A. Nitzan, Tel Aviv University The Abdus Salam African College on Science at the Nanoscale

1. A. Nitzan, Tel Aviv University The Abdus Salam African College on Science at the Nanoscale Cape Town, November 2007 1. Relaxation, reactions and electron transfer in condensed molecular systems2. Fundamentals of molecular conduction3. Inelastic effects in electron transfer and molecular conduction

2. Molecular conduction

3. 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 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.

4. Xe on Ni(110)

5. Moore’s “Law”

6. Fabrication • Stability • Characterization • Funcionality • Control Cornell group

7. Pt/Ir Tip ~1-2 nm 1 nm SAM Au(111) FABRICATION Adsorbed molecule addressed by STM tip Molecule between two electrodes: Break junction: Self-assembled monolayers Van Ruitenbeek, Wittenberg Lectures 2004 Dorogi et al. PRB 52 (95) @ Purdue Molecule lying on a surface Nanopore Nanotube on Au C60 on gold STM tip Au Joachim et al. PRL 74 (95) Reed et al. APL 71 (97) Lieber et al. Nature 391 (98)

8. Fabrication • Stability • Characterization • Funcionality • Control THE MOLECULE Strong electric field System open to electrons and energy Nonequilibrium Relaxation Electron-vibration coupling Heat generation

9. Cape Town, November 2006 • (1a) Relaxation and reactions in condensed molecular systems • Timescales • Relaxation • Solvation • Activated rate processes • Low, high and intermediate friction regimes • Transition state theory • Diffusion controlled reactions • (2) 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 • (3) Inelastic effects in molecular conduction • Dependence on nuclear configurations • Electron-vibration coupling • Timescales • Coherent and incoherent transport • Heating • Current induced nuclear changes • Heat conduction • Inelastic tunneling spectroscopy • (1b) 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 AN, Oxford University Press, 2006 Chapter 16 Chapter 13-15 Chapter 17

10. 1A Relaxation and reactions in molecular systems

11. The importance of timescales

12. Molecular processes in condensed phases and interfaces Molecular timescales Electronic 10-16-10-15s Vibraional period 10-14s Vibrational xxxxrelaxation 1-10-12s Diffusion D~10-5cm2/s 10nm 10-7 - 10-8 s Chemical reactions xxxxxxxxx1012-10-12s Rotational period 10-12s Collision times 10-12s • Diffusion • Relaxation • Solvation • Nuclear rerrangement • Charge transfer (electron and xxxxxxxxxxxxxxxxproton) • Solvent: an active spectator – energy, friction, solvation

13. Molecular vibrational relaxation Golden RuleFourier transform of bath correlation function 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))

14. Molecular vibrational relaxation 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 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)).

15. Frequency dependent friction MARKOVIAN LIMIT WIDE BAND APPROXIMATION

16. Dielectric solvation Born solvation energy 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))

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

18. Continuum dielectric theory of solvation WATER: tD=10 ps tL=125 fs

19. “real” solvation “Newton” 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)). dielectric

20. 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)

21. Electron tunneling through water 1 2 3 Polaronic state (solvated electron) Transient resonance through “structural defects”

22. Electron tunneling through water Time (ms) STM current in pure waterS.Boussaad et. al. JCP (2003)

23. diffusion Chemical reactions in condensed phases • Bimolecular • Unimolecular Diffusion controlled rates R

24. reaction excitation Unimolecular reactions (Lindemann) Thermal interactions

25. Activated rate processes wB Diffusion controlled rates w0 KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action)

26. 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)).

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

28. 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

29. Quantum considerations 1 in the classical case

30. Cape Town, November 2006 • (1a) Relaxation and reactions in condensed molecular systems • Timescales • Relaxation • Solvation • Activated rate processes • Low, high and intermediate friction regimes • Transition state theory • Diffusion controlled reactions

31. Tomorrow: Electron transfer

32. A. Nitzan, Tel Aviv University The Abdus Salam African College on Science at the Nanoscale Cape Town, November 2007 1. Relaxation, reactions and electron transfer in condensed molecular systems2. Fundamentals of molecular conduction3. Inelastic effects in electron transfer and molecular conduction

33. Cape Town, November 2006 • (1a) Relaxation and reactions in condensed molecular systems • Timescales • Relaxation • Solvation • Activated rate processes • Low, high and intermediate friction regimes • Transition state theory • Diffusion controlled reactions

34. The importance of timescales

35. Electron tunneling through water 1 Scoles 2 3 Polaronic state (solvated electron) Transient resonance through “structural defects”

36. Activated rate processes wB Diffusion controlled rates w0 KRAMERS THEORY: Low friction limit High friction limit Transition State theory (action)

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

38. Quantum considerations 1 in the classical case

39. PART 1B Electron transfer

40. Cape Town, November 2006 • (1b) 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 Chapter 16

41. Theory of Electron Transfer • Rate – Transition state theory Transition rate • Boltzmann • Activation energy • Transition probability

42. Electron transfer in polar media • Electrons 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

43. Electron transfer Nuclear motion Nuclear motion Electron transition takes place in unstable nuclear configurations obtained via thermal fluctuations

44. Electron transfer EA Solvent polarization coordinate

45. Transition state theory of electron transfer Adiabatic and non-adiabatic ET processes Landau-Zener problem (For harmonic diabatic surfaces (1/2)KR2)

46. 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 sE. (the latter equality holds only at equilibrium).

47. Electron transfer – Marcus theory Free energy associated with a nonequilibrium fluctuation of Pn q “reaction coordinate” that characterizes the nuclear polarization

48. 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. q=1 q q=0

49. Electron transfer: Activation energy Reorganization energy Activation energy

50. Electron transfer: Effect of Driving (=energy gap)