Theoretical study on the small carbon nano-ladders

1,3-Butadiyne, 1,3,5-hexatriyne, 1,3,5,7-octatetrayne, and 1,3,5,7,9-decapentayne are small oligomeric forms of acetylene. These oligomers participate in cyclization reactions to form ladder-like structures. Enthalpies, ?H, and Gibbs free energies, ?G, of the cyclization reactions were calculated employing MP2 and B3LYP methods. The calculated ?H and ?G were positive, and their variation versus carbon atoms number, n, was fitted in linear functions as ?H(n) = a+bn. The calculations were performed on the structures with carbon numbers up to 20. Also, consecutive cyclization reactions between acetylene molecules were studied. During these consecutive reactions, two different structures, zigzag-ladder-like and cyclic molecules with tetragonal rings, were produced. Among the cyclic structures, the hexagonal form was the most stable structure. The calculated ?H and ?G of formation of zigzag-ladder-like molecules were excellently fitted in linear functions. The obtained functions for ?H and ?G calculated by MP2 method are ?H(n) = 139.67?126.44n and ?G(n) = 80.987?75.684n, respectively.