How Molecules Conduct Introduction to electron transport in

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How Molecules Conduct 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, 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. A. Mosyak, V. Mujica, R. Naaman, U. © Nitzan, TAU Peskin, M. Ratner, D. Segal, T. Seideman, H. Tal-Ezer

A. Nitzan Part A INTRODUCTION © A. Nitzan, TAU

Molecules as conductors © A. Nitzan, TAU

Molecular Rectifiers Aviram Ratner Arieh Aviram and Mark A. Ratner IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA Department of Chemistry, 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. © A. Nitzan, TAU

Xe on Ni(110) © A. Nitzan, TAU

Feynman © A. Nitzan, TAU Chad Mirkin (DPN)

Moore’s “Law” © A. Nitzan, TAU

Moore’s 2 nd law © A. Nitzan, TAU

Molecules get wired © A. Nitzan, TAU

http: //www. hemdweb. co/ April 2002 © A. Nitzan, TAU

The Hedonistic Imperative outlines how genetic engineering and nanotechnology will abolish suffering in all sentient life. The abolitionist project is hugely ambitious but technically feasible. It is also instrumentally rational and ethically mandatory. The metabolic pathways of pain and malaise evolved because they served the fitness of our genes in the ancestral environment. They will be replaced by a different sort of neural architecture. States of sublime well-being are destined to become the genetically pre-programmed norm of mental health. The world's last unpleasant experience will be a © A. Nitzan, precisely dateable event. TAU

Feynman • For a successful Technology, reality must take precedence over public relations, for nature cannot be fooled © A. Nitzan, TAU

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) Dorogi et al. PRB 52 (95) @ Purdue Reed et al. Science 278 (97) @ Yale Nanopore C 60 on gold STM tip Joachim et al. PRL 74 (95) Dekker et al. Nature 386(97) Nanotube on Au Au Reed et© A. Nitzan, TAU al. APL 71 (97) Lieber et al. Nature 391 (98)

Park et. al. Nature 417, 722 -725 (2002) © A. Nitzan, TAU Datta et al

Weber et al, Chem. Phys. 2002 © A. Nitzan, TAU

Electron transfer in DNA © A. Nitzan, TAU

Electronic processes in molecular systems Electron transfer n Electron transmission n Conduction n Parameters that affect molecular conduction n Eleastic and inelastic transmission n Coherent and incoherent conduction n Heating and heat conduction n © A. Nitzan, TAU

Theory of Electron Transfer n n n n n The physics of activated rate process The physics of electron transfer in a nuclear environment A simple model – parabolic potential surfaces The Marcus parabolas The reorganization energy Adiabatic and non adiabatic rates Solvent control Bridge length dependence (“super-exchange”) Transition to hopping Experimental implications © A. Nitzan, TAU

Activated rate processes Diffusion controlled rates KRAMERS THEORY: Low friction limit (action) High friction limit Transition State theory © A. Nitzan, TAU

The physics of transition state rates Assume: (1) Equilibrium in the well (2) Every trajectory on the barrier that goes out makes it © A. Nitzan, TAU

Electron transfer in polar media • Electron are much faster than nuclei • Electronic transitions take place in fixed nuclear configurations • Electronic energy needs to be conserved during the change in electronic charge density Electronic transition Nuclear relaxation © A. Nitzan, TAU

Electron transfer Nuclear motion Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations © A. Nitzan, TAU

Electron transfer © A. Nitzan, TAU

Transition state theory of electron Alternatively – transfer solvent control Adiabatic and non-adiabatic ET processes Landau-Zener problem © A. Nitzan, TAU

Electron transfer – Marcus theory We are interested in changes in solvent configuration that take place at constant solute charge distribution They have the following characteristics: (1) Pn fluctuates because of thermal motion of solvent nuclei. (2) Pe , as a fast variable, satisfies the equilibrium relationship (3) D = constant (depends on only) Note that the relations E = D-4 P; P=Pn + Pe are always satisfied per definition, however D s. E. (the latter equality holds only at equilibrium). © A. Nitzan, TAU

The Marcus parabolas Use q as a reaction coordinate. It defines the state of the medium that will be in equilibrium with the charge distribution rq. Marcus calculated the free energy (as function of q) of the solvent when it reaches this state in the systems q =0 and q=1. © A. Nitzan, TAU

Electron transfer: Activation energy © A. Nitzan, TAU

Electron transfer: Effect of Driving (=energy gap) © A. Nitzan, TAU

Experimental confirmation of the inverted regime Miller et al, JACS(1984) Marcus Nobel Prize: 1992 © A. Nitzan, TAU

Electron transfer – the coupling • From Quantum Chemical Calculations • The Mulliken-Hush formula • Bridge mediated electron transfer © A. Nitzan, TAU

Bridge assisted electron transfer © A. Nitzan, TAU

BEWARE: equations are coming! © A. Nitzan, TAU

Effective donor-acceptor coupling © A. Nitzan, TAU

Marcus expresions for non-adiabatic ET rates Donor-to-Bridge/ Acceptor-to-bridge Bridge Green’s Function Franck-Condonweighted DOS Reorganization energy © A. Nitzan, TAU

Bridge mediated ET rate b’ (Å-1)= 0. 2 -0. 6 for highly conjugated chains 0. 9 -1. 2 for saturated hydrocarbons ~2 for vacuum © A. Nitzan, TAU

Dependence on temperature The integrated elastic (dotted line) and activated (dashed line) components of the transmission, and the total transmission probability (full line) displayed as function of inverse temperature. Parameters are as in Fig. 3. © A. Nitzan, TAU

Steady state evaluation of rates Rate of water flow depends linearly on water height in the cylinder h Two ways to get the rate of water flowing out: (1) Measure h(t) and get the rate coefficient from k=(1/h)dh/dt (2) Keep h constant and measure the steady state outwards water flux J. Get the rate from k=J/h -- Steady state rate © A. Nitzan, TAU

Steady state quantum mechanics Starting from state 0 at t=0: P 0 = exp(-G 0 t) V 0 l G = 2 |Vsl|2 L (Golden Rule) Steady state derivation: © A. Nitzan, TAU

Resonant Transmission – 3 d 1 d 3 d: Total flux from L to R at energy E 0: If the continua are associated with a metal electrode at thermal equilibrium than (Fermi-Dirac distribution) © A. Nitzan, TAU