Efficient mapping of ring currents in fullerenes and other curved carbon networks

Abstract

Ring-current aromaticity of icosahedral C 120 archimedene is probed at the ipsocentric/6-31G* level by direct mapping of the current density induced in its 4-, 6-and 10-sided faces by perpendicular magnetic fields. In contrast to planar phenylene analogues, the 4-faces (and only those faces) support global π ring currents: intense, paratropic (antiaromatic), stronger on the cage interior.

From C58to C62and back: Stability, structural similarity, and ring current

“…When applied to I h -C 60 [23], the pseudo- method gives a pattern that is similar to the results from all previous calculations, with essentially localised circulations in neighbouring hexagons being driven by the paratropic pentagons. Calculations at the empirical Hückel-London (HL) level [39,40] also showed strong paratropic currents in the pentagonal rings, and diatropic currents that are weaker (by an order of magnitude) in the hexagons.…”

“…Frequency calculations at the B3LYP/6-31G* level were carried out to check that optimized geometrical structures of the favoured isomers correspond to local minima on the potential hypersurface; asphericity values and pyramidalization angles were calculated based on the optimized structures. Ring-current calculations were also performed at the pseudo-level [22][23][24] with the SYSMO program [25] for these 3D structures, as discussed below. …”

“…A simple expedient that reproduces the essential features of current maps for 2D molecules is the pseudo- method [22], in which the carbon centres of a conjugated system are formally replaced by hydrogen centres (represented by an STO-3G 1s orbital, with idealized C-C distances of 1.4 Å), thus converting a  system into a  analogue. This / analogy broadly carries over to 3D systems 13 [23]. In our maps, diatropic ('aromatic') ring currents are conventionally represented by anticlockwise, and paratropic ('antiaromatic') by clockwise circulations.…”

The pseudo-π model of the induced magnetic field: fast and accurate visualization of shielding and deshielding cones in planar conjugated hydrocarbons and spherical fullerenes

“…To overcome similar computational barriers, Fowler proposed in 2002 the pseudo-p model, 23 which was found to produce surprisingly accurate results for the RC analysis [24][25][26][27] and multicenter aromaticity bond indices [28][29][30] in a wide range of large planar and spherical organic molecules at very low computational cost. The pseudo-p model relies on early London findings 31 that the p orbitals of a cyclic conjugated carbon skeleton can be effectively modelled by s orbitals of a hydrogen only system with the same geometry and connectivity.…”

Substructural Approach for Assessing the Stability of Higher Fullerenes

“…Therefore, substructures retain the features of their electronic structure regardless of the fullerene they belong to. An illustrative example of their isolation is the schemes of currents proposed in [ 70 , 71 ], which demonstrate well the differences between hexagons and pentagons together with their surroundings, expressed, as a consequence, in their different local aromatization.…”