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 C3 or the C2 symmetry axes (indicated by B| and B⊥, 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 (), nuclear shielding of carbon (σC) and hydrogen (σH), and shielding at the center of mass (σCM). The source of the exceptionally large in-plane component σ⊥ CM, dominating the anomalous average σav CM, 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 C2 symmetry axis is 15.7 nA/T, approximately 1.5 times larger than that calculated for B|. The largest component of the susceptibility is instead the out-of-plane |, which depends on the intensity of the σ-electron currents and on the entire area enclosed within the loops that they form about the C3 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 sp3 hybrid orbital which form the C-H bonds and extending for several bohrs above and below the σh 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.