DFT study and NBO analysis of the mutual interconversion of cumulene compounds

The B3LYP/6-31G* 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 1,2,3,4,5,6,7,8,9-decanonaene (9). The calculations at the B3LYP/6-31G* level of theory showed that the mutual interconversion energy barrier in compounds 1-8 are: 209.73, 131.77, 120.34, 85.00, 80.91, 62.19, 55.56, and 46.83 kJ mol(-1), respectively. The results showed that the difference between the average C=C double bond lengths ((d) over bar) 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) over bar values approach a limiting value. Accordingly, based on the plotted data, the extrapolation to n = infinity, gives nearly the same limiting (d) over bar (i. e., (d) over bar lim). Also, NBO results revealed that the sum of pi-bond occupancies, (pi) over bar (occupancy), decrease from 1 to 8, and inversely, the sum of pi-antibonding orbital occupancies, (pi) over bar (occupancy), increase from compound 1 to compound 8. The Delta((pi) over bar occcupancy - (pi) over bar *occupancy) values for compounds 1-8, is found to follow the same trend as the barrier decrease Of A( heights of mutual interconversion in compounds 1-8, while the decrease of the barrier height of mutual interconversion in compounds 1-8 is found to follow the opposite trend as the increase in the number of carbon atom. Accordingly, besides the previously reported allylic resonant stabilization effect in the transition state structures, the results reveal (d) over bar that the values, Delta((pi) over bar occupancy - (pi) over bar *occupancy), Delta(EHOMO - ELUMO), and the C atom number could be considered as significant criteria for the mutual interconversion in cumulene compounds 1-8. This work reports also useful prodictive linear relationships between mutual interconversion energy barriers (Delta E-O(a)) in cumulene compounds and the following four parameters: (d) over bar, Delta((pi) over bar occupancy - (pi) over bar occupancy), Delta(EHOMO - ELUMO), and C-Number. Copyright (c) 2007 John Wiley & Sons, Ltd.