Model carbyne knots vs ideal knots.

The structure and stability of model carbyne knots built from 60 to 120 carbon atoms with 0, 3, 4,., 7 crossings have been estimated by semiempirical AM1 calculations. The calculations have shown an increase of the knot-cycle energy difference (deltaE) with an increasing number of knot crossings and a decrease of deltaE with an increasing number of atoms constituting the molecule. The deltaE changes nonlinearly with the characteristics of the corresponding ideal knots such as the average crossing number (ACN) and the length-to-diameter ratio (L/D). The molecular mechanic strain energy of carbyne knots correlates similarly with ACN and L/D of ideal knots. The calculated energy of the model carbyne knots correlates also with the electrophoretic mobility or sedimentation coefficient of DNA knots. Thus, similarly to characteristics of ideal knots, the energy of carbyne knots is a rather easily available parameter which can be used for further correlations with some characteristics of DNA knots.