Angular Dependence of Long-Range Proton Coupling Constants Across Four Bonds

A theoretical treatment of long-range proton spin—spin coupling constants, 4JHH′, across four bonds in saturated and unsaturated hydrocarbons is presented. Using the valence bond formalism, explicit theoretical expressions for the `direct'' and ``indirect'' contributions to 4JHH′ are obtained. By introducing a semiempirical criterion for estimating the pertinent exchange integrals, the angular dependence of the ``indirect'' effect is evaluated. The calculated results correlate a wide range of coupling-constant data including those experimental results for which existing theoretical treatments are inadequate. The comparison of the calculated with the experimental data suggests that the ``direct'' contribution to long-range coupling constants in saturated systems is negative in sign and is most important in the vicinity of the eclipsed conformations.