Marcus Theory and Reorganization Energy
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The next question is what happens when the electronic coupling is too small?
The electronic coupling may be small because the crystal structure leads to smaller electronic coupling, or because vibrations disorder the system. In this case the charge carriers become localized and there is polaron formation, leading to geometry relaxation. This is the hopping regime. At a molecular level electron hopping can be cast in the framework of Marcus theory of electron-transfer reactions. Up until recently researchers were using purely phenomenological models.
Assume there is molecule that has had an extra electron injected (M-) and has the optimal geometry for the ionized state. Next to it is a neutral molecule (M) with optimal geometry for the neutral state. When the electron hops, the initial molecule goes back to the optimal geometry for the neutral state and the other molecule accepts the electron and adopts the geometry of the ionized state. Charge hopping can be described as a self exchange electron transfer reaction because the chemical nature of the two partners is the same. Therefore you can use Marcus theory of electron transfer to understand charge transport at the molecular level. There is intramolecular relaxation.
In addition to intramolecular relaxation there is also intermolecular relaxation. The distance between a neutral molecule and ionized molecule is larger because the electron density of the ionized molecule is larger. When the electron is transferred to another molecule the formerly ionized molecules becomes neutral and can move closer to the adjacent neutral molecules. This means hop of the electron is coupled to intermolecular relaxation. Ideally we want these couplings to be zero to minimize vibration which disrupts electronic coupling in a band regime.
References
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