Three-Centers Models for Electron Transfer through a Bridge. 1. Potential Energy Surfaces

Abstract

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.

Organische gemischtvalente Verbindungen: ein Spielplatz für Elektronen und Löcher

“…In diesem Fall kçnnen die elektronischen Kopplungen zwischen dem Grund-und ersten angeregten Zustand (V 12 ) und zwischen dem Grund-und zweiten angeregten Zustand (Brückenzustand) (V 13 ) sowie die Reorganisationsenergien für jeden Übergang durch Anwendung des oben genannten GMH-Dreizustandsmodells aus der Analyse des Absorptionsspektrums extrahiert werden, vorausgesetzt, man berechnet einige Dipolmomente quantenchemisch. [67,106,107,[122][123][124][125][126][127] [63,104,108,109] Mithilfe dieses vibronischen Kopplungsmodells berechneten Coropceanu et al die IV-CT-Banden organischer MV-Verbindungen durch numerische Berechnung der Eigenfunktionen eines Hamilton-Operators, der sowohl kinetische als auch potentielle Energieterme enthält. Die Ergebnisse stimmten ausgezeichnet mit experimentellen Daten überein.…”

On the Conjugation Length for Oligo(ethynylnaphthalene)‐Based Molecular Rods

“…Yield 160 mg, 0.100 mmol, 89 %. 1 75 (m, 12 H), 3.96 (m, 12 H Methods: Absorption spectra were recorded with a Hitachi U3310 spectrophotometer while all fluorescence studies were made with an YvonJobin fluorolog tau-3 spectrometer. Fluorescence spectra were corrected for spectral imperfections using a standard lamp.…”

“…[1][2][3][4][5][6] The level of underlying electron-transfer theory has now advanced to the point at which most aspects of long-range charge migration can be explained. More recently, attention has focussed on the study of medium-length, wire-like supermolecules and oligomeric structures capable of supporting charge transport along the molecular axis.…”

Persistence of the Three-State Description of Mixed Valency at the Localized-to-Delocalized Transition

“…A three-state model including a state for the bridge has been successfully employed to describe a number of bridged mixed valence complexes in the literature previously. 13,49,50 Potential energy surface analysis gives a snapshot of the energetic landscape of a mixed valence system, as well as the ability to simulate IVCT band shapes. The equations that generate a three-state PES along symmetric and asymmetric coordinates are given below:…”