Theory of delocalised charge transfer​​​​​​​

Abstract

Charge transfer in molecular systems occurs between molecules, atoms, or ions, collectively called sites. Theories of charge transfer are fundamental to understanding both natural molecular systems, such as photosynthesis, and artificial molecular systems, such as organic semiconductors or inorganic coordination complexes. Charge transfer in many of these systems is, however, complicated by the existence of delocalisation, where the coupling between sites causes the charge's wavefunction to extend over multiple sites, to the point where it becomes meaningless to describe the charge as occupying any particular site.While quantum-chemical computational techniques exist to calculate charge transfer rates between these delocalised states, they can be computationally expensive (scaling up to exponentially with system size), are inflexible (that is, any change to the system requires a complete recalculation), and offer limited qualitative insight as to how the rate of charge transfer will change with various system properties.To overcome these limitations, this thesis presents a general theory of charge transfer between delocalised molecular states, generalised Marcus theory. Generalised Marcus theory is computationally cheap, flexible, and expressed in closed form. The closed-form nature of generalised Marcus theory allows for qualitative understanding of how charge transfer between delocalised molecular states is affected by changing the charge-transfer properties of the constituent molecules. Importantly, generalised Marcus theory leads to a number of predictions: supertransfer, or the enhancement of charge transfer through the constructive interference of delocalised charge transfer pathways; reorganisation energy suppression, where the environmental impact on charge transfer is somewhat mitigated by delocalisation; and the possibility of energetic tuning, where tuning energy offsets or reorganisation energies can allow significant enhancement to the charge transfer rate.This thesis applies generalised Marcus theory to a system in which delocalised charge transfer occurs, the photosynthetic reaction centre, a dimeric pigment-protein complex consisting of two monomeric branches. The reaction centre in photosynthetic organisms accepts excitons from an antenna system and outputs electrons, serving to convert solar energy into chemical energy. Importantly, excitons are transferred to a delocalised state where the two monomeric branches meet, a pair of molecules called the special pair, and charge separation occurs from this delocalised state. Many organisms only use a single monomeric branch for charge transfer, which raises an open question in biology: why is the reaction centre dimeric?This thesis compares the modern dimeric reaction centre, with delocalised exciton and charge transfer occurring at the special pair, to a model of the ancestral monomeric reaction centre, which lacks one half of the special pair and consequently does not experience exciton or charge delocalisation.By using Sumi's generalised Förster th...