Almost all of the energy that sustains life on Earth was captured from sunlight
during the process of photosynthesis. In the first step of this process, photons
are absorbed by aggregates of pigment molecules called light-harvesting complexes.
In these complexes, pigment molecules are carefully arranged by protein
backbones and are consequently able to absorb excitation at much higher pigment
concentration than for the same pigments in solution. The close proximity
of pigment molecules in light-harvesting complexes may cause significant interaction
between them and consequent delocalisation of excitation over more than
one pigment molecule. These delocalised states are called exciton states. The
electronic degrees of freedom of pigment molecules are modulated by the large
number of vibrational modes in the protein backbone and pigments themselves.
In many light-harvesting complexes, the interaction between pigment molecules
are much stronger than interaction with the vibrational modes. In such systems,
a formalism called Redfield theory, which treats interaction with vibrations perturbatively,
can be used to calculate exciton dynamics.
In this dissertation, we give an overview of the process of photosynthesis and the physical mechanisms underlying light-harvesting. We then derive the Redfield
equation and explain its use in systems containing a single or multiple excitations.
We illustrate calculation of Redfield-dynamics by computing the exciton
dynamics in three systems: a six-member ring demonstrating essential features
of exciton dynamics; FMO, a conduit for excitation in green sulphur bacteria and
LHCII, the main light-harvesting complex in green plants.