Spin Densities in the Perinaphthenyl Free Radical

Valence bond theory is used to calculate π-electron spin densities (ρi) on carbon atoms in the perinaphthenyl free radical,[Complex chemical formula]The results are ρ1=—0.176, ρ2=+0.321, ρ3=—0.220, ρ13=+0.262. The theoretical spin densities ρ1 and ρ2 are compared with the ``experimental'' values |ρ1|=0.098, |ρ2|=0.325 which are obtained from the equation ai=Qρi and the absolute isotropic proton hyperfine splittings (|a1|=2.2, |a2|=7.3 gauss) which have been observed in the electron magnetic resonance of the perinaphthenyl free radical by Sogo, Nakazaki, and Calvin. Valence bond theory thus yields calculated spin densities in this odd-alternate radical which are in reasonably good agreement with the ``experimental'' densities. Molecular-orbital theory without configuration interaction predicts only positive spin densities and is therefore inadequate to describe experimental densities in the perinaphthenyl radical or in any other substance with large negative spin densities.