Adapting the Fo1rster Theory of Energy Transfer for Modeling Dynamics in Aggregated
Gregory D. Scholes, Xanthipe J. Jordanides, and Graham R. Fleming
Question 1: What is a multipolar expansion and physically how is it related to excitation energy transfer between pigments? How is the dipole-dipole approximation related to the multipolar expansions and what is the equation describing dipole-dipole coupling? Why does a multipolar expansion become problematic as two molecules get closer together? How do the authors suggest this problem be alleviated when modeling molecular aggregates?
Question 2: How do the authors differentiate between ‘homogeneous’ and ‘inhomogeneous’ line shapes? Why does this matter when thinking about Forster transport between a weakly coupled donor pigment and acceptor pigment? Write down the Forster theory (not generalized Forster theory!) expression for the ensemble average rate of transport between a donor pigment and an acceptor pigment which have an inhomogeneous distribution of site energies described by G_D(\epsilon) and G_A(\epsilon). Be prepared to explain your equation and discuss what the different components represent physically.
Question 3: In writing down generalized Forster theory, the author’s use a partitioning of the different coupling elements: How do the authors partition coupling and what is the relevant approximation required for the Forster expression to be valid? (i.e. what allows Fermi’s golden rule to be used). In most of the cases we will consider, there will be no ‘bridge’ states. Rewrite the effective coupling between donor and acceptor states when there are no bridge states (eq 11). The author’s noted that effective donor and effective acceptor states are not orthogonal in their treatment - is that still true in the absence of bridge states and why?
Question 4: The authors propose that a specific sequence of timescales in implicit within their treatment of generalized Forster theory. What is that sequence of timescales? Why is that sequence of timescales essential for their equation to be appropriate? Think specifically about how these different timescales are related to terms within the Hamiltonian that we have had to impose assumption on.