Lecture 1Lecture 1

A. Nitzan, Tel Aviv University

SELECTED TOPICS IN CHEMICAL DYNAMICS IN CONDENSED SYSTEMS

Boulder, Aug 2007

IntroductionIntroduction

Chemical dynamics in condensed phases

Molecular relaxation processes

•Quantum dynamics•Time correlation functions•Quantum and classical dissipation•Density matrix formalism•Vibrational relaxation•Electronic relaxation (radiationaless transitions)

•Solvation•Applications in spectroscopy

Condensed phases Molecular reactions

Quantum dynamicsTime correlation functionsStochastic processesStochastic differential equationsUnimolecular reactions: Barrier crossing processesTransition state theoryDiffusion controlled reactionsApplications in biology

Electron transfer and molecular conduction

Quantum dynamicsTunneling and curve crossing processesBarrier crossing processes and transition state theoryVibrational relaxation and Dielectric solvationMarcus theory of electron transferBridge assisted electron transferCoherent and incoherent transferElectrode reactionsMolecular conductionApplications in molecular electronics

electron transport in molecular electron transport in molecular systemssystems

ThanksI. 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

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)

Molecular conductionMolecular conduction

m o lecule

Molecular Rectifiers

Arieh Aviram and Mark A. RatnerIBM Thomas J. Watson Research Center, Yorktown Heights, New

York 10598, USADepartment of Chemistry, New York New York University, New

York 10003, USA

Received 10 June 1974Abstract

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 sigma-bonded (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.43OCTOBER 1996 1637

Need for Critical AssessmentRolf Landauer,Life Fellow,IEEE

AbstractAdventurous 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.

For a successful Technology, reality must take precedence over public relations, for nature cannot be fooled

Feynman:

First Transport Measurements through Single Molecules

Single-wall carbon nanotube on Pt

Dekker et al. Nature 386(97)

Nanopore

Reed et al. APL 71 (97)

Break junction: dithiols between gold

Molecule lying on a surface Molecule between

two electrodes

Dorogi et al. PRB 52 (95) @ Purdue

Au(111)

Pt/Ir Tip

SAM1 nm

~1-2 nm

Self-assembled monolayers

Adsorbed molecule addressed by STM tip

C60 on gold

Joachim et al. PRL 74 (95)

STMtip

Au

Reed et al. Science 278 (97) @ Yale

Nanotube on Au

Lieber et al. Nature 391 (98)

Park et. al. Nature 417,722-725 (2002)

Datta et al

Weber et al, Chem. Phys. 2002

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, , is determined from the slope of the linear fit. (b) Conductance of (GC)n vs 1/length (in total base pairs).

Xu et al (Tao), NanoLet (2004)

=0.43Å-1

Electron transfer in DNA

Electron transmission Electron transmission processes in molecular processes in molecular

systemssystems Electron transferElectron transfer Electron transmissionElectron transmission ConductionConduction Parameters that affect molecular Parameters that affect molecular

conductionconduction Eleastic and inelastic transmissionEleastic and inelastic transmission Coherent and incoherent conductionCoherent and incoherent conduction Heating and heat conductionHeating and heat conduction Possible interaction with lightPossible interaction with light

Chemical processesChemical processes

Gas phase Gas phase reactionsreactions

Follow individual Follow individual collisionscollisions

States: InitialStates: InitialFinal Final Energy flow between Energy flow between

degrees of freedomdegrees of freedom Mode selectivityMode selectivity Yields of different Yields of different

channelschannels

Reactions in Reactions in solutionsolution

Effect of solvent on Effect of solvent on mechanismmechanism

Effect of solvent on Effect of solvent on ratesrates

Dependence on Dependence on solvation, solvation, relaxation, diffusion relaxation, diffusion and heat transport.and heat transport.

I2 I+I

A.L. Harris, J.K. Brown and C.B. Harris, Ann. Rev. Phys. Chem. 39, 341(1988)

molecular absorption at ~ 500nm is first bleached (evidence of depletion of ground state molecules) but recovers after 100-200ps. 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 .

The hamburger-dog dilemma as a lesson in the importance of timescales

1 0 -1 5 1 0 -1 4 1 0 -1 3 1 0 -1 2 1 0 -1 1 1 0 -1 0 1 0 -9 1 0 -8

T I M E (s e c o n d )

v ib ra tio n a l m o tio n

e le c tro nicde pha s ing v ibra tio na l de pha s ing

v ib ra tio n a l re la x a tio n (p o lya to m ic s )e le c tro nic re la xa tio n

c o llis io n tim ein liq u id s

so lv e nt re la xa tio n

m o le c ula r ro ta tio n

p r o to n tr a n sfe rp r o te in in te r n a l m o tio n

e n e rg y tra n s fe r inp h o to s yn th e s is

T o rs io n a ld yn a m ic s o f

D N A

e le c tro n tra ns fe rin pho to s ynthe s is

pho to io niza tio npho to disso c ia tio n

p h o to c h e m ic a l iso m e r iza tio n

TIMESCALES

Typical molecular timescales in chemistry and biology (adapted from G.R. Fleming and P. G. Wolynes, Physics today, May 1990, p. 36) .

(4) Recent research(a) Inelastic issues in molecular

conduction(b) Tunneling trough redox molecular species(c) Molecular heating and molecular heat conduction(d) What can be done with photons?

Boulder August 2007

(1) Relaxation and reactions in condensed molecular systems•Kinetic models•Transition state theory•Kramers theory and its extensions•Low, high and intermediate friction regimes•Diffusion controlled reactions

(2) Electron transfer processes•Simple models•Marcus theory•The reorganization energy•Adiabatic and non-adiabatic limits•Solvent controlled reactions•Bridge assisted electron transfer•Coherent and incoherent transfer•Electrode processes

(3) Molecular conduction•Simple models for molecular conductions•Factors affecting electron transfer at interfaces•The Landauer formula•Molecular conduction by the Landauer formula•Relationship to electron-transfer rates.•Structure-function effects in molecular conduction•How does the potential drop on a molecule and why this is important•Probing molecules in STM junctions•Electron transfer by hopping

Chapter 13-15Chapter 16Chapter 17

PART APART A

Relaxation and reactions Relaxation and reactions in molecular systemsin molecular systems

Molecular processes in Molecular processes in condensed phases and condensed phases and

interfacesinterfaces•Diffusion

•Relaxation

•Solvation

•Nuclear rerrangement

•Charge transfer (electron and xxxxxxxxxxxxxxxxproton)

•Solvent: an active spectator – energy, friction, solvation

Molecular timescales

Diffusion D~10-5cm2/s

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 Molecular vibrational relaxationrelaxation

D

/~ DcVRk e

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))

ˆ ˆ~ ( ) (0)ifi tf i T

k dte F t F

Golden RuleFourier transform of bath correlation function

Molecular vibrational Molecular vibrational relaxationrelaxation

The relaxation of different vibrational levels of the ground electronic state of 16O2 in a solid Ar matrix. Analysis of

these results indicates that the relaxation of the < 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 Frequency dependent frictionfriction

consˆ ˆ~ ( ) (0) tantifi tf i T

t

k dte F t F

ˆ ˆ~ ( ) (0)ifi t

f i Tk dte F t F

1

DWIDE BAND APPROXIMATION

MARKOVIAN LIMIT

Dielectric solvationDielectric solvation

q = + e q = + eq = 0

a b c

C153 / Formamide (295 K)

Wavelength / nm

450 500 550 600

Rel

ativ

e E

mis

sion

Int

ensi

ty

ON O

CF3

Emission spectra of Coumarin 153 in formamide at different times. The times shown here are (in order of increasing peak-wavelength) 0, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, and 50 ps (Horng et al, J.Phys.Chem. 99, 17311 (1995))

2 11 1 2eV (for a charge)

2 s

q

a

Born solvation energy

Continuum dielectric theory of Continuum dielectric theory of solvationsolvation

D 4

(r, ) ( ) (r, )t

D t dt t t E t

D E

( ) ( ) 4 ( )

( ) ( ) ( )

1

4

D E P

P E

D(r, ) r ' (r r ', )E(r ', )εt

t d dt t t t

1 2

( )1

s ee

Di

How does solvent respond to a sudden change in the molecular charge distribution?

Electric displacement

Electric field

Dielectric function

Dielectric susceptibility

polarizationDebye dielectric relaxation model

Electronic response

Total (static) response

Debye relaxation time

(Poisson equation)

Continuum dielectric theory of Continuum dielectric theory of solvationsolvation

0 0( )

0

tE t

E t

1; 0s

D D

dDD E t

dt

1( ) ( 4) ;e s

D

dE

dDD D E

t

/ /( ) (1 )D Dt ts eD t e e E

0 0( )

0

tD t

D t

1; 0s

e D s

dE E D t

dt

/1 1 1( ) Lt

s e s

E t D De

eL D

s

WATER:

D=10 ps L=125 fs

““real” solvationreal” solvationThe 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)).

“Newton”

dielectric

Electron solvationElectron solvationThe 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)

Quantum solvation

(1) Increase in the kinetic energy (localization) – seems NOT to affect dynamics

(2) Non-adiabatic solvation (several electronic states involved)

C153 / Formamide (295 K)

Wavelength / nm

450 500 550 600

Rel

ativ

e E

mis

sion

Int

ensi

ty

ON O

CF3

Electron tunneling Electron tunneling through waterthrough water

E F

W o rkfu n ct io n( in wa te r)

W A T E R

12

3

Polaronic state (solvated electron)

Transient resonance through “structural defects”

Electron tunneling Electron tunneling through waterthrough water

Time (ms)

STM current in pure waterSTM current in pure waterS.Boussaad et. al. JCP (2003)S.Boussaad et. al. JCP (2003)

Chemical reactions in Chemical reactions in condensed phasescondensed phases

Bimolecular

Unimolecular

diffusion

4k DR

Diffusion controlled

rates

Bk TD

mR

2

1

k1 2 k2 1

k2

excitation

reaction

21 2

12 2

k Mkk

k M k

k

M

Thermal interactions

Unimolecular reactions (Lindemann)

Activated rate processesActivated rate processes

E B

r e ac t i o nc o o r di nate

KRAMERS THEORY:

Low friction limit

High friction limit

Transition State theory

0 /

2B B

TSTE k Tk e

0 /

2B BB B

TSTE k Tk e k

/0

B BE k TB

B

k J ek T

(action)

4k DR

Diffusion controlled

rates

Bk TD

m

0

B

Effect of solvent frictionEffect of solvent friction

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)).

TST

The physics of transition The physics of transition state ratesstate rates

0

2BEe

0

( ,TST B f BP xk d P x

v v v v)

212

212

0 1

2

m

m

d e

md e

v

v

vv

v

20exp

( )2exp ( )

B

B

B EB E

E mP x e

dx V x

Assume:

(1) Equilibrium in the well

(2) Every trajectory on the barrier that goes out makes it

E B

0

B

r e ac t i o nc o o r di nate

The (classical) transition The (classical) transition state rate is an upper state rate is an upper

boundbound

E B

r e ac t i o nc o o r di nate

•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

R *

a b

diabatic

R *

1

1

2

Adiabatic

*

0

( , )k dR R P R R

Quantum considerations

1 in the classical case( )b aP R