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Today: Miscellaneous Topics
1
• Electron Transfer Reactions
• Electrostatic effects
• Diffusion‐limited reactions
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Review: Transition States
2
• Fundamental relationship: ‡
• Can we predict ‡ for any system?
Reaction Coordinate
Energy
ΔG
ΔG‡ΔG‡
TransitionState
Reactants
Products
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Electron Transfer
RCSB, PDB 1CAD 3
• Electron transfer essential for metabolic processes: cytochromes in eukaryotes
• Rubredoxin: electron carrier protein in bacteria and archaea
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Simple Model
4
• Simplest model for electron transfer:
• No free energy difference (no change)
• Two iron ions must collide to form electron transfer complex– Can we devise a mechanism?
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Simple Model
Andrei Tomakoff, http://www.mit.edu/~tokmakof/TDQMS/Notes/12.2.%20Marcus.pdf 5
• Encounter complex forms
• Solvent dipoles (water) must reorient to accommodate new charges
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Marcus Theory
6
• Rudolph Marcus (Nobel, 1992):
Δ ̅‡ 1̅
where Δ
Reaction Coordinate
Energy
ΔG
ΔG‡
RearrangedSolvent
EncounterComplex Electron Transferred
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Marcus Theory
7
• Transition State Energy:
‡ ̅
• Solvent Reorientation Energy:
ChargeTransferred (e.g. +1)
IonicRadii
Center‐to‐centerDistance
RelativeDielectric Constant
Index ofRefraction
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Marcus Theory ‐ Significance
Marcus, R. A. Nobel Prize Lecture (www.nobelprize.org) 8
• Parabolic dependence of ‡ vs
G = 0
Δ ̅ , ,
Δ ̅ , ,‡
Δ ̅ ‡4 1
Δ ̅
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Marcus Theory ‐ Significance
Miller, J. R., et al. (1984) JACS. 106: 3047. 9
• Parabolic dependence of ‡ vs
Δ ̅‡4 1
Δ ̅
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Kinetics and Salt Effects
10
• Transition state theory with activities‡
‡‡
• Equilibrium constant (with activity coefficients):‡
‡
• Rate law is then:‡ ‡
‡ ‡
Rate constant withunit activity coefficients
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Ionic Strength and Activities
11
• Recall Debye‐Hückel activities (chapter 4):
• Use these activities to derive an ionic‐strength dependence of :
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Ionic Strength and Activities
12
• Recall Debye‐Hückel activities (chapter 4):
• Use these activities to derive an ionic‐strength dependence of :
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Ionic Strength and Activities
Nolte, H., et al. (1980) Biochemistry. 19: 3705. 13
• Applies for low ionic strengths – Remember assumptions!
• Must prove that effect is truly “ionic” and not salt‐specific– Test with multiple salts
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Diffusion Limited Reactions
14
• Is there a “speed limit” for reactions in solution?
• Diffusion coefficient: Relates distance traveled to time in “crowded” environment
– Small molecules ~ 1 x 10‐5 cm2 s‐1
– Higher D means more distance covered per unit time
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Collision Theory
Tinoco, p. 372. 15
• More collisions with solvent harder for molecules to interact
• Rate of collisions should be:– Proportional to diffusion constant– Proportional to size
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Collision Theory
16
• Arrhenius equation exponent (A):
• For small molecules A ~ 1010
• Termed “diffusion limited reactions”– Low activation energy (not necessarily zero)– Fast A coefficient
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Collision Theory – Fast Rates
Tinoco, p. 374. 17
See a rate of 109 – 1010? Think diffusion controlled!