical chemist and 2013 Nobel Laureate (Chemistry) Karplusequation Robert...
Martin Karplus (German: [ˈmaʁˌtin ˈkaʁplus]; born March 15, 1930) is an Austrian and American theoretical chemist. He is the Director of the Biophysical...
observed. The Karplusequation relates the dihedral angle of vicinal protons to their J-coupling constants as measured by NMR. The equation aids in the...
features such as glycosidic bond angles, dihedral angles (using the Karplusequation), and sugar pucker conformations. For large-scale structure, these...
This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References...
features such as glycosidic bond angles, dihedral angles (using the Karplusequation), and sugar pucker conformations. The presence or absence of imino...
the psi and phi angles, can be generated. One approach is to use the Karplusequation, to generate angle restraints from coupling constants. Another approach...
they must be used in low concentrations to avoid line broadening. Karplusequation Chiral derivatizing agent Mosher's acid Chiral solvating agent Chiral...
features such as glycosidic bond angles, dihedral angles (using the Karplusequation), and sugar pucker conformations. For large-scale structure, these...
Chemistry: A History of Quantum Chemistry, MIT Press, 2011, ISBN 0-262-01618-4 Karplus M., Porter R.N. (1971). Atoms and Molecules. An introduction for students...
approximations of the wave equation by Hiller and Ruiz in 1971[citation needed], it was not until the development of the Karplus-Strong algorithm, the subsequent...
variables, combinatorial reasoning, and proportional reasoning. Robert Karplus, a science educator in the 1960s and 1970s, investigated all these forms...
Chemistry (4th ed.). Saunders College Publishing. p. 196. ISBN 0-03-072373-6. Karplus, Martin, and Porter, Richard Needham. Atoms and Molecules. United States...
and Optical Physics (2nd ed.). Springer. p. 5. ISBN 978-0-387-20802-2. Karplus, Martin; Porter, Richard Needham (1970), Atoms and Molecules: An Introduction...
polymeric and anisotropic liquids. Springer. ISBN 3540262105. Blondel, Arnaud; Karplus, Martin (7 Dec 1998). "New formulation for derivatives of torsion angles...
Biochemistry vol 11 pp. 2192–2198 doi 10.1021/bi00761a029 Bashford and Karplus (1991) J. Phys. Chem. vol 95 pp. 9556–61 doi 10.1021/j100176a093 Gilson...
J. Quantum Chem. 86 (5): 433–439. doi:10.1002/qua.10038. Zhou, Yaoqi; Karplus, Martin; Ball, Keith D.; Bery, R. Stephen (2002). "The distance fluctuation...
frequency component in a signal. Can be used for DTMF digit decoding. Karplus-Strong string synthesis: physical modelling synthesis to simulate the sound...
students embedded it into a finite element code for the first time. Martin Karplus, Michael Levitt, and Arieh Warshel received the Nobel Prize in Chemistry...
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