DFT study and NBO (natural bond orbital) analysis of the mutual interconversion of cumulene compounds

The Becke, Lee, Yang and ParT density functional (B3LYP) method was used to investigate the configurational properties of allene (1,2-propadiene) (1), 1,2,3-butatriene (2), 1,2,3,4-pentateriene (3), 1,2,3,4,5-hexapentaene (4), 1,2,3,4,5,6-heptahexaene (5), 1,2,3,4,5,6,7-octaheptaene (6), 1,2,3,4,5,6,7,8-nonaoctaene (7) and l,2,3,4,5,6,7,8,9-decanonaene (8). B3LYP/6-31G* level of theory showed that the mutual interconversion energy barrier in compounds 1-8 are 50.14, 31.49, 28.75, 20.37, 19.32, 14.31, 14.00 and 10.49 kcal mol(-1), respectively. The results showed a linear relationship between the corresponding B3LYP/6-310* mutual interconversion energy barriers and the average C=C double bond lengths (d), in the ground state geometries of cumulene compounds. The results showed also that the difference between the (W) values in cumulene compounds 1 and 2 is larger than those between 7 and 8, which suggest that with large n (number of carbon atoms in cumulene chain), the d values approach to a limiting value. Also, NBO//B3LYP/6-31G* results revealed that the pi-bond occupancies decrease from I to 8, and inversely, the pi-antibond occupancies increase from compound I to compound 8. The difference between the average of pi-bonds and pi-antibond occupancies (Delta= pi(occupancy)-pi*(occupancy)) could be considered as a criteria for the mutual interconversion in compounds 1-8. These A values decrease from compound 1 to compound 8 series as following: 1,92087, 1.80788, 1.75314, 1.70637, 1.67144, 1.64337, 1.62065 and 1.60170, respectively, as calculated by B3LYP/6-31G* level of theory. The decrease of A values for compounds 1-8, follow the same trend as the barrier heights of mutual interconversion in compounds 1-8. Accordingly, besides the allylic resonant stabilization effect in the transition state structures, the results revealed, particularly, that the Delta value could be considered as significant criteria for the mutual interconversion in cummulene compounds 1-8.