Ring Current Model and Anisotropic Magnetic Response of Cyclopropane

Three-dimensional models of the quantum mechanical current density, induced in the electron cloud of the cyclopropane molecule by a uniform magnetic field applied either along the C-3 or the C-2 symmetry axes (indicated by B-parallel to and B-perpendicular to, respectively), have been constructed via extended calculations. These models of near Hartree-Fock quality, previously shown to provide a good agreement between computed and observed values of magnetic tensors, have been used to interpret the magnitude of the diagonal components of susceptibility (chi), nuclear shielding of carbon (sigma(C)) and hydrogen (sigma(H)), and shielding at the center of mass (sigma(CM)). The source of the exceptionally large in-plane component sigma(CM)(perpendicular to) dominating the anomalous average sigma(CM)(av), is shown to be a strong delocalized current flowing around the methylene moieties and the noncyclic CH2-CH2 fragment. The total current strength for a magnetic field applied in the direction of a C-2 symmetry axis is 15.7 nA/T, approximately 1.5 times larger than that calculated for B-parallel to. The largest component of the susceptibility is instead the out-of-plane chi(parallel to) which depends on the intensity of the sigma-electron currents and on the entire area enclosed within the loops that they form about the C-3 axis, all over its length. In a magnetic field perpendicular to the plane of the carbon atoms, both H and C nuclei sit inside diatropic whirlpools, flowing within the sp(3) hybrid orbital which form the C-H bonds and extending for several bohrs above and below the sigma(h) plane. The average values and the anisotropy of carbon and proton shieldings are strongly biased by the diamagnetic shift of the out-of-plane tensor components partially determined by these vortices. The current density model of cyclopropane is revised according to these findings.