Polaronic Mechanism of Vibronic Localization in Mixed-Valence Cation Radicals with a Non-Conjugated Chromophore on the Bridge

Abstract

In quest of a controllable intramolecular electron transfer (ET) across a bridge, we study the cation-radical form of the parent 1,4-diallyl-butane (I) and its derivatives (II)−(VI). In these mixed-valence (MV) compounds, the bridge of variable length connecting allyl redox sites can be either saturated (−CH2 CH2−) (I, III, and V) or unsaturated, modified by the π-spacer (−HCCH−) (II, IV, and VI). Ab initio calculations for the charge delocalized transition structure and for fully optimized localized form of 1,ω-diallyl cation radicals I–VI allowed us to estimate the potential barriers for ET between the terminal allyl groups, vibronic coupling, and ET parameters. The ET barrier in all compounds with the π-fragment on the bridge is shown to be higher with respect to that in the systems with a saturated bridge. We propose a model based on the concept of a specific polaronic effect of the spacer. Charge localization at an allyl group creates an electric field polarizing the π-fragment and the bridge as a whole. The induced dipole moment interacts with the localized charge giving rise to the additional vibronic stabilization in a self-consistent manner without an appreciable change of localized charge. Utilization of this spacer-driven polaronic effect is expected to provide a route to a controllable ET in bridged MV compounds.

In the quest for an optimal parametric regime of nonadiabatic switching ensuring low heat release in conjunction with high polarizability of mixed-valence molecular dimers

“…In addition, consideration of the above two series of MV compounds provides proof for the applicability of the PKS vibronic model we use here, in which only the interaction of the mobile charge with the out-of-phase vibration is considered (see detailed discussion of this issue in ref. 19 and 20).…”

“…From this point of view consideration of the series of MV molecules in which either t or υ (or both) can be changed systematically within each such series seems to be quite useful. As suitable examples one can mention two series of organic MV dimers, whose electronic and vibronic structures have been recently investigated 19,20 with the use of the approach combining high-level ab initio calculations with the analysis performed using the parametric vibronic model.…”

“…The first of these series includes MV oxidized norbornadiene [C 7 H 8 ] + ( I ) and its polycyclic derivatives [C 12 H 12 ] + ( II ), [C 17 H 16 ] + ( III ), [C 27 H 24 ] + ( IV ) and [C 32 H 28 ] + ( V ), each containing two terminal CC chromophores acting as redox centers and the bridges of increasing length mediating the charge transfer between these chromophores. 19 Note that in the above calculations we have just used the values of the parameters obtained in ref. 19 for one of the compounds of this series, namely, for II .…”

“…In our recent studies focused on the effect of localization–delocalization in bridged MV organic compounds 18,19 (see also references therein for the discussion of different vibronic models proposed in the problem of mixed-valency) we employed the two-mode vibronic model that combines a fairly wide range of applicability and providing due account for the main physical interactions with simplicity and visibility. This model involves: (1) the interaction of mobile electrons with the fully symmetric local displacements (“breathing” modes), which modulates the effective sizes of the redox sites but leaves the fixed length of the bridge connecting these sites and playing the role of mediator for the electron delocalization, and (2) the so-called “intercenter” vibration, which exclusively changes the length of the bridge 18,19 thus affecting electron delocalization. The first kind of coupling lies in the background of the conventional PKS model 17 which underlies the Robin & Day classification of MV compounds according to the degree of localization.…”

“…Depending of the kind of MV molecule either PKS or intercenter vibration can produce the main impact on the localization–delocalization properties. Meanwhile, the combined ab initio and parametric analysis 18,19 has revealed the dominant role of the PKS vibrations in organic bridged MV compounds, and also the fact that these vibrations are rather well separated from the rest of molecular vibrations obtained through ab initio calculations. That is why in the present study we employ the PKS model.…”