The granny and square carbyne knots: Theoretical NMR spectra

The structure, stability and theoretical C-13 NMR spectra of the C-60 carbo n clusters of carbyne knot type were studied by the ab initio calculations. The C-60 carbyne six crossings granny and square knots (composite knots) b elong to the D-2 and D-2h point-group of symmetry, respectively, whereas al l the six crossings prime-knots exhibit no symmetry. Semiempirical AM1 calc ulations performed for granny and square knots, formed from 40, 50,... 120 carbon atoms, show that the energy of the granny knot is always slightly lo wer than that of the square knot. The two mathematical knots are distinguis hable only by using a sophisticated topological polynomial while the molecu lar carbyne granny and square knots seem to be easier differentiable experi mentally by using the C-13 NMR spectra. (C) 1999 Elsevier Science B.V. All rights reserved.