### Energy Transfer

#### Yield of Transfer

For any single molecule in the excited state, the probability of excitation transfer to a neighboring molecule reflects the competition for the exciton from different processes at rates described by appropriate rate constants. These will usually be 1st order, except for the photochemical reaction, where the rate constant is 2nd order. The rate constants are such that in photosynthetic systems, transfer occurs many hundred times faster than fluorescence, so that excitation travels by a biased random walk to visit the reaction center several times during the lifetime limit determined by fluorescence decay.

The bias in the random walk is supplied by the energy difference of donor and acceptor molecules. Once energy reaches the "red" manifold of the chlorophyll electronic energy levels, there is a "shallow" trap leading to the reaction center. The distribution of energy within an antenna system is determined by the enthalpic factor represented by the intrinsic energy difference (as given by E = hn), and an entropic term due to the relative number of each sort of chlorophyll. For example, for two chlorophyll populations of the same energy (lmax), if set A contains 100 molecules, and set B contains 10, the probability of finding on exciton in A will be 10 x that in B. If B has a lower energy than A by 60 meV, then the probability will be about equal.

ktr
ftr = -------------------------------
kf + ktr + kd + k'rc[open traps]

#### Forster equation

The excitation transfer between two molecules which are close together, and appropriately oriented, occurs by inductive resonance transfer, as described by Forster theory.

k2.s
ktr = K' ------
R6

K' a constant

k2 "orientation factor" - alignment of dipoles

R distance between molecules

s "overlap integral" - energy match between donor and acceptor