Computed Gyration Tensors of Knotted Chiral and Achiral Topological Stereoisomers of C 60 Cyclocarbons.

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 D 3 symmetry and the other to the figure eight knot with approximate S 4 symmetry. The response in each case can be attributed largely to the magnetic dipole term that arises in a near degenerate E-like excited state. An oriented achiral figure eight knot is as optically active in some directions as the chiral knot in any direction, and its absolute eigenvalues are larger.