An X-Ray Diffraction Study of the Crystal Structure of Cyclopropane Carbohydrazide. II. A Theory of Isotropic Hyperfine Interactions in π-Electron Radicals

NOTE: Text or symbols not renderable in plain ASCII arre indicated by [...]. Abstract is included in .pdf document. I. The crystal structure of cyclopropanecarbohydrazide has been determined and refined using Fourier and least-squares methods. The crystals are monoclinic with [...] and [...]; the space group is [...], and there are four molecules in the unit cell. The molecules are held together by chains of NH [...] O hydrogen bonds running parallel to the b axis and by a network of weak NH [...] N bonds running along the twofold screw axes which relate the terminal nitrogen atoms. The value of [...] for the C-C distance between the cyclopropane and carbonyl groups suggests the presence of a fairly strong conjugative effect. II. Indirect proton hyperfine interactions in [pi]-electron radicals are first discussed in terms of a hypothetical C H fragment which holds one unpaired [pi]-electron and two [sigma]-C H bonding electrons. Molecular orbital theory and valence bond theory yield almost identical results for the unpaired electron density at the proton due to exchange coupling between the [pi]-electron and the [sigma]-electrons. The unpaired electron spin density at the proton tends to be antiparallel to the average spin of the [pi]-electrons, and this leads to a negative proton hyperfine coupling constant. This theory of indirect hyperfine interaction in the C H fragment is generalized to the case of polyatomic [pi]-election radical systems - e.g., large planar aromatic radicals. In making this generalization there is introduced an unpaired [pi]-electron spin density operator [...], where N refers to carbon atom N . Molecular orbital theory without configuration interaction gives zero order spin densities [...] which are either positive or zero. If [...] is positive, the calculated proton N hyperfine coupling constant is negative, and negative paramagnetic proton nuclear resonance shifts are predicted in such cases. Certain aromatic radicals (e.g., odd-alternate aromatics) contain one or more carbon atoms [...] for which the zero order spin density is exactly zero, [...]. In such cases [pi]-[pi] configuration interaction gives rise to a first order density at atoms [...], [...], which may be positive or negative, leading to negative or positive hyperfine couplings of the protons [...]. A previously proposed linear relation between the hyperfine splitting due to proton N, [...], and the unpaired spin density at N, [...] is derived using molecular orbital theory without [pi]-[pi] configuration interaction, assuming the [sigma]-[pi] coupling to be first order. It is shown that even when the effects of [pi]-[pi] configuration interaction are included in the calculations, the above simple linear relation is still exact, provided the [pi]-[pi] configuration interaction is treated as a first order perturbation on the [pi]-part of the wave functions and one assumes the excitation energies of the [sigma]-[pi] excited states to be approximately the same