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

Abstract

AbstractThe 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 ($\bar d$) 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 $\bar d$ values approach a limiting value. Accordingly, based on the plotted data, the extrapolation to n = ∞, gives nearly the same limiting $\bar d$(i. e., $\bar d_{\lim } $). Also, NBO results revealed that the sum of π‐bond occupancies, $\bar \pi _{{\rm occupancy}} $, decrease from 1 to 8, and inversely, the sum of π‐antibonding orbital occupancies, $\bar \pi _{{\rm occupancy}}^* $, increase from compound 1 to compound 8. The decrease of $\Delta (\bar \pi _{{\rm occupancy}} - \bar \pi _{{\rm occupancy}}^* )$ values for compounds 1–8, is found to follow the same trend as the barrier 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 that the $\bar d$ values, $\Delta (\bar \pi _{{\rm occupancy}} - \bar \pi _{{\rm occupancy}}^* )$, Δ(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 predictive linear relationships between mutual interconversion energy barriers ($\Delta E_0^a $) in cumulene compounds and the following four parameters: ${\bar d}$, $\Delta (\bar \pi _{{\rm occupancy}} - \bar \pi _{{\rm occupancy}}^* )$, Δ(EHOMO − ELUMO), and CNumber. Copyright © 2007 John Wiley & Sons, Ltd.