Three-centers models for electron transfer through a bridge. 1. Potential energy surfaces.

Three centers models adapted to the description of electron transfer through a bridge are discussed, with a special emphasis on potential energy surfaces. A short historical review of the available models is given, with a particular interest on the Bersuker-Borshch-Chibotaru model (1989) and the Lambert-Nöll-Schelter model (2002). We propose our own model, inspired from the Bersuker-Borshch-Chibotaru model, but with a more physical discussion of the parameters and coordinates. The diabatic surfaces, before the intervention of electronic couplings between external site and bridge, consist of three revolution paraboloids of equal radii. The bottoms of the paraboloids do not form in general an equilateral triangle; they form an isosceles one. At this stage, the basic parameters are the ones describing the position of the third paraboloid (corresponding to a redox process on the bridge) with respect to the other two. We define in particular an energy shift parameter (Delta) and a depth parameter (d), the latter corresponding to the position of this paraboloid in the third dimension, i.e., along a coordinate of reaction perpendicular to the usual reaction coordinate. The topology of diabatic and adiabatic surfaces is discussed. As an application, we explain the contrasted behavior of two mixed valence systems bridged by anthracene and dimethoxybenzodithiophene, which differ by the value of the d parameter.