I discuss the concept of σ-aromaticity in Chapter 2.3.1. The arguments for its existence in cyclopropane include surface delocalization of electron density, MO energies, an energetic stability greater than predicted by traditional assessments of its ring strain energy, and a negative value of its NICS(0) and NICS(1).

Fowler, Baker and Lillington have computed the ring current in cyclopropane, cyclobutane and cyclopentane.1 The later two are computed for their planar conformations, which are not local minima, but make the graphical comparisons simpler. Unfortunately, I do not have electronic access to the journal article and so cannot link to their images, but the plots of the current density of cyclopropane clearly indicates a large diatropic current circling the outside of the ring. In the interior of the ring is a smaller paratropic current.

For this concept to have applicability, cyclobutane should express σ-antiaromaticity. The ring current map for cyclobutane does show a strong paratropic current in the inside of the ring with a weaker diatropic current on the outside of the ring. The current map of cyclopentane shows an interior paratropic and external diatropic currents of nearly identical magnitude, suggestive of a simple superposition of circulation due to five local bonds. Thus, cyclopropane expresses significant σ-aromaticity, cyclobutane is weakly σ-antiaromatic, and cyclopentane is non-aromatic.

References

(1) Fowler, P. W.; Baker, J.; Mark Lillington, M., "The Ring Current in Cyclopropane," Theor. Chem. Acta 2007, 118, 123-127, DOI: 10.1007/s00214-007-0253-2.

InChI:

cyclopropane: InChI=1/C3H6/c1-2-3-1/h1-3H2

cyclobutane: InChI=1/C4H8/c1-2-4-3-1/h1-4H2

cyclopentane: InChI=1/C5H10/c1-2-4-5-3-1/h1-5H2