Ring current model and anisotropic magnetic response of cyclopropane

Three-dimensional models of the quantum mechanical current density, induced inthe electron cloud of the cyclopropane molecule by a uniform magnetic field applied either alongthe C3 or the C2 symmetry axes (indicated by B| and B⊥, respectively), have been constructedvia extended calculations. These models of near Hartree-Fock quality, previously shown toprovide a good agreement between computed and observed values of magnetic tensors, havebeen used to interpret the magnitude of the diagonal components of susceptibility (), nuclearshielding of carbon (σC) and hydrogen (σH), and shielding at the center of mass (σCM). Thesource of the exceptionally large in-plane component σ⊥CM, dominating the anomalous averageσavCM, is shown to be a strong delocalized current flowing around the methylene moieties andthe noncyclic CH2-CH2 fragment. The total current strength for a magnetic field applied in thedirection of a C2 symmetry axis is 15.7 nA/T, approximately 1.5 times larger than that calculatedfor B|. The largest component of the susceptibility is instead the out-of-plane |, which dependson the intensity of the σ-electron currents and on the entire area enclosed within the loops thatthey form about the C3 axis, all over its length. In a magnetic field perpendicular to the plane ofthe carbon atoms, both H and C nuclei sit inside diatropic whirlpools, flowing within the sp3hybrid orbital which form the C-H bonds and extending for several bohrs above and below theσh plane. The average values and the anisotropy of carbon and proton shieldings are stronglybiased by the diamagnetic shift of the out-of-plane tensor components partially determined bythese vortices. The current density model of cyclopropane is revised according to these findings.