Spin distribution in the diphenylpicrylhydrazyl (DPPH) radical measured by neutron diffraction

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Abstract
A complete experimental determination of the spin density has been performed on a DPPH : C6H6 single crystal using the polarized neutron diffraction technique. A parametric description of the spin density has been used, this being necessary for non-centrosymmetrical crystals. A large amount of the spin density (61 per cent) remains localized on the central hydrazyl group, in accordance with magnetic resonance data, with a slight excess of Nβ over Nα. The remaining part of the spin density (39 per cent) is delocalized on the three aromatic rings of DPPH, the amount of spin transferred on to a ring depending on the twist angle of the ring with respect to the hydrazyl backbone. On every ring the spin density changes its sign from carbon to carbon atom, in accordance with magnetic resonance and quantum theory. The spin populations measured for the carbons of the rings compare well with the hyperfine coupling constants of the adjacent protons, which permits a direct experimental verification of McConnell's first relation. These neutron diffraction results are compared with two quantum-mechanical calculations performed for the isolated DPPH radical, using the experimental geometry measured in the crystal. Both calculations reproduce fairly well the details of the spin density observed on the rings. The experimental spin distribution on the central nitrogen atoms is better reproduced by the local spin density (LSD) method than by the unrestricted Hartree-Fock (UHF) method, which overlocalizes the spin density on atom Nβ. None of these calculations predicts accurately the amount of delocalization on the rings.