Vibrational barrier for resonance π-bond movement in conjugated linear crystals

Abstract

The movement of the covalently bonded electron in a conjugate double bond concomittant with the change in the length of this bond was studied by a two-state model. From the Bloch travelling wave formalism, we derived such movement for a periodic conjugate system and reduced it to a two-state problem, involving the (simultaneous) movement of neighboring bonds or neighboring segment of (up to eight) bonds, in a hypothetical C 2 n+1 H 2 n+3 linear system and C 4 n+2 H 4 n+2 cyclic system. The vibration of such a conjugate “linear” crystal with alternating single-double bonds between equivalent atoms was derived from the lagrangian formalism. The limits of frequency for the acoustic (0 → ω 0) as well as for the optical ( ▪) branches were obtained. Introduction of antisymmetric (optical branch) vibration was shown to give rise to a double-harmonic oscillator problem which in the case of weak electronic interaction studied here was shown to lead to a double-minimum potential well. As a result, a potential barrier exists for such concerted movement of π-bonds. The size of this potential barrier, the frequency of bond transfer and the stabilization energy were computed for up to the simultaneous movement of eight bonds. The frequency of movement computed with purely Bloch electronic effect was shown to be significantly larger than when vibrational barrier was included. This study, (1) gives insight to the rate of internal electron transfer, (2) points to the need of including vibration in the rate study of concerted reactions involving transfer of bonds, and (3) shows the possibility of cooperative (“covalon”) conduction effect between bond transfer and antisymmetric vibration when the frequencies of these two match.