Intramolecular electron delocalization: A four-site model

The question of electron localization in isolated molecules and mixed-valence vs. averaged-valence structure is examined both from purely electronic and from vibronic viewpoints. Generally, a four-site model, in which two sites encompass a localization region in the molecule, is useful; the variation of the distance between the two sites in each region provides the vibronic coupling to localize the electrons. In a simple Hückel picture, we derive a closed-form perturbation-theoretic criterion for the stability ot the localized (distorted) geometry; it is favored except for excessively polar structures. Adding the elastic energy of the framework increases the stability of the delocalized (averaged-valence or undistorted) geometry relative to the localized one. We present a diabatic coordinate curve-crossing analysis of the intramolecular electron-transfer problem, which permits straightforward classification of mixed-valent states and transfer processes. The vibronic picture leading to localization is quite similar to that employed in the pseudo-Jahn-Teller effect.