### Abstract

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_{||} 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 CH_{2}-CH_{2} 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_{||}. 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 sp^{3} 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.

Original language | English |
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Pages (from-to) | 2002-2018 |

Number of pages | 17 |

Journal | Journal of Chemical Theory and Computation |

Volume | 6 |

Issue number | 7 |

DOIs | |

Publication status | Published - 13 Jul 2010 |

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## Cite this

*Journal of Chemical Theory and Computation*,

*6*(7), 2002-2018. https://doi.org/10.1021/ct100175j