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 (χ), nuclear shielding of carbon (σ^C) and hydrogen (σ^H), and shielding at the center of mass (σ^CM). The source of the exceptionally large in-plane component σ_;⊥ ^CM, dominating the anomalous average σ_av ^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 χ_||, 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 σ_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.