Unrestricted Hartree—Fock Calculations. II. Spin Properties of Pi-Electron Radicals

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Abstract
Unrestricted Hartree—Fock wavefunctions have been computed for a large number of conjugated‐hydrocarbon pi‐electron radicals. Pi‐electron spin‐density and charge‐density functions have been computed with and without annihilation of the major contaminating spin multiplet in the wavefunction. Three different empirical relations have been used to relate our results to proton isotropic hyperfine splittings measured in ESR experiments. These are the simple McConnell expression; the Colpa and Bolton relation which includes a term depending on the excess charge density at the carbon atom; and that due to Giacometti, Nordia, and Pavan which introduces a contribution from the spin densities in the bonds between the carbon and its nearest neighbors. When the Pariser—Parr method with semiempirical electron‐repulsion integrals is employed in the unrestricted Hartree—Fock calculation, then the experimental splittings are almost always bounded by those computed with spin densities before and after the annihilation of the major contaminating spin state, but spin densities after annihilation are closer to the experimental values derived with the empirical relations. This was found to be true for all the three relations used, but the simplest one gave slightly less satisfactory results. The general problem of the interpretation of spin densities obtained from an unrestricted Hartree—Fock wavefunction which is not an eigenstate of spin is discussed. It is found, however, that unrestricted computations with semiempirical integrals give small splittings of the underlying ``closed''shell orbitals, so that a single annihilation is a good approximation to projection and the spin densities after annihilation should be satisfactory from a theoretical point of view.

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