Molecular Conduction and Electron Transfer in Condensed Molecular Systems

1. A. Nitzan, Tel Aviv University Asian/Pacific Regional College on Science at the Nanoscale Beijing, August 2006 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. Cornell group

7. Pt/Ir Tip ~1-2 nm 1 nm SAM Au(111) First Transport Measurements through Single Molecules Adsorbed molecule addressed by STM tip Molecule lying on a surface Molecule between two electrodes Single-wall carbon nanotube on Pt Self-assembled monolayers Break junction: dithiols between gold Dekker et al. Nature 386(97) Dorogi et al. PRB 52 (95) @ Purdue Reed et al. Science 278 (97) @ Yale Nanopore Nanotube on Au C60 on gold STM tip Au Joachim et al. PRL 74 (95) Lieber et al. Nature 391 (98) Reed et al. APL 71 (97)

8. Beijing, August 2006 • (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 • (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 • (1a) 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 • (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 AN, Oxford University Press, 2006 Chapter 16 Chapter 13-15 Chapter 17

9. 1A Relaxation and reactions in molecular systems

10. Molecular processes in condensed phases and interfaces Molecular timescales Diffusion D~10-5cm2/s 10nm 10-7 - 10-8 s 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 • Diffusion • Relaxation • Solvation • Nuclear rerrangement • Charge transfer (electron and xxxxxxxxxxxxxxxxproton) • Solvent: an active spectator – energy, friction, solvation

11. 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))

12. 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)).

13. Frequency dependent friction MARKOVIAN LIMIT WIDE BAND APPROXIMATION

14. 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))

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

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

17. “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

18. 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)

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

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

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

22. reaction excitation Unimolecular reactions (Lindemann) Thermal interactions

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

24. 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)).

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

26. 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

27. Quantum considerations 1 in the classical case

28. Beijing, Aug 2006 • (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 • Quantum effects AN, Oxford University Press, 2006 Chapter 13-15

29. PART 1B Electron transfer

30. Beijing Aug 2006 • (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 Chapter 16 AN, Oxford University Press, 2006

31. Theory of Electron Transfer • Activation energy • Transition probability • Rate – Transition state theory Transition rate • Rate – Solvent controlled • NOTE: “solvent controlled” is the term used in this field for the Kramers low friction limit.

32. 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

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

34. Electron transfer EA Solvent polarization coordinate

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

36. Solvent controlled electron transfer Correlation between the fluorescence lifetime and the longitudinal dielectric relaxation time, of 6-N-(4-methylphenylamino-2-naphthalene-sulfon-N,N-dimethylamide) (TNSDMA) and 4-N,N-dimethylaminobenzonitrile (DMAB) in linear alcohol solvents. The fluorescence signal is used to monitor an electron transfer process that precedes it. The line is drawn with a slope of 1. (From E. M. Kosower and D. Huppert, Ann. Rev. Phys. Chem. 37, 127 (1986))

37. 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).

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

39. 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

40. Electron transfer: Activation energy Reorganization energy Activation energy

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

42. Experimental confirmation of the inverted regime Marcus papers 1955-6 Miller et al, JACS(1984) Marcus Nobel Prize: 1992

43. Electron transfer – the coupling • From Quantum Chemical Calculations • The Mulliken-Hush formula • Bridge mediated electron transfer

44. Bridge assisted electron transfer EB

46. Effective donor-acceptor coupling

47. Donor-to-Bridge/ Acceptor-to-bridge Bridge Green’s Function Franck-Condon-weighted DOS Reorganization energy Marcus expresions for non-adiabatic ET rates

48. 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

49. Bridge mediated ET rate Charge recombination lifetimes in the compounds shown in the inset in dioxane solvent. (J. M. Warman et al, Adv. Chem. Phys. Vol 106, 1999). The process starts with a photoinduced electron transfer – a charge separation process. The lifetimes shown are for the back electron transfer (charge recombination) process.

50. constant Incoherent hopping STEADY STATE SOLUTION