Bending Effect of sp-Hybridized Carbon (Carbyne) Chains on Their Structures and Properties

Density functional theory (DFT) calculations were exploited to evaluate the bending of polyynic and polycumulenic atomic carbon chains. It was found that the chains can be easily bent with a small arc-chord ratio. Furthermore, the bending of the chains caused the variation of bond lengths, leading to the change in the chain lengths; namely, the chain was first shortened slightly and then elongated with increasing arc-chord ratio. Furthermore, the bending decreased all bond angles as an oscillation manner, in which the larger decrease of bond angles occurred on even-ordinal-number carbon atoms than on corresponding odd-ordinal-number carbons, and the largest decrease was at the middle of the chain. With increasing the bending, the HOMO-LUMO energy gap of the polyynic chain was decreased, whereas the gap of the polycumulenic chain remained almost unchanged. This indicates that bending can increase the electric conductance of the polyynic chain, whereas the conductance of the polycumulenic chain is not affected by bending. Furthermore, it was found that strain energy due to bending is determined by bent angles (theta(i)) at all carbon atoms as E-strain = 2.54 Sigma(n-1)(i=2)(1 - cos(theta(i))). Because the strain energy even due to a large bending is still much smaller than the energy required for breaking a carbon bond in a chain, it should be very difficult to break the chain by bending.