40
Rates of Electron Transfer: Marcus Theory Chem 204 March 31, 2014

Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

Embed Size (px)

Citation preview

Page 1: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

Rates  of  Electron  Transfer:  Marcus  Theory  

Chem  204  March  31,  2014  

Page 2: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 3: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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”)?  

Page 4: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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)?  

Page 5: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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)?  

Page 6: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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!  

Page 7: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

Redox  potenYals  and  band  edges  

Page 8: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 9: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

•  What  is  K?  

•  What  is  ∆G?  

•  What  is  k  (rate  constant)?  

Fe(II)    +    Fe(III)  à  Fe(III)  +  Fe(II)    in  water  

Page 10: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

•  What  is  K?    K  =  1  

•  What  is  ∆G?  

•  What  is  k  (rate  constant)?  

Fe(II)    +    Fe(III)  à  Fe(III)  +  Fe(II)    in  water  

Page 11: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

•  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  

Page 12: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

•  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  

Page 13: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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?  

Page 14: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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)  

Page 15: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 16: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 17: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

Other  redox  mediators  in  biology  NAD+/NADH

E for reduction = 0.32 V NAD+  structure  nicotinamide adenine dinucleotide  

Page 18: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 19: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 20: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 21: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 22: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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?  

Page 23: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 24: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 25: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 26: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

ET in Aerobic Respiration

Page 27: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

•  NoYce  that  Nature  does  things  in  liEle  reversible  steps  to  maximize  the  useful  work!  

Page 28: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

OK,  now  let’s  think  about  mechanism  

A.  Is  a  version  of  the  Fe(II)/Fe(III)  reacYon  we  saw  earlier.  

Page 29: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 30: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 31: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 32: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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.      

Page 33: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 34: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 35: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 36: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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  

Page 37: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

Harry  Gray’s  lab,  Caltech  

Page 38: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

Protein  Bridges  Rate  of  ET  in  proteins  as  a  funcYon  of  distance  

Page 39: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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

Page 40: Rates&of&Electron&Transfer:& Marcus&Theory&butane.chem.uiuc.edu/murphycj/chem204spring2014/slides/2014/March... · Rudolph A Marcus: “Marcus Theory” Professor, ... G. L. Gloss

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.