Search jonathanpmiller.com: Search On : All Words Any Words Submit Web Site

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:

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

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 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 <=90 angle <= 180):

Angle: degrees

Alternativelty, download Flash version.

Comments to jonathan@jonathanpmiller.com