Spin Polarization in an Aliphatic Fragment: Comparison between Proton Hyperfine Interaction and Spin–Spin Coupling

Abstract

Expressions are derived for proton hyperfine interaction constants (hfs) in an aliphatic chain arising from a single unpaired pπ electron on the first carbon atom. The method used is the Dirac vector model. Only spin polarization is considered, while electron delocalization is neglected. The resulting expressions are very similar to those derived by Alexander for proton spin–spin coupling. This makes it possible to use experimental spin–spin data for a semiempirical estimate of the contribution of spin polarization to the aliphatic proton hfs. It is found that spin polarization contributes substantially to the hfs of protons removed up to five bonds from the pπ center. The contribution of spin polarization to α-proton hfs is positive and amounts to about 50% of the observed value. For β and γ protons spin polarization contributes, respectively, negative and positive spin densities of the order found experimentally. Deviations from the calculated values are discussed in terms of spin delocalization and conformational effects.