Spin Polarization Versus Spin Delocalization. Topological Electron and Spin Density Analysis of the Rotational Automerization of Allyl Radical Including Electron Correlation Effects

The rotational automerization A → B‡ → A of allyl radical was examined at the levels UHF, PUHF, MP2, CID, CCD, CISD, and QCISD. Analyses of the reaction path, of vibrational modes, and of activation energies show methodological deficiencies at the MP2, CID, CCD, and CISD levels which are not related in a simple fashion to the spin contamination of the reference wave functions. Graphical analysis of electron and spin density functions and electron and spin populations reveal the underlying fundamental problem. The electron density relaxation always is described well along the automerization path, but the spin density relaxations differ greatly. All post-HF methods affect the spin density qualitatively in the same way: Correlation increases the importance of the interaction of the unpaired spin with the spins of the paired electrons via the spin delocalization mechanism relative to the spin polarization mechanism. However, the methods differ greatly in the relative importance of these mechanisms, and significantly different spin density distributions within the ethene part of B are the consequence. QCISD theory yields results that are in very good agreement with all available experimental data. The results corroborate that the PUHF method represents a valuable alternative for studies of spin density distributions in general and the method of choice for large radicals