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Vicinal Coupling (3J, H-C-C-H)

Coupling is mediated by the interaction of orbitals within the bonding framework. It is therefore dependent upon overlap, and hence upon dihedral angle. The relationship between the dihedral angle and the vicinal coupling constant 3J (as observed from 1H NMR spectra) is given theoretically by the Karplus equations:

3Jab = J0cos2f-0.28 (0o < f < 90o)
3Jab = J180cos2f-0.28 (90o < f < 180o)

where J0 = 8.5 and J180 = 9.5 are constants which depend upon the substituents on the carbon atoms and f is the dihedral angle. The dihedral angle is defined by:

An approximate calculated relationship (ignoring the small constant of 0.28 in this graph) between the dihedral angle and the coupling constant may be illustrated below:

In some cases the axial-axial coupling constant for an antiperiplanar 180o H-C-C-H configuration may be more than 9.5 Hz. Indeed for rigid cyclohexanes it is around 9-13 Hz, because the dihedral angle is close to 180o, where the orbitals overlap most efficiently.

Enter the coupling constant in box as a numeral (e.g. 2.38) to calculate the theoretical dihedral angle in the molecule to assist with molecular modelling.

Enter Coupling Constant (predicted <=0 angle <= 90): Angle: degrees

Enter Coupling Constant (predicted <=90 angle <= 180): Angle: degrees

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What's New: A book chapter has recently been published (Recent Advances in Asymmetric Diels-Alder Reactions; author J.P. Miller) that may be of interest in organic chemistry:
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