A. Nitzan, Tel Aviv University
SELECTED TOPICS IN CHEMICAL
DYNAMICS IN CONDENSED SYSTEMS
Boulder, Aug 2007
Lecture 1
Introduction
Chemical dynamics in condensed phases
Molecular relaxation
processes
Condensed phases
Molecular reactions
Electron transfer and
molecular conduction
•Quantum dynamics
•Time correlation
functions
•Quantum and
classical dissipation
•Density matrix
formalism
•Vibrational relaxation
•Electronic relaxation
Quantum dynamics
Time correlation
functions
Stochastic processes
Stochastic differential
equations
Unimolecular
reactions: Barrier
crossing processes
Transition state theory
Diffusion controlled
reactions
Applications in
biology
Quantum dynamics
Tunneling and curve
crossing processes
Barrier crossing processes
and transition state theory
Vibrational relaxation and
Dielectric solvation
Marcus theory of electron
transfer
Bridge assisted electron
transfer
Coherent and incoherent
transfer
Electrode reactions
Molecular conduction
Applications in molecular
electronics
(radiationaless transitions)
•Solvation
•Applications in
spectroscopy
electron transport in molecular
systems
Reviews:
Annu. Rev. Phys. Chem. 52, 681– 750 (2001)
Science, 300, 1384-1389 (2003);
MRS Bulletin, 29, 391-395 (2004);
Bulletin of the Israel Chemical Society, Issue 14, p. 3 (2003) (Hebrew)
J. Phys.: Condens. Matter 19, 103201 (2007)
Thanks
I. Benjamin, D. Beratan, A. Burin, G. Cuniberty, B. Davis, S. Datta, D. Evans,
B. Feinberg, M. Galperin, A. Ghosh, H. Grabert, P. Hänggi, G. Ingold, M.
Jouravlev, J. Jortner, S. Kohler, R. Kosloff, A. Landau, L. Kronik, J. Lehmann,
M. Majda, A. Mosyak, V. Mujica, R. Naaman, F. v Oppen, U. Peskin, M. Ratner,
D. Segal, T. Seideman, S. Skourtis, H. Tal-Ezer, A. Troisi, S. Tornow
Molecular conduction
molecule
Molecular Rectifiers
Arieh Aviram and Mark A. Ratner
IBM Thomas J. Watson Research Center, Yorktown Heights, New
York 10598, USA
Department of Chemistry, New York New York University, New
York 10003, USA
Received 10 June 1974
Abstract
The construction of a very simple electronic device, a
rectifier, based on the use of a single organic molecule is
discussed. The molecular rectifier consists of a donor pi
system and an acceptor pi system, separated by a sigmabonded (methylene) tunnelling bridge. The response of such
a molecule to an applied field is calculated, and rectifier
properties indeed appear.
Xe on Ni(110)
Moore’s “Law”
IEEE TRANSACTIONS ON ELECTRON DEVICES VOL.43
OCTOBER 1996 1637
Need for Critical Assessment
Rolf Landauer,Life Fellow,IEEE
Abstract
Adventurous technological proposals are subject to
inadequate critical assessment. It is the proponents
who organize meetings and special issues. Optical
logic, mesoscopic switching devices and quantum
parallelism are used to illustrate this problem.
Feynman:
For a successful Technology, reality must take
precedence over public relations, for nature
cannot be fooled
First Transport Measurements through Single Molecules
Adsorbed molecule
addressed by STM tip
Molecule between
two electrodes
Self-assembled monolayers
Break junction:
dithiols between gold
Molecule lying
on a surface
Single-wall carbon
nanotube on Pt
Pt/Ir Tip
~1-2 nm
1 nm
SAM
Au(111)
Dekker et al. Nature 386(97)
Dorogi et al. PRB 52 (95) @
Purdue
Reed et al. Science 278 (97) @ Yale
Nanopore
C60 on gold
STM
tip
Joachim et al. PRL 74 (95)
Nanotube on Au
Au
Reed et al. APL 71 (97)
Lieber et al. Nature 391 (98)
Park et. al. Nature 417,722-725 (2002)
Datta et al
Weber et al, Chem. Phys. 2002
b=0.43Å-1
Xu et al (Tao),
NanoLet (2004)
loge of GCGC(AT)mGCGC conductance vs length
(total number of base pairs). The solid line is a linear fit
that reflects the exponential dependence of the
conductance on length. The decay constant, b , is
determined from the slope of the linear fit. (b)
Conductance of (GC)n vs 1/length (in total base pairs).
Electron transfer in DNA
Electron transmission processes in
molecular systems








Electron transfer
Electron transmission
Conduction
Parameters that affect molecular conduction
Eleastic and inelastic transmission
Coherent and incoherent conduction
Heating and heat conduction
Possible interaction with light
Chemical processes
Gas phase reactions





Follow individual
collisions
States: InitialFinal
Energy flow between
degrees of freedom
Mode selectivity
Yields of different
channels
Reactions in solution



Effect of solvent on
mechanism
Effect of solvent on rates
Dependence on solvation,
relaxation, diffusion and
heat transport.
I2 I+I
molecular absorption at
~ 500nm is first
bleached (evidence of
depletion of ground
state molecules) but
recovers after 100200ps. Also some
transient state which
absorbs at ~ 350nm
seems to be formed. Its
lifetime strongly
depends on the solvent
(60ps in alkane solvents,
2700ps (=2.7 ns) in
CCl4). Transient IR
absorption is also
observed and can be
assigned to two
intermediate species.
A.L. Harris, J.K. Brown and C.B. Harris, Ann. Rev. Phys. Chem. 39, 341(1988)
The hamburger-dog dilemma as a lesson in the
importance of timescales
TIMESCALES
collision time
in liquids
molecular rotation
solvent relaxation
electronic
dephasing vibrational dephasing
vibrational relaxation (polyatomics)
electronic relaxation
vibrational motion
10-15
10-14
10-11
10-10
10-9
10-8
10-13
10-12
TIME (second)
energy transfer in proton transfer
photosynthesis
protein internal motion
Torsional
photoionization
electron transfer
dynamics of
photodissociation
in photosynthesis
DNA
photochemical isomerization
Typical molecular timescales in chemistry and biology (adapted from
G.R. Fleming and P. G. Wolynes, Physics today, May 1990, p. 36).
Boulder August 2007
(3)
(2)Molecular
Electronconduction
transfer
Chapter
Chapter
16
Chapter13-15
17
(1) models
Relaxation
and reactions in
•Simple
for molecular
(4)
Recent research
processes
conductions
condensed
molecular
systems
(a)
Inelastic
issues
in
molecular
•Simpleaffecting
modelselectron transfer at
•Factors
•Kinetic
models
conduction
interfaces
•Marcus
theory
•Transition
state theory
•The
Landauer
formula
(b)
Tunneling
trough
•The reorganization redox
energy
•Kramers
theory
and
its
extensions
•Molecular
conduction
by
the
Landauer
molecular
species
•Adiabatic and non-adiabatic
•Low, highheating
and intermediate
formula
(c) Molecular
and
limits
•Relationship
to electron-transfer
rates.
friction
regimes
molecular
heat
conduction
•Solvent
controlled
reactions
•Structure-function
effects
inreactions
molecular
•Diffusion
controlled
(d)
What assisted
can be done
withtransfer
•Bridge
electron
conduction
photons?
•How
does
theand
potential
drop on a
•Coherent
incoherent
moleculetransfer
and why this is important
•Probing
molecules
in STM junctions
•Electrode
processes
•Electron transfer by hopping
PART A
Relaxation and reactions in
molecular systems
Molecular processes in condensed
phases and interfaces
•Diffusion
Molecular timescales
•Relaxation
Diffusion D~10-5cm2/s
•Solvation
•Nuclear rerrangement
•Charge transfer (electron and
xxxxxxxxxxxxxxxxproton)
•Solvent: an active spectator –
energy, friction, solvation
Electronic 10-16-10-15s
Vibraional 10-14s
Vibrational
xxxxrelaxation 1-10-12s
Chemical reactions
xxxxxxxxx1012-10-12s
Rotational 10-12s
Collision times 10-12s
Molecular vibrational relaxation

k f i ~

dte
iif t
Fˆ ( t )Fˆ (0)

T
Golden RuleFourier transform of bath correlation function

c  / 
kVR ~ e  D 
D
Relaxation in the X2Σ+ (ground electronic state) and A2Π (excite electronic
state) vibrational manifolds of the CN radical in Ne host matrix at T=4K,
following excitation into the third vibrational level of the Π state. (From V.E.
Bondybey and A. Nitzan, Phys. Rev. Lett. 38, 889 (1977))
Molecular vibrational relaxation
The relaxation of
different vibrational
levels of the ground
electronic state of
16O in a solid Ar
2
matrix. Analysis of
these results indicates that the relaxation of the n < 9 levels is
dominated by radiative decay and possible transfer to impurities.
The relaxation of the upper levels probably takes place by the
multiphonon mechanism. (From A. Salloum, H. Dubust, Chem.
Phys.189, 179 (1994)).
Frequency dependent friction



iifi
t if tˆ
kkf fi i~~ dtedte

(ˆt(0)
)Fˆ (0) constant
F (tFˆ)F
T
T
 t
MARKOVIAN LIMIT
WIDE BAND
APPROXIMATION
1
D
Dielectric solvation
C153 / Formamide (295 K)
q=0
Relative Emission Intensity
CF3
q=+e
Born solvation energy
Emission spectra of
a
b
q=+e
N
O
O
c
Coumarin 153 in
 q2  
1
formamide at different
  1    1  2eV (for a charge)
2a    s 
times. The timesshown
here are (in order of
increasing peakwavelength) 0, 0.05, 0.1,
0.2, 0.5, 1, 2, 5, and 50 ps
(Horng et al, J.Phys.Chem.
450
500
99, 17311 (1995))
550
Wavelength / nm
600
Continuum dielectric theory of solvation
How does solvent respond to a sudden change in
the molecular charge distribution?
  D  4
t
1  2
(Poisson equation)
t
Dt(r,
D(r,
) t ) dr 'dtdt( tε(rt )Er(r,
', tt ) t )E(r ', t )
 
D       E  
D( )  E ( )  4 P ( )
P ( )   ( ) E ( )
 1

4
 
 ( )   e 
Electronic
Total (static)1  i D
Dielectric
Electric
Electric
Debye dielectric
relaxation
function
displacement
fieldmodel
response
polarization
response
Dielectric
s
e
susceptibility
Debye
relaxation time
Continuum dielectric theory of solvation
d
1
(D  e E)  
(D   s E) ;
dt
D
t0
0
E (t )  
t0
E
t0
0
D( t )D
 ( t )  
(1

s
D
t

0



  D  4

dD
1

D  s E;
dt
D
D
 t  0
 t /  Dd E    s  t /E D 1 D  ;  t  0 


e
dt)   e ee
D 
s E
 1
1  t / L
E (t ) 
D     De
s
 e  s 
1
e
L  D
s
WATER:
D=10 ps
L=125 fs
“real” solvation
“Newton”
dielectric
The experimental solvation
function for water using sodium
salt of coumarin-343 as a probe.
The line marked ‘expt’ is the
experimental solvation function
S(t) obtained from the shift in the
fluorescence spectrum. The other
lines are obtained from
simulations [the line marked ‘Δq’
–simulation in water. The line
marked S0 –in a neutral atomic
solute with Lennard Jones
parameters of the oxygen atom].
(From R. Jimenez et al, Nature
369, 471 (1994)).
Electron solvation
C153 / Formamide (295 K)
Relative Emission Intensity
CF3
450
N
500
550
O
O
600
The first observation of hydration
dynamics of electron. Absorption
profiles of the electron during its
hydration are shown at 0, 0.08, 0.2,
0.4, 0.7, 1 and 2 ps. The absorption
changes its character in a way that
suggests that two species are
involved, the one that absorbs in the
infrared is generated immediately
and converted in time to the fully
solvated electron. (From: A. Migus, Y.
Gauduel, J.L. Martin and A. Antonetti,
Phys. Rev Letters 58, 1559 (1987)
Wavelength / nm
Quantum solvation
(1) Increase in the kinetic energy (localization) – seems NOT to affect
dynamics
(2) Non-adiabatic solvation (several electronic states involved)
Electron tunneling through water
1
Work
function
(in water)
2
3
EF
WATER
Transient
resonance
through
“structural
defects”
Polaronic
state
(solvated
electron)
Electron tunneling through water
Time (ms)
STM current in pure water
S.Boussaad et. al. JCP (2003)
Chemical reactions in condensed
phases
Bimolecular
Unimolecular
Diffusion
controlled
rates
diffusion
k  4 DR
R
kBT
D
m
Unimolecular reactions
(Lindemann)
2
k2
reaction
k12 k21 excitation
k
1
k21 Mk2
k
k12 M  k2
M
Thermal interactions
Activated rate processes
B
EB
0
reaction
coordinate
KRAMERS THEORY:
Low friction limit
High friction limit
Transition State
theory
k

kBT
0 J B e  EB / kBT
0 B  EB / kBT
k
e
2
kTST
0  EB / kBT

e
2
Diffusion
controlled
rates
k  4 DR
kBT
D
m
(action)
B
 kTST

Effect of solvent friction
TST
A compilation of gas and liquid phase data showing the turnover
of the photoisomerization rate of trans stilbene as a function of
the “friction” expressed as the inverse self diffusion coefficient of
the solvent (From G.R. Fleming and P.G. Wolynes, Physics Today,
1990). The solid line is a theoretical fit based on J. Schroeder and
J. Troe, Ann. Rev. Phys. Chem. 38, 163 (1987)).
The physics of transition state rates
B
Assume:
EB
(1) Equilibrium in the well
0
reaction
coordinate
(2) Every trajectory on the barrier that goes out makes it

kTST   d v v P ( x B , v )  v f  P  x B 
0

 d vv e
0

 dv e

 12 b mv 2
 12 b mv 2
0  b E B

e
2
exp   b E B 
2
b
m

1
0  b EB
P
(
x
)


e

B
EB
2
2b m
dx
exp

b
V
(
x
)




The (classical) transition state
rate is an upper bound
EB
reaction
coordinate
•Assumed equilibrium in the well – in reality
population will be depleted near the barrier
•Assumed transmission coefficient unity above
barrier top – in reality it may be less
Quantum considerations
2
1
a
b
1
R*
R*
diabatic
Adiabatic

k   dR R P ( R , R )Pba ( R)
*
0
1 in the
classical case