Computed Gyration Tensors of Knotted Chiral and Achiral Topological Stereoisomers of C₆₀ Cyclocarbons

Abstract

The electronic origins of the computed optical rotations of the simplest chiral and achiral chemical knots with comparatively simple compositions and large, anticipated magnetoelectric polarizabilities are provided. Linear response theory (LRT) is used to calculate the gyration at 1064 nm of two knotted polyyne chains, topological stereoisomers of cyclo[60]carbon. One isomer is analogous to the trefoil knot with approximate D3 symmetry and the other the figure eight knot with approximate S4 symmetry. The response in each case can be attributed largely to the magnetic dipole term that arises in the degenerate E excited state. An oriented achiral figure eight knot is considerably more optically active in some directions than the chiral knot in any direction.