Helical chirality in model mirror-imaged carbyne trefoil knots

A new method for understanding the helical chirality of molecular knots has been developed on the basis of the helix theory. Our results show that the model right-handed carbyne trefoil knot is composed of three small right-handed helices with right-handed chirality, and the left-handed one has three small left-handed helices with left-handed chirality. These two trefoils present mirror-imaged symmetry. Moreover, the rotation strengths of the two carbyne trefoils have been suggested by an analogy to helicene. Helical chirality analysis leads us to infer that helical structure is the essence of molecular knot's chirality, which is also a possible measure for the chirality of a molecular knot.