**Vicinal Coupling ( ^{3}J, 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 ^{3}J (as observed
from ^{1}H NMR spectra) is given *theoretically* by the **Karplus equations**:

^{3}J_{ab} = J^{0}cos^{2}f-0.28 (0^{o} < f < 90^{o})

^{3}J_{ab} = J^{180}cos^{2}f-0.28 (90^{o} < f < 180^{o})

where J^{0} = 8.5 and J^{180} = 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 180^{o} 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 180^{o}, 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 |

Get it as an Android App on Google Play with far more features and ability to use your own versions of the Karplus equation.

Alternatively, download Flash version (with very limited features, based on the basic calculator above).

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:

free open access.

Comments to jonathan@jonathanpmiller.com or via a form.