1. © A. Nitzan, TAU Introduction to electron transport in molecular systems 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. Mosyak, V. Mujica, R. Naaman, U. Peskin, M. Ratner, D. Segal, T. Seideman, H. Tal-Ezer Thanks 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)

2. © A. Nitzan, TAU PART B: Molecular conduction: Main results and phenomenology A. Nitzan ( nitzan@post.tau.ac.il ; http://atto.tau.ac.il/~nitzan/nitzan.html ) nitzan@post.tau.ac.il PART A: Introduction: electron transfer in molecular systems PART C: Inelastic effects in molecular conduction Introduction to electron transport in molecular systems http://atto.tau.ac.il/~nitzan/tu04-X.ppthttp://atto.tau.ac.il/~nitzan/tu04-X.ppt (X=A,B,C)

3. © A. Nitzan, TAU Molecules as conductors

4. © A. Nitzan, TAU Aviram Ratner 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. 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

5. © A. Nitzan, TAU Xe on Ni(110)

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

7. © A. Nitzan, TAU Moore’s “Law”

8. © A. Nitzan, TAU Moore’s 2nd law

9. © A. Nitzan, TAU Molecules get wired

10. © A. Nitzan, TAU Cornell group

11. © A. Nitzan, TAU Science, Vol 302, Issue 5645, 556-559, 24 October 2003 MOLECULAR ELECTRONICS: Next-Generation Technology Hits an Early Midlife Crisis Robert F. Service Researchers had hoped that a new revolution in ultraminiaturized electronic gadgetry lay almost within reach. But now some are saying the future must wait Two years ago, the nascent field of molecular electronics was riding high. A handful of research groups had wired molecules to serve as diodes, transistors, and other devices at the heart of computer chips. Some had even linked them together to form rudimentary circuits, earning accolades as Science's 2001 Breakthrough of the Year (Science, 21 December 2001, p. 2442). The future was so bright, proponents predicted that molecular electronics-based computer chips vastly superior to current versions would hit store shelves in 2005 Now, critics say the field is undergoing a much-needed reality check. This summer, two of its most prominent research groups revealed that some of their devices don't work as previously thought and may not even qualify as molecular electronics. And skeptics are questioning whether labs will muster commercial products within the next decade, if at all

12. © A. Nitzan, TAU 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.

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

14. © A. Nitzan, TAU 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 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 (97) @ Yale Nanotube on Au Lieber et al. Nature 391 (98)

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

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

17. © A. Nitzan, TAU Electron transfer in DNA

18. © A. Nitzan, TAU 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

19. © A. Nitzan, TAU 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

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

21. © 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

22. © A. Nitzan, TAU Theory of Electron Transfer Activation energy Activation energy Transition probability Transition probability Rate – Transition state theory or solvent controlled Rate – Transition state theory or solvent controlled

23. © 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

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

25. © A. Nitzan, TAU Electron transfer

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

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

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

29. © A. Nitzan, TAU Electron transfer: Activation energy

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

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

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

33. © A. Nitzan, TAU Bridge assisted electron transfer

34. © A. Nitzan, TAU

35. Effective donor-acceptor coupling

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

37. © A. Nitzan, TAU Bridge mediated ET rate  ’ ( Å -1 ) = 0.2-0.6 for highly conjugated chains 0.9-1.2 for saturated hydrocarbons ~ 2 for vacuum

38. © A. Nitzan, TAU Incoherent hopping constant STEADY STATE SOLUTION

39. © A. Nitzan, TAU ET rate from steady state hopping

40. © 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.

41. © A. Nitzan, TAU The photosythetic reaction center Michel - Beyerle et al

42. © A. Nitzan, TAU Dependence on bridge length

43. © A. Nitzan, TAU DNA (Giese et al 2001)

44. © A. Nitzan, TAU Steady state evaluation of rates Rate of water flow depends linearly on water height in the cylinder 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 h

45. © A. Nitzan, TAU Steady state quantum mechanics V0lV0l Starting from state 0 at t=0: P 0 = exp(-   t)   = 2  |V 0l | 2  L (Golden Rule) Steady state derivation:

46. © A. Nitzan, TAU pumping damping

47. © A. Nitzan, TAU Resonance scattering V 1r V 1l

48. © A. Nitzan, TAU Resonance scattering j = 0, 1, {l}, {r} For each r and l

49. © A. Nitzan, TAU SELF ENERGY

51. Resonant tunneling V 1r V 1l

52. © A. Nitzan, TAU Resonant Tunneling Transmission Coefficient

53. © A. Nitzan, TAU Resonant Transmission – 3d 1d 3d: 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)

54. © A. Nitzan, TAU CONDUCTION 2 spin states Zero bias conduction L R  –  e|   f(E 0 ) (Fermi function)

55. © A. Nitzan, TAU Landauer formula (maximum=1) Maximum conductance per channel For a single “channel”: