LaserInduced Control of Condensed Phase Electron Transfer

1
LaserInduced Control of Condensed Phase Electron
Transfer

• Rob D. Coalson, Dept. of Chemistry, Univ. of
  Pittsburgh
• Yuri Dakhnovskii, Dept. of Physics, Univ. of
  Wyoming
• Deborah G. Evans, Dept. of Chemistry, Univ. of
  New Mexico
• Vassily Lubchenko, Dept. of Chemistry, M.I.T.

NH3
CN
NH3
CN
3
2
H3N
Ru
N
Ru
CN
C
H3N
NC
NH3
CN
polar Solvent
2
Tunneling in A 2-State System
q
Lgt
Rgt
Proton Transfer
V(x)
tropolone
q
Multi (Double) Quantum Well Structure
q
e-
Electron Transport In Solids
Rgt
Lgt
V(x)
AlGaAs
GaAs
GaAs
q
3
1. . . . . N
Ru2
Ru3
e-
Atomic Orbitals
Dgt
Agt
Molecular Electron Transfer
Dgt
Agt
Acceptor
Donor
Equivalent 2-state model
?
For any of these systems ?(t)gt cD(t) Dgt
cA(t) Agt
1
where
HAA
HAD
cA
cA
d

ih
dt
cD
cD
HDA
HDD
For a Symmetric Tunneling System HAA HDD 0
HAD HAD ? (lt 0)
4
Given initial preparation in Dgt, for a symmetric
system
PD(t) 1 PA(t) cos2(?t)
t
?
2?
5
?
e-
Now, apply an electric field
E
Dgt
Agt
R
R
0
2
2
Q How does this modify the Hamiltonian??
A It modifies the site energies according to
-? E
Permanent dipole moment of A
HAA
?
eoR/2
0
- E
H
Thus

?
?
HDD
-eoR/2
0
6
Analysis in the case of time-dependent E(t)
Eocos?ot
Consider first the symmetric case
?
0
1
0
d
cA
-
cA
i
?Eocos?ot

dt
cD
cD
0
-1
?
0
Permanent dipole moment difference
Letting cA(t) e i a sin?ot cAI(t)
cD(t) e i a sin?ot cDI(t)
?Eo

?Eo

sin?ot
t
Where a
N.B. ??0Eocos?ot'dt'
?o
(h)?o
Thus, Interaction Picture S.E. reads
0
cAI
e-2i a sin?ot ?
cAI
d
i

dt
cDI
cDI
e2i a sin?ot ?
0
7
?
e i b sin?t ? Jm(b) e i m?t
Now note
m-?
?
? e2i a sin?ot ? ? Jm(2a) e i m?ot
So
m-?
? ?Jo(2a) , for ?/?o ltlt 1
RWA
Thus, the shuttle frequency is renormalized to
?Jo(2a)
?
?


ltlt1
?
0
NB Trapping or localization occurs at
certain Eo values!
0
2.5
5.5
a
Grossman - Hänggi, Dakhnovskii
Metiu
8
Add coupling to a condensed phase environment


1
0
1
0

VD(x)
?
H T
-
?Eocos?ot
0
1
?
VA(x)
0
-1
Nuclear coordinate kinetic energy
Nuclear coordinate
Field couples only to 2-level system
VA(x)
VD(x)
?D(x,t)
?A(x,t)
x
9
TVD(x)
?
-
1
0
?D(x,t)
Now
?Eocos?ot
?
TVA(x)
0
-1
?A(x,t)
?D(x,t)
d

i
dt
?A(x,t)
10
Construction of (Diabatic) Potential Energy
functions for Polar ET Systems
A
D
VD(x)
A
D
VA(x)
11
A few features of classical Nonadiabatic ET
Theory Marcus, Levich-Doganadze

TV1(x)
?

Hamiltonian

H

?
TV2(x)
(diabatic) nuclear coord. potential for
electronic state 2
non-adiabatic coupling matrix element
kinetic E of nuclear coordinates
?1(x,t)
States
?(t)gt
?2(x,t)
12
Given initial preparation in electronic state 1
(and assuming nuclear coordinates are
equilibrated on V1(x))
1
2
?1(x,0)
Then, P2(t) fraction of molecules
in electronic state 2
lt ?2(x,t) ?2(x,t)gt ? k1?2t
x
where k1?2 (Golden Rule) rate constant
13
In classical Marcus (Levich-Doganadze) theory,
k1?2 is determined by 3 molecular parameters ?,
Er, ?
( )
½
?
-(Er- ?)2/4Er kBT
k1?2 ?2
e
ErkT
w/ Er Reorganization Energy ? Reaction
Heat
1
2
?
Er
x
( )
½
?
-(Er ?)2/4Er kBT
k2?1 ?2
For the backwards Reaction
e
ErkT
14
To obtain electronic state populations at
arbitrary times, solve kinetic Master Eqns.
dP1(t)/dt - k1?2P1(t) k2?1P2(t)
dP2(t)/dt k1?2P1(t) - k2?1P2(t)
Note that long-time asymptotic Equilibrium
distributions are then given by
P2(?)
k1?2
?/kBT
Keq


e

P1(?)
k2?1
for Marcus formula rate constants
N.B. Marcus theory for nonadiabatic ET reactions
works experimentally. See
Closs Miller, Science 240, 440 (1988)
15
Control of Rate Constants in Polar Electronic
Transfer Reactions Via an Applied cw Electric
Field
The Hamiltonian is
VD
VA
x

hD
0
?
1
0
0
?12Eocos?ot


H

?
hA
0
0
-1
0
The forward rate constant is Y. Dakhnovskii, J.
Chem. Phys.
100, 6492
(1994)
?
?

Re

? Jm(a)
?
kD?A ?2

-i hA t
i hD t
2
dt e i m?ot tr ?

?
D
e
e
m-?
0
?
a 2 ?12 Eo/ h?o
16
( )
½
?
?
?2
? Jm(2?12Eo/h?o)
kD?A
2
4
ErkT
A?D
m-?

-(Er ? hm?o)2/4Er kBT
e
Rate constants in presence of cw E-field
17
300
D
200
J1
2
Schematically
A
100
J0
2
Energy
0
J-1
2
-100
h?o
-200
0
5
x
In polar electron transfer reactions, for
Reorganization Energy Er ? h?o (the quantum of
applied
laser field)
18
Jo(a)
2
J1(a)
2
J2(a)
2
a
19
Dramatic perturbations of the one-way rate
constants may be obtained by varying the laser
field intensity
Forward rate constant
Activationless reaction, Er1eV
20
Dakhnovskii and RDC showed how this property can
be used to control Equilibrium Constants with an
applied cw field
D
A
bias
?
21
Results for activationless reaction
PD(00)
PA(00)
?eq
Y. Dakhnovskii and RDC, J. Chem. Phys. 103, 2908
(1995)
22
Activationless ET
? 100 cm -1
Evans, RDC, Dakhnovskii Kim, PRL 75, 3649 (95)
Er ? h?o 1eV
23
REALITY CHECK on coherent control of mixed
valence ET reactions in polar media
?
?E
?
(1)
E
?

• Orientational averaging will
• reduce magnitude of desired effects

Lock ET system in place w/ thin polymer films
24
(2) Dielectric breakdown of medium?

• To achieve resonance effects for ? 34D
• Er h?o 1eV
• Electric field ? 107 V/cm
• Giant dipole ET complex, solvent w/ reduced Er,
• pulsed laser reduce likelihood of catastrophe

(3) Direct coupling of E(t) to polar solvent
?
?
Dipole moment of solvent molecules ltlt Dipole
moment of giant ET complex
25

• h?0 ? 1eV intense fields ? (multiphoton)
  excitation to higher
• energy states in the ET molecule, which
  are not considered in
• the present 2-state model.

h?
1eV
h?
1eV
h?
1eV
h?
1eV
26
Absolute Negative Conductance in Semiconductor
Superlattice
-

-Keay et al., Phys. Rev. Lett. 75, 4102 (1995)
27
Absolute Negative Conductance in Semiconductor
Superlattice
-Keay et al., Phys. Rev. Lett. 75, 4102 (1995)
28
Immobilized long-range Intramolecular Electron
Transfer Complex
D
Tethered Alkane Chain molecule
?
E
(h?)
A
?
k
(Inert) Substrate
29
Light Absorption by Mixed Valence ET Complexes
in Polar Solvents
h??
h??
Transmitted Photons
Ru3
Incident Photons
Ru2
Solvent
h??
h??
h??
h??
30
Absorption Cross Section Formula
31
Marcus Gaussian
permanent dipole moment difference
32
Barrierless
Hush Absorption

PRL 77, 2917 (1996) J. Chem. Phys. 105, 9441
(1996)
33
emission
absorption
Stimulated Emission using two incoherent lasers
J. Chem. Phys. 109, 691 (1998)
34
J. Chem. Phys. 109, 691 (1998)