Karplus equation
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The Karplus equation, named after Martin Karplus, describes the correlation between coupling constants and back bone torsion angles in nuclear magnetic resonance spectroscopy. This equation is an important tool for the elucidation of 3D structures through NMR methods, and it takes one of several forms, depending on whether one, two, or three-dimensional NMR spectroscopy is being performed. For one-dimensional NMR, it is the following:
where J is the coupling constant, φ is the carbon - carbon dihedral angle, and A, B, and C are empirically derived parameters.
This equation is applicable to free rotating systems, and is not limited to the carbon-carbon backbone. It is also used in a carbon-nitrogen backbone in protein NMR studies.
It describes the relationship between the NMR coupling constant and the dihedral angle between vicinal hydrogens. If the protons are orthogonal to each other there is no interaction, however if they are at angle between 0-90° there will be an interaction.
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