Outer Sphere ET and Marcus Theory Exercises

These questions deal in part with concepts presented in today's assigned reading, so please read the assigned sections before working out your answers.
  1. In class, it was described how Marcus derived an expression for the activation energy ΔG* in terms of the driving force ΔG° and the reorganization energy, λ. Now, take this one step further and derive an expression for the electron transfer rate constant by substituting Marcus' result into the Arrhenius equation.
  2. Take a look at the specific case given here for a two-parabola model. print it out and write on it what are the values (arbitrary units) of ΔG*, ΔG° and the reorganization energy, λ.
  3. Take a look at a different specific case given here for a two-parabola model. print it out and write on it what are the values (arbitrary units) of ΔG*, ΔG° and the reorganization energy, λ.
  4. Take a look at yet another specific case given here for a two-parabola model. print it out and write on it what are the values (arbitrary units) of ΔG*, ΔG° and the reorganization energy, λ.
  5. For the above three cases, what is the value of the constant displacement (a) of the two parabolas on the x axis?
  6. To what does the value of the constant displacement (a) of the two parabolas on the x axis correspond physically?
  7. Modify the two-parabola model in a manner appropriate to describe intramolecular electron transfer for the [(H3N)5Ru(spacer)Ru(NH3)5]5+ ion, where spacer = 4,4'-bipyridine. Illustrate your modification by drawing the appropriately modified diagram.
  8. In the latter problem, is the activation energy greater or lesser than that given by Marcus theory? By how much?