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Rates of Electron Transfer: Marcus Theory
Chem 204 March 31, 2014
Scheduling Note:
• Wednesday: We will cover baEeries, fuel cells, some Big Picture Energy
• Friday: no lecture! Email homework to TA! • Monday: Solar Energy Conversion (not on Exam III)
• Next Wednesday, April 9: Review for Exam III; Exam III in evening (!), usual places, conflict exam sign-‐up
How does an electron get from one atom to another?
• Through orbitals that overlap from one atom to another?
• Through space?
• In one concerted step from electron donor to acceptor (“superexchange”)?
• In mulYple steps from electron donor to acceptor (“hopping”)?
How fast can an electron go from one atom to another?
• Faster than the speed of light? (hint: no)
• Within a femtosecond (10-‐15 s)?
• Within a nanosecond (10-‐9 s)?
• Within a millisecond (10-‐3 s)?
How fast can an electron go from one atom to another?
• Faster than the speed of light? (hint: no)
• Within a femtosecond (10-‐15 s)?
• TheoreYcal max: rate constant ~1013 s-‐1
• Within a nanosecond (10-‐9 s)?
• Within a millisecond (10-‐3 s)?
How fast can an electron go from one atom to another?
• Faster than the speed of light? (hint: no)
• Within a femtosecond (10-‐15 s)?
• TheoreYcal max: rate constant ~1013 s-‐1
• Within a nanosecond (10-‐9 s)?
• Within a millisecond (10-‐3 s)?
Range: down to 1 per sec or less!
Redox potenYals and band edges
Redox in nature: Overview of the metabolism of S. aciditrophicus.
McInerney M J et al. PNAS 2007;104:7600-7605
©2007 by National Academy of Sciences
Before we think about rates of electron transfer, let’s think about energy, reactants, and products
• What is K?
• What is ∆G?
• What is k (rate constant)?
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
• What is K? K = 1
• What is ∆G?
• What is k (rate constant)?
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
• What is K? K = 1 (by inspecYon)
• What is ∆G? ∆G = 0 (by inspecYon)
• What is k (rate constant)?
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
• What is K? K = 1 (by inspecYon)
• What is ∆G? ∆G = 0 (by inspecYon)
• What is k (rate constant)? “slow” (by measurement using isotope labels)
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
Fe(II) + Fe(III) à Fe(III) + Fe(II) in water
Draw reacYon coordinate diagram: energy vs. reacYon coordinate; If k is small, what does imply about the acYvaYon energy?
Many proteins have metal ions that undergo electron transfer
Native Cyt c: E° = 262 mV Met80His: E° = 41 mV
These cytochrome proteins have iron ions bound in “heme” groups; Iron is redox acYve and its redox potenYal is tuned with metal ion environment (an inducYve effect)
Different types of hemes
NN
NN
CH3
CH3
CH3 CH3
CH3
S
C47
OOH
C53 O
OH
S
CH3Cys
Cys
Fe
NN
NN
CH3
CH3
CH3
CH2
C47
OOH
C53 O
OH
O
H
OH
Fe
NN
NN
CH3
CH3
CH3 CH3
CH2
CH2
CO
OHC O
OH
Fe
heme b heme a heme c
Nitrogen Fixation
N2 + 8 H+ + 8 e− + 16 ATP → 2 NH3 + H2 + 16 ADP + 16 Pi
nitrogenase, from Protein Data Bank; FeMo cluster has 7-8 Fe’s and one Mo
Other redox mediators in biology NAD+/NADH
E for reduction = 0.32 V NAD+ structure nicotinamide adenine dinucleotide
Other redox mediators in biology
Coenzyme Q (ubiquinone)
O
O
CH3
O
O
CH3
CH3CH2 CH C
CH3
CH2 Hn
O
OH
CH3
OH
O
CH3
CH3CH2 CH C
CH3
CH2 Hn
2e-, 2H+
n = 6-10
Flavin mononucleotide
(FMN): colors change with redox
form NH
N
N
NCH3
CH3
CH2(CHOH)3CH2OPO3
O
O
2-
NH
N
NH
NCH3
CH3
CH2(CHOH)3CH2OPO3
O
O
2-
.
NH
NH
NH
NCH3
CH3
CH2(CHOH)3CH2OPO3
O
O
2-
e-, H+
e-, H+
lmax = 337, 445 nm
lmax = 565 nm
colorless
Q
SQ
HQ
Flavodoxins: FMN in a protein
J Mol Biol 1999 Dec 3;294(3):725-43
Reduction potentials of FMN couplesEo’Q/SQ Eo’SQ/HQ
Free FMN -238 mV -172 mV
FMN in Flavodoxins -50 to -260 mV -400 mV
How can you tell if an organic molecule is oxidized or reduced?
Compound is reduced if: number of C-H bonds increases; or if number of C-O, C-N, or C-X bonds decreases
Compound is oxidized if: number of C-H bonds decreases; or if number of C-O, C-N, C-X bonds increases
X = halide
Photosynthesis
6 CO2 (g) + 6 H2O (l) à C6H12O6 (aq) + 6 O2 (g)
thermodynamically uphill; requires photons
What is being oxidized and what is being reduced?
Photosynthesis
6 CO2 (g) + 6 H2O (l) à C6H12O6 (aq) + 6 O2 (g)
thermodynamically uphill; requires photons
What is being oxidized and what is being reduced? Carbon dioxide is reduced, and water is oxidized to oxygen gas
Electron Transfer in Aerobic Respiration and Photosynthesis
CO2
anabolic cycles
organic compounds
catabolic cycles
aerobic respiration photosynthesis
O2
2H2O ATP ADP + Pi ATP ADP + Pi
2H2O
http://people.ok.ubc.ca/wsmcneil/bio/electronchain.htm
NADH → Complex I → Q → Complex III → cytochrome c → Complex IV → O2 ↑ Complex II
Mitochondrial Electron Transport Chain
O2 acts as a terminal electron acceptor in cellular respiration
ET in Aerobic Respiration
• NoYce that Nature does things in liEle reversible steps to maximize the useful work!
OK, now let’s think about mechanism
A. Is a version of the Fe(II)/Fe(III) reacYon we saw earlier.
Rudolph A Marcus: “Marcus Theory”
Professor, Department of Chemistry, Caltech (1978-present) B.Sc. (1943) & Ph.D. (1946), McGill University Polytechnic Institute of Brooklyn (1951-64) University of Illinois (1964-78) Nobel Prize in Chemistry, 1992
Rudolph A Marcus: “Marcus Theory”
Consider a system where you have an electron donor linked to an electron acceptor: “D-‐-‐-‐L-‐-‐-‐A” which will become D+ -‐-‐-‐L -‐-‐-‐A-‐ once electron is transferred
orbital overlap integral = HAB
Lambda is “reorganizaYon energy”: Atoms in environment have to move around to accommodate changes in charge; Lambda is energy that product system has at its lowest energy nuclear configuraYon compared to the energy it would have at reactant’s lowest energy nuclear configuraYon.
Energy vs. nuclear coordinate
Marcus treats reorganizaYon energy as a classical Hooke’s Law (spring)
system….eventually…
⎭⎬⎫
⎩⎨⎧
⋅⋅⋅+°Δ−⋅
⋅⋅⋅⋅
TRGH
TRh = k ABET
λλ
λπ
4)(exp4 2
22
3
So the rate constant for electron transfer depends on reorganizaYon energy in a complex way; free energy change for the reacYon; temperature; and the degree of orbital overlap of the iniYal and final states.
Acc. Chem. Res., 1996, 29, 522
-DG
Log
k -DG = l
Marcus Theory’s Really Weird Prediction: The Inverted Region
⎭⎬⎫
⎩⎨⎧
⋅⋅⋅+°Δ−⋅
⋅⋅⋅⋅
TRGH
TRh = k ABET
λλ
λπ
4)(exp4 2
22
3
-∆G = lambda at max. So rate of ET should slow down as ∆G gets more negative
Theory: late 1950’s; Experiment: 1988
G. L. Gloss & J. R. Miller Science,240, 440 (1988)
kET vs ∆G for different donor acceptor pairs across the same bridge
Two proteins with irons that undergo ET
Cyt c/CcP complex: 26.5 Å is Fe-Fe distance
FeIII(H2O)6 ------ FeII(H2O)6
Vacuum: 1017 years H2O: 5 x 104 years Polypeptide: ms - micros
20 Å
Clearly, the bridge is important!
Experiment: Modify the hisYdines of a redox-‐acYve protein with a metal complex that can do ET and measure rates by monitoring spectroscopy
Harry Gray’s lab, Caltech
Protein Bridges Rate of ET in proteins as a funcYon of distance
Heme iron proteins ET rate influence by local amino acids
Cyt c Mb/Hb Catalase HRP/CcP Cyt P450
N
N
Fe
NNH
OO Fe
O
Coord. Sat. Min.
H-bond Tyr push Asp-His H-bond push Arg pull
Cys push H-bond pull
Homework! Due Wed.! 5 points!
• 1. Why do we draw potenYal energy curves as parabolas?
• 2. People think that electrons would move through delocalized orbitals like pi orbitals faster than in localized orbitals like s orbitals. Suggest an experiment to test this hypothesis.