Kinetic-Thermodynamic Connections:Hammond PostulateVariation in ΔGOshows up in ΔG‡.However, this isn’t mathematical.• Can relationship between ΔG‡and ΔG0be stated mathematically?• Is Hammond’s Postulate correct?Kinetic-Thermodynamic Connections:Marcus TheoryRudy Marcus (Nobel Prize, 1992):Reaction coordinate energies can be depicted by simple, intersecting parabolae.HHHHOHHHBrHO-Br-++Idea: Use parabola as simple model of bond making and breaking.C―Br C―OMarcus TheoryHHHHOHHHBrHO-Br-++HHHHOHHHOHHO-HO-++HHHBrHHHBrBr-Br-++First, consider this reaction to be an amalgamation of two symmetric reactions:0 0Marcus TheoryHHHHOHHHBrHO-Br-++First, consider this reaction to be an amalgamation of two symmetric reactions:ΔG‡symm,OH(41.8 kcal/mol)ΔG‡symm,Br(23.7 kcal/mol)OHHOH HHBrBrH HH0 0Marcus TheorySimplify by averaging two potential wells:BrHOH HHHHHHOHHHBrHO-Br-++ΔG‡int= ½(ΔG‡symm,OH+ ΔG‡symm,Br)0Marcus TheorySimplify by averaging two potential wells:BrHOH HHHHHHOHHHBrHO-Br-++ΔG‡intThen, two curves arey = 4ΔG‡intx2andy = 4ΔG‡int(1-x)2But this still isn’t right—doesn’t includeΔG0for the reaction.0ΔG‡intΔG0ΔG‡New equations:y = 4ΔG‡intx2y = 4ΔG‡int(1-x)2+ ΔG0Address exo-/endothermicityby moving right-hand curve.Potential energy surface is actually continuous;contains “avoided curve crossing”Weird thing at ΔG0= -4ΔG‡int:ΔG‡becomes zero!ΔG0ΔG‡intWeirder thing at ΔG0< -4ΔG‡int:ΔG‡becomes positive again!Reaction has to backwards to go forwards!ΔG0ΔG‡ΔG‡intPredicted result:The “Marcus Inverted Region”.Here, k decreaseswith increasing exothermicity.(→ more exothermic)ΔG0= -4ΔG‡intThe Marcus Inverted RegionVery difficult to find reactions fast enough to test this hypothesis.Need:Photoexcitation-Electron transfer:(RuIIL32+)* + FeIIIL’(+)• Large thermodynamic driving force• Low intrinsic barriersexcited-state ionRuIIIL33++ FeIIL’The Marcus Inverted RegionVery difficult to find reactions fast enough to test this hypothesis.Need:Photoexcitation-Electron transfer:Example: Turro, C.; Zaleski, J. M.; Karabatsos, Y. M.; Nocera, D. G. J. Am. Chem. Soc. 1996, 118, 6060-6067.RuIIL32+(RuIIL32+)*• Large thermodynamic driving force• Low intrinsic barriersground-state ionexcited-state ionhνexcited electron makes this species a powerful reductant.The Marcus Inverted RegionVery difficult to find reactions fast enough to test this hypothesis.Need:Photoexcitation-Electron transfer:RuIIL32+(RuIIL32+)* + FeIIIL’(+)• Large thermodynamic driving force• Low intrinsic barriersground-state ionexcited-state ionhνRuIIIL33++ FeIIL’ΔG0= -30 to -40 kcal/mol(depends on L)Rate of reaction is really fast (picoseconds)—low barrier to electron transfer.The Marcus Inverted Region(RuIIL32+)* + FeIIIL’(+)RuIIIL33++ FeIIL’In fact, barrier is actually the result of solvent reorganization (rather than electron transfer).RuII(2+)*FeIII(+)RuIII(3+)FeIIHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHpartly orderedpartly orderedmore orderedless orderedThe Marcus Inverted Region(RuIIL32+)* + FeIIIL’(+)RuIIIL33++ FeIIL’In fact, barrier is actually the result of solvent reorganization (rather than electron transfer).RuII(2+)*FeIII(+)HOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHHOHpartly orderedpartly orderedsolvent orderin reactantssolvent orderin productsThe Marcus Inverted Region(RuIIL32+)* + FeIIIL’(+)RuIIIL33++ FeIIL’Problem: Reaction is fast, but not faster than diffusion of reactants towards each other;Rate of reaction limited by rate of diffusion.kETkdActual expression:()dETdETobskkkkk+=The Marcus Inverted RegionSolution: Eliminate diffusion term by attaching reductantto oxidant.AACloss, G. L.; Miller, J. R. Science 1988, 240, 440.The Marcus Inverted RegionAgain, reaction barrier is due to solvent reorganization.AAOH3C=δ-δ+ΔG0ΔG‡Nonintuitively, solvent has to order more before