Download Beratan questions Day 1 for Erice

Question 1. Marcus theory in photosynthesis.
(a) Shown on the next page are the lifetimes (the inverse of the reaction rates) for
the first three electron transfer processes that occur in the photosynthetic
reaction centers of purple bacteria. The numbers next to the arrows pointed to
the right indicate charge transfer reactions that lead to charge separation across
the membrane and successful conversion of the photon into a charge separated
state. Arrows pointed to the left indicate charge recombination rates. Dashed
lines on the vertical axis indicate the energies of the excited state and the three
charge-separated states compared to the ground state. These latter rate
processes “waste” the solar energy and just produce heat. Use electron transfer
theory arguments to rationalize why all of the back reactions are 102 to 104
slower than the forward reactions. It is known that the distance and “tunneling
barriers” for the forward and reverse reactions are not very different.
(b) Use the energies displayed in the plot to make a rough estimate of the
reorganization energy for the bacterial reaction center protein. You can use the
data from the “primary” charge separation and recombination rates (1012 s-1 and
108 s-1, respectively) to do this.
(c) The energy diagram indicates that the absorbed photon energy is about 1.4 eV,
but the voltage stored in the charge-transfer state is only about 0.5 V. Nature
thus dissipates over 60% of the photon’s energy in accomplishing the transmembrane electron transfer. What performance benefit does the organism
derive from dissipating this much energy?
Recall the Marcus theory reorganization energy: Gact = (G + )2/4