Ring Current Model and Anisotropic Magnetic Response of Cyclopropane

Abstract

Three-dimensional models of the quantum mechanical current density, induced in\ud the electron cloud of the cyclopropane molecule by a uniform magnetic field applied either along\ud the C3 or the C2 symmetry axes (indicated by B| and B⊥, respectively), have been constructed\ud via extended calculations. These models of near Hartree-Fock quality, previously shown to\ud provide a good agreement between computed and observed values of magnetic tensors, have\ud been used to interpret the magnitude of the diagonal components of susceptibility (), nuclear\ud shielding of carbon (σC) and hydrogen (σH), and shielding at the center of mass (σCM). The\ud source of the exceptionally large in-plane component σ⊥\ud CM, dominating the anomalous average\ud σav\ud CM, is shown to be a strong delocalized current flowing around the methylene moieties and\ud the noncyclic CH2-CH2 fragment. The total current strength for a magnetic field applied in the\ud direction of a C2 symmetry axis is 15.7 nA/T, approximately 1.5 times larger than that calculated\ud for B|. The largest component of the susceptibility is instead the out-of-plane |, which depends\ud on the intensity of the σ-electron currents and on the entire area enclosed within the loops that\ud they form about the C3 axis, all over its length. In a magnetic field perpendicular to the plane of\ud the carbon atoms, both H and C nuclei sit inside diatropic whirlpools, flowing within the sp3\ud hybrid orbital which form the C-H bonds and extending for several bohrs above and below the\ud σh plane. The average values and the anisotropy of carbon and proton shieldings are strongly\ud biased by the diamagnetic shift of the out-of-plane tensor components partially determined by\ud these vortices. The current density model of cyclopropane is revised according to these findings

The ring current model of the pentaprismane molecule

“…[5] However, the use of the isotropic (i.e., average) NICS may cause information loss and misunderstanding. [13, 14] It has recently been shown that, on the magnetic criterion,[15, 16] cyclopropane, supposedly a strongly σ‐aromatic molecule on the basis of its isotropic NICS value,[5, 17–21] might instead be portrayed as a π‐complex of one ethylene and one methylene fragments, in agreement with an early suggestion by Walsh. [22, 23] In general, magnetic response cannot be correctly interpreted allowing for the average virtual shielding σ at the center of mass (CM), as shown in some noticeable case.…”

“…The presence of CC bond vortices constitutes a common feature of C n H n planar conjugated hydrocarbons containing a ring of carbon atoms,[25] with the exception of the saturated cyclopropane molecule, characterized by saddle flow about the center of the CC bonds. [15, 16, 55] However, the spatial extension of the CC bond diatropic vortex in pentaprismane is much larger than those of triprismane[12] and cubane. [10]…”

“…The average central shielding is an unsuitable magnetotropicity criterion, as it accounts for spurious effect. [13–16] Calculated values of the central shielding tensor are reported in Tables 4–19 in Section 2 of Supporting Information.…”

“…The magnetotropicity of cyclopropane should be re‐examined ex novo in the light of these findings. [15, 16, 19]…”

Polygonal current models for polycyclic aromatic hydrocarbons and graphene sheets of various shapes

“…In fact, the I B eff obtained for C 24 H 12 , 12.74 nA/T, can be matched with the all-electron ab initio value determined by Fliegl et al [43] via numerical integration of the current density vector field along the outer edge of the molecule, I B 5 18 nA/T, and against the benchmark of benzene for diatropic current strength, that is, the near Hartree-Fock ab initio estimate of I B , 11.7 nA/T from the p-current and 1.1 from the r-current. [77,78] These findings prove that the dominant (up to 80% of total) p-contribution to the out-of-plane component of the magnetizability of hexagonal PAHs can be fully rationalized via a PCM in terms of periphery-only ring currents. [42] This is confirmed by displaying magnetic field-induced pelectron contributions to the current density J B , represented via bulging arrows in Figures 3c, 3f, and 3i.…”