Lecture 1 A. Nitzan, Tel Aviv University SELECTED TOPICS IN CHEMICAL DYNAMICS IN CONDENSED SYSTEMS Boulder, Aug 2007

Introduction

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 dynamics Time correlation functions Stochastic processes Stochastic differential equations Unimolecular reactions: Barrier crossing processes Transition state theory Diffusion controlled reactions Applications in biology Electron transfer and molecular conduction 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

electron transport in molecular systems 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 Reviews: Annu. Rev. Phys. Chem. 52, 681– 750 (2001) Science, 300, (2003); MRS Bulletin, 29, (2004); Bulletin of the Israel Chemical Society, Issue 14, p. 3 (2003) (Hebrew) J. Phys.: Condens. Matter 19, (2007)

Molecular conduction

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 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.43 OCTOBER 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. 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 Purdue Au(111) Pt/Ir Tip SAM 1 nm ~1-2 nm Self-assembled monolayers Adsorbed molecule addressed by STM tip C 60 on gold Joachim et al. PRL 74 (95) STM tip Au Reed et al. Science 278 Yale Nanotube on Au Lieber et al. Nature 391 (98)

Park et. al. Nature 417, (2002) Datta et al

Weber et al, Chem. Phys. 2002

log e 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 processes in molecular systems Electron transfer Electron transfer Electron transmission Electron transmission Conduction Conduction Parameters that affect molecular conduction Parameters that affect molecular conduction Eleastic and inelastic transmission Eleastic and inelastic transmission Coherent and incoherent conduction Coherent and incoherent conduction Heating and heat conduction Heating and heat conduction Possible interaction with light Possible interaction with light

Chemical processes Gas phase reactions Follow individual collisions Follow individual collisions States: Initial  Final States: Initial  Final Energy flow between degrees of freedom Energy flow between degrees of freedom Mode selectivity Mode selectivity Yields of different channels Yields of different channels Reactions in solution Reactions in solution Effect of solvent on mechanism Effect of solvent on mechanism Effect of solvent on rates Effect of solvent on rates Dependence on solvation, relaxation, diffusion and heat transport. Dependence on solvation, relaxation, diffusion and heat transport.

I 2  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 ps. 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

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 Chapter 16 Chapter 17

PART A Relaxation and reactions in molecular systems

Molecular processes in condensed phases and interfaces Diffusion Relaxation Solvation Nuclear rerrangement Charge transfer (electron and xxxxxxxxxxxxxxxxproton) Solvent: an active spectator – energy, friction, solvation Molecular timescales Diffusion D~10 -5 cm 2 /s Electronic s Vibraional s Vibrational xxxxrelaxation s Chemical reactions xxxxxxxxx s Rotational s Collision times s

Molecular vibrational relaxation Relaxation in the X 2 Σ+ (ground electronic state) and A 2 Π (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)) Golden Rule  Fourier transform of bath correlation function

Molecular vibrational relaxation The relaxation of different vibrational levels of the ground electronic state of 16 O 2 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 friction WIDE BAND APPROXIMATION MARKOVIAN LIMIT

Dielectric solvation 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, (1995)) Born solvation energy

Continuum dielectric theory of solvation How does solvent respond to a sudden change in the molecular charge distribution? Electric displacement Electric field Dielectric function Dielectric susceptibility polarization Debye dielectric relaxation model Electronic response Total (static) response Debye relaxation time (Poisson equation)

Continuum dielectric theory of solvation WATER:  D =10 ps  L =125 fs

“real” solvation 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 S 0 –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 solvation 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) 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 Polaronic state (solvated electron) Transient resonance through “structural defects”

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 Diffusion controlled rates R

excitation reaction Thermal interactions Unimolecular reactions (Lindemann)

Activated rate processes KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action) Diffusion controlled rates 00 BB

Effect 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 state rates Assume: (1) Equilibrium in the well (2) Every trajectory on the barrier that goes out makes it

The (classical) transition state rate is an upper bound 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 1 in the classical case