A. Nitzan, Tel Aviv University ELECTRON TRANSFER AND TRANSMISSION IN MOLECULES AND MOLECULAR JUNCTIONS AEC, Grenoble, Spet 2005 Lecture 1 Introduction Introduction to electron transport in molecular systems Reviews: Annu. Rev. Phys. Chem. 52, 681– 750 (2001) [http://atto.tau.ac.il/~nitzan/nitzanabs.html/#213] Science, 300, 1384-1389 (2003); MRS Bulletin, 29, 391-395 (2004); Bulletin of the Israel Chemical Society, Issue 14, p. 3-13 (Dec 2003) (Hebrew) Thanks I. Benjamin, A. Burin, G. Cuniberty, B. Davis, S. Datta, D. Evans, M. Galperin, A. Ghosh, H. Grabert, P. Hänggi, G. Ingold, J. Jortner, S. Kohler, R. Kosloff, J. Lehmann, M. Majda, A. Mosyak, V. Mujica, R. Naaman, F. v Oppen, U. Peskin, M. Ratner, D. Segal, T. Seideman, H. Tal-Ezer, A. Troisi 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) Feynman Chad Mirkin (DPN) Moore’s “Law” Moore’s 2nd law Molecules get wired Cornell group 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. This editorial,disguised as a scientific paper, is obviously a plan for more honesty. We do not, in the long run, build effective public support for science and technology by promising more than we can deliver. 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 Electron transfer in DNA 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 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 Grenoble Sept 2005 (3) (2)Molecular Electronconduction transfer (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 Coming March 2006 •How photons? does theand potential drop on a •Coherent incoherent Chapter Chapter 16 moleculetransfer and why this is important Chapter13-15 17 •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 iif t Fˆ ( t )Fˆ (0) T Golden RuleFourier 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)). 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 timesshown 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? 1 2 D 4 t t Dt(r, D(r, ) t ) dr 'dtdt( tε(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 t0 0 E (t ) t0 E t0 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 EB 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 2b 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 ) Pba ( R ) * 0 1 in the classical case